• Journal of the Korean Mathematical Society
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• 제48권4호
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• pp.669-689
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• 2011

The notion of quasi-Einstein manifolds arose during the study of exact solutions of the Einstein field equations as well as during considerations of quasi-umbilical hypersurfaces. For instance, the Robertson-Walker spacetimes are quasi-Einstein manifolds. The object of the present paper is to study Lorentzian quasi-Einstein manifolds. Some basic geometric properties of such a manifold are obtained. The applications of Lorentzian quasi-Einstein manifolds to the general relativity and cosmology are investigated. Theories of gravitational collapse and models of Supernova explosions [5] are based on a relativistic fluid model for the star. In the theories of galaxy formation, relativistic fluid models have been used in order to describe the evolution of perturbations of the baryon and radiation components of the cosmic medium [32]. Theories of the structure and stability of neutron stars assume that the medium can be treated as a relativistic perfectly conducting magneto fluid. Theories of relativistic stars (which would be models for supermassive stars) are also based on relativistic fluid models. The problem of accretion onto a neutron star or a black hole is usually set in the framework of relativistic fluid models. Among others it is shown that a quasi-Einstein spacetime represents perfect fluid spacetime model in cosmology and consequently such a spacetime determines the final phase in the evolution of the universe. Finally the existence of such manifolds is ensured by several examples constructed from various well known geometric structures.

• Journal of the Korean Society for Railway
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• 제10권6호
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• pp.742-750
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• 2007

This paper presents a mathematical model for a double-fleet operation in Korean high speed rail (HSR). KORAIL has a plan to launch new HSR units in 2010, which are composed of 10 railcars. The double-fleet operation assigns a single-unit or two-unit fleet to a segment, accommodating demand fluctuation. The proposed model assumes stochastic demand and uses chance-constrained constraints to assure a preset service level. It can be used in the tactical planning stage of the rail management as it includes several real-world conditions, such as the capacities of the infra-structures and operational procedures. In the solution approach, the expected revenue in the objective function is linearized by using expected marginal revenue, and the chance-constrained constraints are linearized by assuming that demands are normally distributed. Subsequently, the model can be solved by a mixed-integer linear programming solver fur small size problems. The test results of the model applied to Friday morning train schedules for one month sample data from KTX operation in 2004 shows that the proposed model could be utilized to determine the effectiveness of double-fleet operation, which could significantly increase the expected profit and seat utilization rates when properly maneuvered.

• Steel and Composite Structures
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• 제16권4호
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• pp.417-436
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• 2014

During an earthquake, steel frame columns can be subjected to high axial forces combined with inelastic rotation demand resulting from story drift. Generally, the whole beam or component can be represented with one element. In elasto-plastic analysis, subdivision is necessary if the plastic deformation occurs within two ends of beams. If effects of the joint panel are necessarily considered in the analysis, the joint panel should be represented with an independent element. It is a special element to represent the shear deformation of the joint panel in the beam-column connection zone. Several analytical models for panel zone (PZ) behavior exist, in terms of shear force-shear distortion relationships. Among these models, the Krawinkler PZ model is the most popular one which is used in the AISC code. Some studies have pointed out that Krawinkler's model gives good results for the range of thin to medium column flanges thickness. This paper, introduces a new model to estimate the response of shear force-shear distortion for the PZ including column axial force. The model is applicable to both thin and thick column flange. To achieve an appropriate PZ mathematical model first, the effects of PZ strength and stiffness on connection response are parametrically studied using finite element models. More than one thousand and four-hundred beam-column connections are included in the parametric study, with varied parameters; then based on analytical results a simple mathematical model is presented. A comparison between the results of proposed method herein with FE analyses shows the average error especially in thick column flange is significantly reduced which demonstrates the accuracy, efficiency, and simplicity of the proposed model.

• Journal of the Korean School Mathematics Society
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• 제8권3호
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• pp.357-366
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• 2005

This Study suggests some ideas how we develop a network of content structure based on informal context and method how we decide a sequence of mathematical syllabus from those Structures. 10th grade students in the process conceptual development was observed and interviewed in 2 hour teaching and learning experiment. Three related characteristics of student's thought in structuring math. Content and sequencing it were investigated as follows : (a) the reasoning that they do reflective abstraction well(or do not well) in acquisition of conceptual knowledge. (b) the method that teacher can use resuits in (a) to organize the content structure. (c) the ways that teacher find the process knowledge in informal content structure. That is, this study investigated the way we, curriculum designer, can create well defined content structure and instructional sequence strongly based on the learners' understanding.

