Search results for: mechanical quadrature methods

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

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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: D. Falliano, D. De Domenico, G. Ricciardi, E. Gugliandolo

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This paper is focused on the mechanical characterization of foamed concrete specimens with protein-based foaming agent. Unlike classic foamed concrete, a peculiar property of the analyzed foamed concrete is the extrudability, which is achieved via a specific additive in the concrete mix that significantly improves the cohesion and viscosity of the fresh cementitious paste. A broad experimental campaign was conducted to evaluate the compressive strength and the indirect tensile strength of the specimens. The study has comprised three different cement types, two water/cement ratios, three curing conditions and three target dry densities. The variability of the strength values upon the above mentioned factors is discussed.

Keywords: Cement type, curing conditions, density, extrudable concrete, foamed concrete, mechanical characterization.

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

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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: Guangbin Wang, Fuping Tan, Deyu Sun

Abstract:

In this paper, we present new preconditioned generalized mixed-type splitting (GMTS) methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GMTS methods converge faster than the GMTS method whenever the GMTS method is convergent. Finally, we give a numerical example to confirm our theoretical results.

Keywords: Preconditioned, GMTS method, linear system, convergence, comparison.

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Authors: Dong Wook Lee

Abstract:

This paper presents a method to analyze the stiffness of the expansion joint with structural support using a hybrid method combining computational and analytical methods. Many expansion joints found in tubes and ducts of mechanical structures are designed to absorb thermal expansion mismatch between their structural members and deal with misalignments introduced from the assembly/manufacturing processes. One of the important design perspectives is the system’s vibrational characteristics. We calculate the stiffness as a characterization parameter for structural joint systems using a combined Finite Element Analysis (FEA) and an analytical method. We apply the methods to two sample applications: external configurations of aircraft engines and nuclear power plant structures.

Keywords: Expansion joint, expansion joint stiffness, Finite Element Analysis, FEA, nuclear power plants, aircraft engine external configurations.

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Authors: Zhengsheng Wang, Xiangyong Ji, Yong Du

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The projection methods, usually viewed as the methods for computing eigenvalues, can also be used to estimate pseudospectra. This paper proposes a kind of projection methods for computing the pseudospectra of large scale matrices, including orthogonalization projection method and oblique projection method respectively. This possibility may be of practical importance in applications involving large scale highly nonnormal matrices. Numerical algorithms are given and some numerical experiments illustrate the efficiency of the new algorithms.

Keywords: Pseudospectra, eigenvalue, projection method, Arnoldi, IOM(q)

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Authors: M. T. Z. Butt, T. Ahmad, N. A. Siddiqui

Abstract:

Commercially SA 516 Grade 70 is frequently used for the manufacturing of pressure vessels, boilers and storage tanks etc. in fabrication industry. Heat input is the major parameter during welding that may bring significant changes in the microstructure as well as the mechanical properties. Different welding technique has different heat input rate per unit surface area. Materials with large thickness are dealt with different combination of welding techniques to achieve required mechanical properties. In the present research two schemes: Scheme 1: SMAW (Shielded Metal Arc Welding) & GTAW (Gas Tungsten Arc Welding) and Scheme 2: SMAW & SAW (Submerged Arc Welding) of hybrid welding techniques have been studied. The purpose of these schemes was to study hybrid welding effect on the microstructure and mechanical properties of the weldment, heat affected zone and base metal area. It is significant to note that the thickness of base plate was 12 mm, also welding conditions and parameters were set according to ASME Section IX. It was observed that two different hybrid welding techniques performed on two different plates demonstrated that the mechanical properties of both schemes are more or less similar. It means that the heat input, welding techniques and varying welding operating conditions & temperatures did not make any detrimental effect on the mechanical properties. Hence, the hybrid welding techniques mentioned in the present study are favorable to implicate for the industry using the plate thickness around 12 mm thick.

Keywords: Grade 70, GTAW, hybrid welding, SAW, SMAW.

