Search results for: structural equation models

Authors: Reza Mohammadi, Mahdieh Sahebi

Abstract:

We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: Fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis.

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Authors: S.A. Alqallaf, S.A. Al-Mawsawi, A. Haider

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In order to evaluate the performance of a unified power flow controller (UPFC), mathematical models for steady state and dynamic analysis are to be developed. The steady state model is mainly concerned with the incorporation of the UPFC in load flow studies. Several load flow models for UPFC have been introduced in literature, and one of the most reliable models is the decoupled UPFC model. In spite of UPFC decoupled load flow model simplicity, it is more robust compared to other UPFC load flow models and it contains unique capabilities. Some shortcoming such as additional set of nonlinear equations are to be solved separately after the load flow solution is obtained. The aim of this study is to investigate the different control strategies that can be realized in the decoupled load flow model (individual control and combined control), and the impact of the location of the UPFC in the network on its control parameters.

Keywords: UPFC, Decoupled model, Load flow.

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Authors: Marco A. S. González, Marlova P. Kulakowski, Luciano G. Breitenbach, Felipe Kirch

Abstract:

The AEC sector has an expressive environmental responsibility. Actually, most building materials have severe environmental impacts along their production cycle. Professionals enrolled in building design may choice the materials and techniques with less impact among the viable options. This work presents a study about embodied energy in materials of two typical Brazilian constructive alternatives. The construction options considered are reinforced concrete structure and structural masonry. The study was developed for the region of São Leopoldo, southern Brazil. Results indicated that the energy embodied in these two constructive systems is approximately 1.72 GJ·m^-2 and 1.26 GJ·m^-2, respectively. It may be concluded that the embodied energy is lower in the structural masonry system, with a reduction around to 1/4 in relation to the traditional option. The results can be used to help design decisions.

Keywords: Civil construction, sustainability, embodied energy.

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Authors: I. Algul, G. Akgun, H. Kurtaran

Abstract:

Dynamic analysis of composite doubly curved panels with variable thickness subjected to different pulse types using Generalized Differential Quadrature method (GDQ) is presented in this study. Panels with variable thickness are used in the construction of aerospace and marine industry. Giving variable thickness to panels can allow the designer to get optimum structural efficiency. For this reason, estimating the response of variable thickness panels is very important to design more reliable structures under dynamic loads. Dynamic equations for composite panels with variable thickness are obtained using virtual work principle. Partial derivatives in the equation of motion are expressed with GDQ and Newmark average acceleration scheme is used for temporal discretization. Several examples are used to highlight the effectiveness of the proposed method. Results are compared with finite element method. Effects of taper ratios, boundary conditions and loading type on the response of composite panel are investigated.

Keywords: Generalized differential quadrature method, doubly curved panels, laminated composite materials, small displacement.

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Authors: A.R. Ismail, M. R. A. Rani, Z. K. M. Makhbul, M. J. M. Nor, M. N. A. Rahman

Abstract:

The environmental factors such as temperature and relative humidity are very contribute to the effect of comfort, health, performance and worker productivity. To ensure an ergonomics work environment, it is possible to require a specific attention especially in industries. The aim of this study is to show the effect of temperature and relative humidity on worker productivity in automotive industry by taking a workstation in an automotive plant as the location to conduct the study. From the analysis of the data, there were relationship between temperature and relative humidity on worker productivity. Mathematical equation to represent the relationship between temperatures and relative humidity on the production rate is modelled. From the equation model, the production rate for the workstation can be predicted base on the value of temperature and relative humidity.

Keywords: WBGT, Relative Humidity, Comfort, Productivity.

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Authors: Abdurrahim Dal, Tuncay Karaçay

Abstract:

Dynamics of a rotor supported by air bearings is strongly depends on the pressure distribution between the rotor and the bearing. In this study, internal pressure in air bearings is numerical and experimental analyzed for different radial clearances. Firstly the pressure distribution between rotor and bearing is modeled using Reynold's equation and this model is solved numerically. The rotor-bearing system is also modeled in four degree of freedom and it is simulated for different radial clearances. Then, in order to validate numerical results, a test rig is designed and the rotor bearing system is run under the same operational conditions. Pressure signals of left and right bearings are recorded. Internal pressure variations are compared for numerical and experimental results for different radial clearances.