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Authors: Guojia Ma, Guoqiang Lin, Shuili Gong, Gang Sun, Dawang Wang

Abstract:

A diamond-like carbon (DLC) based solid-lubricant film was designed and DLC films were successfully prepared using a microwave plasma enhanced magnetron sputtering deposition technology. Post-test characterizations including Raman spectrometry, X-ray diffraction, nano-indentation test, adhesion test, friction coefficient test were performed to study the influence of substrate bias voltage on the mechanical properties of the W- and S-doped DLC films. The results indicated that the W- and S-doped DLC films also had the typical structure of DLC films and a better mechanical performance achieved by the application of a substrate bias of -200V.

Keywords: Adhesive Strength, Coefficient of Friction, Substrate Bias, W- and S-doped DLC film

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Authors: K. Krizova, R. Hela, S. Keprdova

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This paper introduces selected composition of conventional concretes and their resulting mechanical properties at different ages of concrete. With respect to utilization of mineral admixtures, fly ash and ground limestone agents were included in addition to pure Portland binder. The proposal of concrete composition remained constant in basic concrete components such as cement and representation of individual contents of aggregate fractions; weight dosing of admixtures and water dose were only modified. Water dose was chosen in order to achieve identical consistence by settlement for all proposals of concrete composition. Mechanical properties monitored include compression strength, static and dynamic modulus of concrete elasticity, at ages of 7, 28, 90, and 180 days.

Keywords: Cement, mineral admixtures, microstructure of concrete, mechanical properties.

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Authors: Olatunde I. Sekunowo, Stephen I. Durowaye, Oluwashina P. Gbenebor

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Copper being one of the major intrinsic residual impurities in steel possesses the tendency to induce severe microstructural distortions if not controlled within certain limits. Hence, this paper investigates the effect of this element on the mechanical properties of construction steel with a view to ascertain its safe limits for effective control. The experiment entails collection of statistically scheduled samples of hot rolled profiles with varied copper concentrations in the range of 0.12-0.39 wt. %. From these samples were prepared standard test specimens subjected to tensile, impact, hardness and microstructural analyses. Results show a rather huge compromise in mechanical properties as the specimens demonstrated 54.3%, 74.2% and 64.9% reduction in tensile strength, impact energy and hardness respectively as copper content increases from 0.12 wt. % to 0.39 wt. %. The steel’s abysmal performance is due to the severe distortion of the microstructure occasioned by the development of incoherent complex compounds which weaken the pearlite reinforcing phase. It is concluded that the presence of copper above 0.22 wt. % is deleterious to construction steel performance.

Keywords: Construction steel, mechanical properties, processing method, trace elements.

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Authors: Alireza BozorgianÏî Navid Majdi Nasab, Hassan Mirzazadeh

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In this paper, the effect of modified clay on the mechanical efficiency of epoxy resin is examined. Studies by X ray diffraction and microscopic transient electron method show that modified clay distribution in polymer area is intercalated kind. Examination the results of mechanical tests shows that existence of modified clay in epoxy area increases pressure yield strength, tension module and nano composite fracture toughness in relate of pure epoxy. By microscopic examinations it is recognized too that the action of toughness growth of this kind of nano composite is due to crack deflection, formation of new surfaces and fracture of clay piles.

Keywords: Nano clay, Epoxy, Toughness, Composite

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Authors: Michael Tupý, Dagmar Měřínská, Alice Tesaříková-Svobodová, Christian Carrot, Caroline Pillon, Vít Petránek

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The mechanical properties of blends consisting of plasticized poly(vinyl butyral) (PVB) and plasticized poly(vinyl chloride) (PVC) are studied, in order to evaluate the possibility of using recycled PVB waste derived from windshields. PVC was plasticized with 38% of diisononyl phthalate (DINP), while PVB was plasticized with 28% of triethylene glycol, bis(2-ethylhexanoate) (3GO). The optimal process conditions for the PVB/PVC blend in 1:1 ratio were determined. Entropy was used in order to theoretically predict the blends miscibility. The PVB content of each blend composition used was ranging from zero to 100%. Tensile strength and strain were tested. In addition, a comparison between recycled and original PVB, used as constituents of the blend, was performed.