Keywords: Air bearing, internal pressure, Reynold’s equation, rotor.

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Authors: Yanshuang Zhang, Byungho Jeong

Abstract:

In many cases, there are some time lag between the consumption of inputs and the production of outputs. This time lag effect should be considered in evaluating the performance of organizations. Recently, a couple of DEA models were developed for considering time lag effect in efficiency evaluation of research activities. Multi-periods input(MpI) and Multi-periods output(MpO) models are integrate models to calculate simple efficiency considering time lag effect. However, these models can’t discriminate efficient DMUs because of the nature of basic DEA model in which efficiency scores are limited to ‘1’. That is, efficient DMUs can’t be discriminated because their efficiency scores are same. Thus, this paper suggests a super-efficiency model for efficiency evaluation under the consideration of time lag effect based on the MpO model. A case example using a long term research project is given to compare the suggested model with the MpO model.

Keywords: DEA, Super-efficiency, Time Lag.

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Authors: Mohammad M. Toufigh, Ahad Ouria

Abstract:

This paper presents an analytical method to solve governing consolidation parabolic partial differential equation (PDE) for inelastic porous Medium (soil) with consideration of variation of equation coefficient under cyclic loading. Since under cyclic loads, soil skeleton parameters change, this would introduce variable coefficient of parabolic PDE. Classical theory would not rationalize consolidation phenomenon in such condition. In this research, a method based on time space mapping to a virtual time space along with superimposing rule is employed to solve consolidation of inelastic soils in cyclic condition. Changes of consolidation coefficient applied in solution by modification of loading and unloading duration by introducing virtual time. Mapping function is calculated based on consolidation partial differential equation results. Based on superimposing rule a set of continuous static loads in specified times used instead of cyclic load. A set of laboratory consolidation tests under cyclic load along with numerical calculations were performed in order to verify the presented method. Numerical solution and laboratory tests results showed accuracy of presented method.

Keywords: Mapping, Consolidation, Inelastic porous medium, Cyclic loading, Superimposing rule.

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Authors: Shewit Tsegaye, Kinde A. Fante

Abstract:

This paper presents the comparison and performance evaluation of synchronous machine excitation models. The two models, DC1A and AC4A, are among the IEEE standardized model structures for representing the wide variety of synchronous machine excitation systems. The performance evaluation of these models is done using SIMULINK simulation software. The simulation results obtained using transient analysis show that the DC1A excitation system is more reliable and stable than AC4A excitation system.

Keywords: Excitation system, synchronous machines, AC and DC regulators.

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Authors: Xin Luo, Jin Huang, Chuan-Long Wang

Abstract:

The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods.

Keywords: Darcy's equation, anisotropic, mechanical quadrature methods, extrapolation methods, a posteriori error estimate.

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Authors: Verónica Diaz Quezada

Abstract:

This research examines the teaching models used by secondary math teachers when teaching logarithmic, quadratic and exponential functions. For this, descriptive case studies have been carried out on 5 secondary teachers. These teachers have been chosen from 3 scientific-humanistic and technical schools, in Chile. Data have been obtained through non-participant class observation and the application of a questionnaire and a rubric to teachers. According to the results, the didactic model that prevails is the one that starts with an interactive strategy, moves to a more content-based structure, and ends with a reinforcement stage. Nonetheless, there is always influence from teachers, their methods, and the group of students.

Keywords: Teaching models, math teachers, functions, secondary education.