Keywords: Poly(vinyl butyral), poly(vinyl chloride), windshield, polymer waste, mechanical properties.

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Authors: G.Mehdiyeva, M.Imanova, V.Ibrahimov

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Beginning from the creator of integro-differential equations Volterra, many scientists have investigated these equations. Classic method for solving integro-differential equations is the quadratures method that is successfully applied up today. Unlike these methods, Makroglou applied hybrid methods that are modified and generalized in this paper and applied to the numerical solution of Volterra integro-differential equations. The way for defining the coefficients of the suggested method is also given.

Keywords: Integro-differential equations, initial value problem, hybrid methods, predictor-corrector method

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Authors: A. Buasri, N. Chaiyut, K. Borvornchettanuwat, N. Chantanachai, K. Thonglor

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Inorganic nanoparticles filled polymer composites have extended their multiple functionalities to various applications, including mechanical reinforcement, gas barrier, dimensional stability, heat distortion temperature, flame-retardant, and thermal conductivity. Sodium stearate-modified calcium carbonate (CaCO3) nanoparticles were prepared using surface modification method. The results showed that sodium stearate attached to the surface of CaCO3 nanoparticles with the chemical bond. The effect of modified CaCO3 nanoparticles on thermal properties of polypropylene (PP) was studied by means of differential scanning calorimetry (DSC) and Thermogravimetric analysis (TGA). It was found that CaCO3 significantly affected the crystallization temperature and crystallization degree of PP. Effect of the modified CaCO3 content on mechanical properties of PP/CaCO3 nanocomposites was also studied. The results showed that the modified CaCO3 can effectively improve the mechanical properties of PP. In comparison with PP, the impact strength of PP/CaCO3 nanocomposites increased by about 65% and the hardness increased by about 5%.

Keywords: Polypropylene Nanocomposites, Modified Calcium Carbonate, Sodium Stearate, Surface Treatment

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Authors: Nashrawan N. Taha, Andrew M. Cox

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In a multi-cultural learning context, where ties are weak and dynamic, combining qualitative with quantitative research methods may be more effective. Such a combination may also allow us to answer different types of question, such as about people’s perception of the network. In this study the use of observation, interviews and photos were explored as ways of enhancing data from social network questionnaires. Integrating all of these methods was found to enhance the quality of data collected and its accuracy, also providing a richer story of the network dynamics and the factors that shaped these changes over time.

Keywords: Mixed Methods, Social Network Analysis, multi-cultural learning, Social Network Dynamics.

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Authors: Lazim Abdullah, Nurhakimah Ab. Rahman

Abstract:

Linear systems are widely used in many fields of science and engineering. In many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. Therefore it is important to perform numerical algorithms or procedures that would treat general fuzzy linear systems and solve them using iterative methods. This paper aims are to solve fuzzy linear systems using four types of Jacobi based iterative methods. Four iterative methods based on Jacobi are used for solving a general n × n fuzzy system of linear equations of the form Ax = b , where A is a crisp matrix and b an arbitrary fuzzy vector. The Jacobi, Jacobi Over-Relaxation, Refinement of Jacobi and Refinement of Jacobi Over-Relaxation methods was tested to a five by five fuzzy linear system. It is found that all the tested methods were iterated differently. Due to the effect of extrapolation parameters and the refinement, the Refinement of Jacobi Over-Relaxation method was outperformed the other three methods.

Keywords: Fuzzy linear systems, Jacobi, Jacobi Over- Relaxation, Refinement of Jacobi, Refinement of Jacobi Over- Relaxation.

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Authors: Katarzyna Antosz, DorotaStadnicka

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Having regard to the necessity of maintaining the technical infrastructure in a proper condition that ensures production continuity, companies decide to implement modern methods of technological machines park management. These methods include TPM, RCM and outsourcing. Large companies, in particular, are ready to invest in the implementation of these methods because of a great number of machines and a wide range of tasks of their technical service. Methodology of implementing these methods is well known. The aim of the studies, of which the results are presented in this publication, was the identification of real actions that are conducted in enterprises within the application of the TPM method. The studies were carried out in large manufacturing companies of different industries located on a certain area. The study’s results point to the actions actually performed within TPM as well as to the effects of those actions achieved by the studied enterprises.