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Authors: Meng-Hao Tsai, Tsuei-Chiang Huang

Abstract:

Interior brick-infill partitions are usually considered as non-structural components and only their weight is accounted for in practical structural design. In this study, their effect on the progressive collapse resistance of an RC building subjected to sudden column loss is investigated. Three notional column loss conditions with four different brick-infill locations are considered. Column-loss response analyses of the RC building with and without brick infills are carried out. Analysis results indicate that the collapse resistance is only slightly influenced by the brick infills due to their brittle failure characteristic. Even so, they may help to reduce the inelastic displacement response under column loss. For practical engineering, it is reasonably conservative to only consider the weight of brick-infill partitions in the structural analysis.

Keywords: Progressive collapse, column loss, brick-infill partition, compression strut.

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Authors: V. Ghadamyari, F. Samadi, F. Kowsary

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An inverse geometry problem is solved to predict an unknown irregular boundary profile. The aim is to minimize the objective function, which is the difference between real and computed temperatures, using three different versions of Conjugate Gradient Method. The gradient of the objective function, considered necessary in this method, obtained as a result of solving the adjoint equation. The abilities of three versions of Conjugate Gradient Method in predicting the boundary profile are compared using a numerical algorithm based on the method. The predicted shapes show that due to its convergence rate and accuracy of predicted values, the Powell-Beale version of the method is more effective than the Fletcher-Reeves and Polak –Ribiere versions.

Keywords: Boundary elements, Conjugate Gradient Method, Inverse Geometry Problem, Sensitivity equation.

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Authors: Dalila Hamami, Baghdad Atmani

Abstract:

Modelling is a widely used tool to facilitate the evaluation of disease management. The interest of epidemiological models lies in their ability to explore hypothetical scenarios and provide decision makers with evidence to anticipate the consequences of disease incursion and impact of intervention strategies.

All models are, by nature, simplification of more complex systems. Models that involve diseases can be classified into different categories depending on how they treat the variability, time, space, and structure of the population. Approaches may be different from simple deterministic mathematical models, to complex stochastic simulations spatially explicit.

Thus, epidemiological modelling is now a necessity for epidemiological investigations, surveillance, testing hypotheses and generating follow-up activities necessary to perform complete and appropriate analysis.

The state of the art presented in the following, allows us to position itself to the most appropriate approaches in the epidemiological study.

Keywords: Bio-PEPA, Cellular automata, Epidemiological modelling, multi agent system, ordinary differential equations, PEPA, Process Algebra, Tuberculosis.

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Authors: M. Akbari, S. Sadodin

Abstract:

In this paper, the melting of a semi-infinite body as a result of a moving laser beam has been studied. Because the Fourier heat transfer equation at short times and large dimensions does not have sufficient accuracy; a non-Fourier form of heat transfer equation has been used. Due to the fact that the beam is moving in x direction, the temperature distribution and the melting pool shape are not asymmetric. As a result, the problem is a transient threedimensional problem. Therefore, thermophysical properties such as heat conductivity coefficient, density and heat capacity are functions of temperature and material states. The enthalpy technique, used for the solution of phase change problems, has been used in an explicit finite volume form for the hyperbolic heat transfer equation. This technique has been used to calculate the transient temperature distribution in the semi-infinite body and the growth rate of the melt pool. In order to validate the numerical results, comparisons were made with experimental data. Finally, the results of this paper were compared with similar problem that has used the Fourier theory. The comparison shows the influence of infinite speed of heat propagation in Fourier theory on the temperature distribution and the melt pool size.

Keywords: Non-Fourier, Enthalpy technique, Melt pool, Radiational boundary condition

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Authors: Yiqin Lin, Liang Bao, Yimin Wei

Abstract:

In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

Keywords: Arnoldi process, Krylov subspace, Iterative method, Sylvester equation, Dissipative matrix.

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Authors: Arti Vaish, Harish Parthasarathy

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The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.

Keywords: General theory of relativity, electromagnetism, metric tensor, Maxwells equations, test functions, finite element method.