Keywords: Infrastructure management, modern methods, technical infrastructure, TPM.

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Authors: Mehmet Yörükoğlu, Serhat Aydın

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Since the discovery of the manuscript, mechanical methods for storing, transferring and using the information have evolved into digital methods over the time. In this process, libraries that are the center of the information have also become digitized and become accessible from anywhere and at any time in the world by taking on a structure that has no physical boundaries. In this context, some criteria for information obtained from digital libraries have become more important for users. This paper evaluates the user criteria from different perspectives that make a digital library more useful. The Step-Wise Weight Assessment Ratio Analysis-Weighted Aggregated Sum Product Assessment (SWARA-WASPAS) method is used with flexibility and easy calculation steps for the evaluation of digital library criteria. Three different digital libraries are evaluated by information technology experts according to five conflicting main criteria, ‘interface design’, ‘effects on users’, ‘services’, ‘user engagement’ and ‘context’. Finally, alternatives are ranked in descending order.

Keywords: Digital library, multi criteria decision making, SWARA-WASPAS method.

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Authors: Joffroy Beauquier, Yongjie Hu

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The intrusion detection problem has been frequently studied, but intrusion detection methods are often based on a single point of view, which always limits the results. In this paper, we introduce a new intrusion detection model based on the combination of different current methods. First we use a notion of distance to unify the different methods. Second we combine these methods using the Pearson correlation coefficients, which measure the relationship between two methods, and we obtain a combined distance. If the combined distance is greater than a predetermined threshold, an intrusion is detected. We have implemented and tested the combination model with two different public data sets: the data set of masquerade detection collected by Schonlau & al., and the data set of program behaviors from the University of New Mexico. The results of the experiments prove that the combination model has better performances.

Keywords: Intrusion detection, combination, distance, Pearson correlation coefficients.

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Authors: Ricardo C. Silva, Luiza A. P. Cantao, Akebo Yamakami

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Based on the fuzzy set theory this work develops two adaptations of iterative methods that solve mathematical programming problems with uncertainties in the objective function and in the set of constraints. The first one uses the approach proposed by Zimmermann to fuzzy linear programming problems as a basis and the second one obtains cut levels and later maximizes the membership function of fuzzy decision making using the bound search method. We outline similarities between the two iterative methods studied. Selected examples from the literature are presented to validate the efficiency of the methods addressed.

Keywords: Fuzzy Theory, Nonlinear Optimization, Fuzzy Mathematics Programming.

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Authors: M. Li, V. D. Thi, M. Khelifa, M. El Ganaoui

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This study presents an overview of the work carried out by the use of wood waste as coarse aggregate in mortar. The paper describes experimental and numerical investigations carried on pervious concrete made of wood chips and also sheds lights on the mechanical properties of this new product. The properties of pervious wood-concrete such as strength, elastic modulus, and failure modes are compared and evaluated. The characterization procedure of the mechanical properties of wood waste ash are presented and discussed. The numerical and tested load–deflection response results are compared. It was observed that the numerical results are in good agreement with the experimental results.

Keywords: Wood waste ash, characterization, mechanical properties, finite element analysis, flexural behavior, bending tests.

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Authors: D. Kriebel, J. E. Mehner

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The paper introduces a method to efficiently simulate nonlinear changing electrostatic fields occurring in micro-electromechanical systems (MEMS). Large deflections of the capacitor electrodes usually introduce nonlinear electromechanical forces on the mechanical system. Traditional finite element methods require a time-consuming remeshing process to capture exact results for this physical domain interaction. In order to accelerate the simulation process and eliminate the remeshing process, a formulation of a strongly coupled electromechanical transducer element will be introduced which uses a combination of finite-element with an advanced mesh morphing technique using radial basis functions (RBF). The RBF allows large geometrical changes of the electric field domain while retain high element quality of the deformed mesh. Coupling effects between mechanical and electrical domains are directly included within the element formulation. Fringing field effects are described accurate by using traditional arbitrary shape functions.