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Authors: Muñoz-Sanchez, Victor Manuel, Perez-Flores, Antonio Manuel

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The main objective of this paper is to establish the relationship between models of state organization and the various types of collective identity expressed by the Spanish. The question of nationalism and identity ascription in Spain has always been a topic of special importance due to the presence in that country of territories where the population emits very different opinions of nationalist sentiment than the rest of Spain. The current situation of sovereignty challenge of Catalonia to the central government exemplifies the importance of the subject matter. In order to analyze this process of interrelation, we use a secondary data mining by applying the multiple correspondence analysis technique (MCA). As a main result a typology of four types of expression of collective identity based on models of State organization are shown, which are connected with the party position on this issue.

Keywords: Models of organization of the state, nationalism, collective identity, Spain, political parties.

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Authors: Vladimír Frišták, Martin Pipíška, Juraj Lesný

Abstract:

Alginite has been evaluated as an efficient pollution control material. In this paper, alginite from maar Pinciná (SR) for removal of Cd²⁺ ions from aqueous solution was studied. The potential sorbent was characterized by X-ray fluorescence analysis (RFA) analysis, Fourier transform infrared spectral analysis (FT-IR) and specific surface area (SSA) was also determined. The sorption process was optimized from the point of initial cadmium concentration effect and effect of pH value. The Freundlich and Langmuir models were used to interpret the sorption behavior of Cd²⁺ ions, and the results showed that experimental data were well fitted by the Langmuir equation. Alginite maximal sorption capacity (Q_max) for Cd²⁺ ions calculated from Langmuir isotherm was 34 mg/g. Sorption process was significantly affected by initial pH value in the range from 4.0-7.0. Alginite is a comparable sorbent with other materials for toxic metals removal. 

Keywords: Alginites, Cd2+, sorption, Qmax

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Authors: Karam Y. Maalawi, Hanan E.M EL-Sayed

Abstract:

This paper presents an exact analytical model for optimizing stability of thin-walled, composite, functionally graded pipes conveying fluid. The critical flow velocity at which divergence occurs is maximized for a specified total structural mass in order to ensure the economic feasibility of the attained optimum designs. The composition of the material of construction is optimized by defining the spatial distribution of volume fractions of the material constituents using piecewise variations along the pipe length. The major aim is to tailor the material distribution in the axial direction so as to avoid the occurrence of divergence instability without the penalty of increasing structural mass. Three types of boundary conditions have been examined; namely, Hinged-Hinged, Clamped- Hinged and Clamped-Clamped pipelines. The resulting optimization problem has been formulated as a nonlinear mathematical programming problem solved by invoking the MatLab optimization toolbox routines, which implement constrained function minimization routine named “fmincon" interacting with the associated eigenvalue problem routines. In fact, the proposed mathematical models have succeeded in maximizing the critical flow velocity without mass penalty and producing efficient and economic designs having enhanced stability characteristics as compared with the baseline designs.

Keywords: Functionally graded materials, pipe flow, optimumdesign, fluid- structure interaction

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Authors: Saemee Jun, Dong-Hyeon Shin, Tae-Sang Ahn, Hyung-Joon Kim

Abstract:

Building loss estimation methodologies which have been advanced considerably in recent decades are usually used to estimate socio and economic impacts resulting from seismic structural damage. In accordance with these methods, this paper presents the evaluation of an annual loss probability of a reinforced concrete moment resisting frame designed according to Korean Building Code. The annual loss probability is defined by (1) a fragility curve obtained from a capacity spectrum method which is similar to a method adopted from HAZUS, and (2) a seismic hazard curve derived from annual frequencies of exceedance per peak ground acceleration. Seismic fragilities are computed to calculate the annual loss probability of a certain structure using functions depending on structural capacity, seismic demand, structural response and the probability of exceeding damage state thresholds. This study carried out a nonlinear static analysis to obtain the capacity of a RC moment resisting frame selected as a prototype building. The analysis results show that the probability of being extensive structural damage in the prototype building is expected to 0.01% in a year.

Keywords: Expected annual loss, Loss estimation, RC structure, Fragility analysis.