Keywords: electromechanical, electric field, transducer, simulation, modeling, finite-element, mesh morphing, radial basis function

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Authors: Olesia Mikhailova, Pavel Rovnaník

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In the present work, metakaolin-based geopolymer including different polymer admixtures was studied. Different types of commercial polymer admixtures VINNAPAS^® and polyethylene glycol of different relative molecular weight were used as polymer admixtures. The main objective of this work is to investigate the influence of different types of admixtures on the properties of metakaolin-based geopolymer mortars considering their different dosage. Mechanical properties, such as flexural and compressive strength were experimentally determined. Also, study of the microstructure of selected specimens by using a scanning electron microscope was performed. The results showed that the specimen with addition of 1.5% of VINNAPAS^® 7016 F and 10% of polyethylene glycol 400 achieved maximum mechanical properties.

Keywords: Metakaolin, geopolymer, polymer admixtures, mechanical properties, microstructure.

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Authors: Amir Atrian, Javad Jafari Fesharaki, Gh. Hossein Majzoobi, Mahsa Sheidaee

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The analytical solution of functionally graded piezoelectric hollow cylinder which is under radial electric potential and non-axisymmetric thermo-mechanical loads, are presented in this paper. Using complex Fourier series and estimation of power law for variations of material characterizations through the thickness, the electro thermo mechanical behavior of the FGPM cylinder is obtained. The stress and displacement distributions and the effect of electric potential field on the cylinder behavior are also presented and some applicable results are offered at the end of the paper.

Keywords: Analytical, FGM, Fourier series, Non-axisymmetric, Piezoelectric, Thermo-elasticity

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Authors: Salma Siddika, Fayeka Mansura, Mahbub Hasan

Abstract:

The term hybrid composite refers to the composite containing more than one type of fiber material as reinforcing fillers. It has become attractive structural material due to the ability of providing better combination of properties with respect to single fiber containing composite. The eco-friendly nature as well as processing advantage, light weight and low cost have enhanced the attraction and interest of natural fiber reinforced composite. The objective of present research is to study the mechanical properties of jute-coir fiber reinforced hybrid polypropylene (PP) composite according to filler loading variation. In the present work composites were manufactured by using hot press machine at four levels of fiber loading (5, 10, 15 and 20 wt %). Jute and coir fibers were utilized at a ratio of (1:1) during composite manufacturing. Tensile, flexural, impact and hardness tests were conducted for mechanical characterization. Tensile test of composite showed a decreasing trend of tensile strength and increasing trend of the Young-s modulus with increasing fiber content. During flexural, impact and hardness tests, the flexural strength, flexural modulus, impact strength and hardness were found to be increased with increasing fiber loading. Based on the fiber loading used in this study, 20% fiber reinforced composite resulted the best set of mechanical properties.

Keywords: Mechanical Properties; Coir, Jute, Polypropylene, Hybrid Composite.

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Authors: Elena A. Railean

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Although scientific methods have been the subject of a large number of papers, the term ‘scientific methods in educational management’ is still not well defined. In this paper, it is adopted the metasystems perspective to define the mentioned term and distinguish them from methods used in time of the scientific management and knowledge management paradigms. In our opinion, scientific methods in educational management rely on global phenomena, events, and processes and their influence on the educational organization. Currently, scientific methods in educational management are integrated with the phenomenon of globalization, cognitivisation, and openness, etc. of educational systems and with global events like the COVID-19 pandemic. Concrete scientific methods are nested in a hierarchy of more and more abstract models of educational management, which form the context of the global impact on education, in general, and learning outcomes, in particular. However, scientific methods can be assigned to a specific mission, strategy, or tactics of educational management of the concrete organization, either by the global management, local development of school organization, or/and development of the life-long successful learner. By accepting this assignment, the scientific method becomes a personal goal of each individual with the educational organization or the option to develop the educational organization at the global standards. In our opinion, in educational management, the scientific methods need to confine the scope to the deep analysis of concrete tasks of the educational system (i.e., teaching, learning, assessment, development), which result in concrete strategies of organizational development. More important are seeking the ways for dynamic equilibrium between the strategy and tactic of the planetary tasks in the field of global education, which result in a need for ecological methods of learning and communication. In sum, distinction between local and global scientific methods is dependent on the subjective conception of the task assignment, measurement, and appraisal. Finally, we conclude that scientific methods are not holistic scientific methods, but the strategy and tactics implemented in the global context by an effective educational/academic manager.

Keywords: Educational management, scientific management, educational leadership, scientific method in educational management.

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Authors: Oana Pop, Constantin Barbulescu, Mircea Nemes, Stefan Kilyeni

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The tracing methods determine the contribution the power system sources have in their supplying. The methods can be used to assess the transmission prices, but also to recover the transmission fixed cost. In this paper is presented the influence of the modification of commons structure has on the specific price of transfer. The operator must make use of a few basic principles about allocation. Most tracing methods are based on the proportional sharing principle. In this paper Kirschen method is used. In order to illustrate this method, the 25- bus test system is used, elaborated within the Electrical Power Engineering Department, from Timisoara, Romania.

Keywords: Power systems, P-U bus, P-Q bus, tracing methods.

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Authors: Liping Zhou, Liang Bao, Yiqin Lin, Yimin Wei, Qinghua Wu

Abstract:

This article is devoted to the numerical solution of large-scale quadratic eigenvalue problems. Such problems arise in a wide variety of applications, such as the dynamic analysis of structural mechanical systems, acoustic systems, fluid mechanics, and signal processing. We first introduce a generalized second-order Krylov subspace based on a pair of square matrices and two initial vectors and present a generalized second-order Arnoldi process for constructing an orthonormal basis of the generalized second-order Krylov subspace. Then, by using the projection technique and the refined projection technique, we propose a restarted generalized second-order Arnoldi method and a restarted refined generalized second-order Arnoldi method for computing some eigenpairs of largescale quadratic eigenvalue problems. Some theoretical results are also presented. Some numerical examples are presented to illustrate the effectiveness of the proposed methods.

Keywords: Quadratic eigenvalue problem, Generalized secondorder Krylov subspace, Generalized second-order Arnoldi process, Projection technique, Refined technique, Restarting.

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Authors: M. V. G. Silva, J. Gazzola, I. M. Dal Fabbro, A. C. L. Lino

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Computer aided design accounts with the support of parametric software in the design of machine components as well as of any other pieces of interest. The complexities of the element under study sometimes offer certain difficulties to computer design, or ever might generate mistakes in the final body conception. Reverse engineering techniques are based on the transformation of already conceived body images into a matrix of points which can be visualized by the design software. The literature exhibits several techniques to obtain machine components dimensional fields, as contact instrument (MMC), calipers and optical methods as laser scanner, holograms as well as moiré methods. The objective of this research work was to analyze the moiré technique as instrument of reverse engineering, applied to bodies of nom complex geometry as simple solid figures, creating matrices of points. These matrices were forwarded to a parametric software named SolidWorks to generate the virtual object. Volume data obtained by mechanical means, i.e., by caliper, the volume obtained through the moiré method and the volume generated by the SolidWorks software were compared and found to be in close agreement. This research work suggests the application of phase shifting moiré methods as instrument of reverse engineering, serving also to support farm machinery element designs.

Keywords: Reverse engineering, Moiré technique, three dimensional image generation.

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Authors: Andrei A. Kolyshkin

Abstract:

In the present paper some recommendations for the use of software package “Mathematica" in a basic numerical analysis course are presented. The methods which are covered in the course include solution of systems of linear equations, nonlinear equations and systems of nonlinear equations, numerical integration, interpolation and solution of ordinary differential equations. A set of individual assignments developed for the course covering all the topics is discussed in detail.

Keywords: Numerical methods, "Mathematica", e-learning.

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