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Authors: Görkem Arslan Kılınç

Abstract:

Due to the high construction, operation, and maintenance costs of tall buildings, quantification of the area in the plan layout which provides a financial return is an important design criterion. The area of the “core and the structural system elements” does not provide financial return but must exist in the plan layout. Some characteristic items of tall office buildings affect the size of these areas. From this point of view, 15 tall office buildings were systematically investigated. The typical office floor plans of these buildings were re-produced digitally. The area of the “core and the structural system elements” in each building and the characteristic items of each building were calculated. These characteristic items are the size of the long and short plan edge, plan length/width ratio, size of the core long and short edge, core length/width ratio, core area, slenderness, building height, number of floors, and floor height. These items were analyzed by correlation and regression analyses. Results of this paper put forward that; characteristic items which affect the area of "core and structural system elements" are plan long and short edge size, core short edge size, building height, and the number of floors. A one-unit increase in plan short side size increases the area of the "core and structural system elements" in the plan by 12,378 m2. An increase in core short edge size increases the area of the core and structural system elements in the plan by 25,650 m2. Subsequent studies can be conducted by expanding the sample of the study and considering the geographical location of the building.

Keywords: Core area, correlation analysis, floor area, regression analysis, space efficiency, tall office buildings.

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Authors: Evgeny Pyshkin, Maxim Mozgovoy, Vladislav Volkov

Abstract:

The paper follows a discourse on computer-assisted language learning. We examine problems of foreign language teaching and learning and introduce a metamodel that can be used to define learning models of language grammar structures in order to support teacher/student interaction. Special attention is paid to the concept of a virtual language lab. Our approach to language education assumes to encourage learners to experiment with a language and to learn by discovering patterns of grammatically correct structures created and managed by a language expert.

Keywords: Computer-assisted instruction, Language learning, Natural language grammar models, HCI.

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Authors: Zöhre Kara Kayikci, Günther Palm

Abstract:

A word recognition architecture based on a network of neural associative memories and hidden Markov models has been developed. The input stream, composed of subword-units like wordinternal triphones consisting of diphones and triphones, is provided to the network of neural associative memories by hidden Markov models. The word recognition network derives words from this input stream. The architecture has the ability to handle ambiguities on subword-unit level and is also able to add new words to the vocabulary during performance. The architecture is implemented to perform the word recognition task in a language processing system for understanding simple command sentences like “bot show apple".

Keywords: Hebbian learning, hidden Markov models, neuralassociative memories, word recognition.

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Authors: D. I. De Souza, G. P. Azevedo, R. Rocha

Abstract:

In this paper we will develop a sequential life test approach applied to a modified low alloy-high strength steel part used in highway overpasses in Brazil.We will consider two possible underlying sampling distributions: the Normal and theInverse Weibull models. The minimum life will be considered equal to zero. We will use the two underlying models to analyze a fatigue life test situation, comparing the results obtained from both.Since a major chemical component of this low alloy-high strength steel part has been changed, there is little information available about the possible values that the parameters of the corresponding Normal and Inverse Weibull underlying sampling distributions could have. To estimate the shape and the scale parameters of these two sampling models we will use a maximum likelihood approach for censored failure data. We will also develop a truncation mechanism for the Inverse Weibull and Normal models. We will provide rules to truncate a sequential life testing situation making one of the two possible decisions at the moment of truncation; that is, accept or reject the null hypothesis H0. An example will develop the proposed truncated sequential life testing approach for the Inverse Weibull and Normal models.

Keywords: Sequential life testing, normal and inverse Weibull models, maximum likelihood approach, truncation mechanism.

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Authors: S. Daneshmand, A. Ahmadi Nadooshan, C. Aghanajafi

Abstract:

Traditional wind tunnel models are meticulously machined from metal in a process that can take several months. While very precise, the manufacturing process is too slow to assess a new design's feasibility quickly. Rapid prototyping technology makes this concurrent study of air vehicle concepts via computer simulation and in the wind tunnel possible. This paper described the Affects layer thickness models product with rapid prototyping on Aerodynamic Coefficients for Constructed wind tunnel testing models. Three models were evaluated. The first model was a 0.05mm layer thickness and Horizontal plane 0.1μm (Ra) second model was a 0.125mm layer thickness and Horizontal plane 0.22μm (Ra) third model was a 0.15mm layer thickness and Horizontal plane 4.6μm (Ra). These models were fabricated from somos 18420 by a stereolithography (SLA). A wing-body-tail configuration was chosen for the actual study. Testing covered the Mach range of Mach 0.3 to Mach 0.9 at an angle-of-attack range of -2° to +12° at zero sideslip. Coefficients of normal force, axial force, pitching moment, and lift over drag are shown at each of these Mach numbers. Results from this study show that layer thickness does have an effect on the aerodynamic characteristics in general; the data differ between the three models by fewer than 5%. The layer thickness does have more effect on the aerodynamic characteristics when Mach number is decreased and had most effect on the aerodynamic characteristics of axial force and its derivative coefficients.

Keywords: Aerodynamic characteristics, stereolithography, layer thickness, Rapid prototyping, surface finish.

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Authors: M. Aminu Sanda

Abstract:

This paper explores competencies that managers of small firms in Ghana use to enhance operational flexibility towards the attainment of higher productivity. This is because the requisite competence required of such managers to be effective performers continues to be a challenge. Data was collected from managers of three hundred small firms using a standardized self-completion questionnaire and analyzed using the Amos-based structural equation model approach. Findings from factor and confirmatory factor analyses showed that the only competence exhibited by managers toward effective performance is realistic practices evident at the workplace. It is concluded that a manager’s self-confidence and involvement in areas that he/she is good at, and his/her possession of skills that enables performance at high capacity are indications of the manger’s effectiveness. The study outcome provides a knowledge base helpful to policy-makers, especially in Ghana, in determining the requisite managerial competences required by small firm managers for effective performance.

Keywords: Managerial competence, small firm, effective performance, developing economy, Ghana.

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Authors: V. Phupha, T. Lantharthong, N. Rugthaicharoencheep

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The problem of generation expansion planning (GEP) has been extensively studied for many years. This paper presents three topics in GEP as follow: statistical model, models for generation expansion, and expansion problem. In the topic of statistical model, the main stages of the statistical modeling are briefly explained. Some works on models for GEP are reviewed in the topic of models for generation expansion. Finally for the topic of expansion problem, the major issues in the development of a longterm expansion plan are summarized.

Keywords: Generation expansion planning, strategies, power system

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Authors: Kristjan Kuhi, Kati K. Kaare, Ott Koppel

Abstract:

Modern management in most fields is performance based; both planning and implementation of maintenance and operational activities are driven by appropriately defined performance indicators. Continuous real-time data collection for management is becoming feasible due to technological advancements. Outdated and insufficient input data may result in incorrect decisions. When using deterministic models the uncertainty of the object state is not visible thus applying the deterministic models are more likely to give false diagnosis. Constructing structured probabilistic models of the performance indicators taking into consideration the surrounding indicator environment enables to estimate the trustworthiness of the indicator values. It also assists to fill gaps in data to improve the quality of the performance analysis and management decisions. In this paper authors discuss the application of probabilistic graphical models in the road performance measurement and propose a high-level conceptual model that enables analyzing and predicting more precisely future pavement deterioration based on road utilization.

Keywords: Probabilistic graphical models, performance indicators, road performance management, data collection

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Authors: Afshin Ahmadi Nadooshan, Ebrahim Shirani

Abstract:

Different numerical methods are employed and developed for simulating interfacial flows. A large range of applications belong to this group, e.g. two-phase flows of air bubbles in water or water drops in air. In such problems surface tension effects often play a dominant role. In this paper, various models of surface tension force for interfacial flows, the CSF, CSS, PCIL and SGIP models have been applied to simulate the motion of small air bubbles in water and the results were compared and reviewed. It has been pointed out that by using SGIP or PCIL models, we are able to simulate bubble rise and obtain results in close agreement with the experimental data.

Keywords: Volume-of-Fluid, Bubble Rising, SGIP model, CSS model, CSF model, PCIL model, interface, surface tension force.

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