• Journal of Power Electronics
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• 제16권2호
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• pp.631-642
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• 2016

Usually, the output characteristics of a photovoltaic (PV) array are significantly affected by non-uniform irradiance which is caused by ambient obstacles, clouds, orientations, tilts, etc. Some local maximum power points (LMPP) in the current-voltage (I-V) curves of a PV array can result in power losses of the array. However, the output power at the global maximum power point (GMPP) is different in different interconnection schemes in a PV array. Therefore, based on the theoretical analysis and mathematical derivation of different topological structures of a PV array, this paper investigated the output characteristics of dual series PV arrays with different interconnections. The proposed mathematical models were also validated by experimental results. Finally, this paper also concluded that in terms of performance, the total cross tied (TCT) interconnection was not always the optimal structure, especially in a dual series PV array. When one of the PV modules was severely mismatched, the TCT worked worse than the series parallel (SP) structure. This research can provide guidance for switching the interconnection to gain the greatest energy yield in a changeable- structure PV system.

• The Journal of the Korea Contents Association
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• 제10권10호
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• pp.68-77
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• 2010

In the case of operating steam generators for long periods in nuclear power plants, sludge is accumulated inside the steam generator. This phenomenon could adversely affect the operation of the steam generator. This paper is about the design of a sludge washing apparatus which can remove the sludge efficiently and the control methods of the apparatus. In this paper, to design the sludge washing apparatus, firstly, we design nozzles for spraying high-pressure water through applying mathematical models and lab tests. Secondly, we establish the mathematical theory for performance parameters required to drive the sludge washing apparatus. Thirdly, we design physical structures of the apparatus based on the established performance parameters. Finally, we present the control methods of the apparatus. The sludge washing apparatus presented in this paper moves along the walls of the steam generator according to cracks in the tube array, and spray the high pressure water to remove the sludge. By this way, a relatively large amount of sludge formed in the inner surfaces can be washed very effectively.

• Smart Structures and Systems
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• 제15권3호
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• pp.665-682
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• 2015

Structural identification or St-Id is 'the parametric correlation of structural response characteristics predicted by a mathematical model with analogous characteristics derived from experimental measurements'. This paper describes a St-Id exercise on Humber Bridge that adopted a novel two-stage approach to first calibrate and then validate a mathematical model. This model was then used to predict effects of wind and temperature loads on global static deformation that would be practically impossible to observe. The first stage of the process was an ambient vibration survey in 2008 that used operational modal analysis to estimate a set of modes classified as vertical, torsional or lateral. In the more recent second stage a finite element model (FEM) was developed with an appropriate level of refinement to provide a corresponding set of modal properties. A series of manual adjustments to modal parameters such as cable tension and bearing stiffness resulted in a FEM that produced excellent correspondence for vertical and torsional modes, along with correspondence for the lower frequency lateral modes. In the third stage traffic, wind and temperature data along with deformation measurements from a sparse structural health monitoring system installed in 2011 were compared with equivalent predictions from the partially validated FEM. The match of static response between FEM and SHM data proved good enough for the FEM to be used to predict the un-measurable global deformed shape of the bridge due to vehicle and temperature effects but the FEM had limited capability to reproduce static effects of wind. In addition the FEM was used to show internal forces due to a heavy vehicle to to estimate the worst-case bearing movements under extreme combinations of wind, traffic and temperature loads. The paper shows that in this case, but with limitations, such a two-stage FEM calibration/validation process can be an effective tool for performance prognosis.

• Structural Engineering and Mechanics
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• 제40권1호
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• pp.65-84
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• 2011

In this paper a simple mathematical model for approximate static analysis of combined system of framed tube, shear core and two outrigger-belt truss structures subjected to lateral loads is presented. In the proposed methodology, framed tube is modeled as a cantilevered beam with a box section and interaction between shear core and outrigger-belt truss system with framed tube is modeled using torsional springs placed at location of outrigger-belt truss; these torsional springs act in a direction opposite to rotation generated by lateral loads. The effect of shear lag on axial deformation in flange is quadratic and in web it is a cubic function of geometry. Here the total energy of the combined system is minimized with respect to lateral deflection and rotation in plane section. Solution of the resulting equilibrium equations yields the unknown coefficients of shear lag along with the stress and displacement distributions. The results of a numerical example, 50 storey building subjected to three different types of lateral loading obtained from SAP2000 are compared to those of the proposed method and the differences are found to be reasonable. The proposed method can be used during the preliminary design stages of a tall building and can provide a better understanding of the effects of various parameters on the overall structural behavior.

• Journal of the Korea institute for structural maintenance and inspection
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• 제7권3호
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• pp.251-262
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• 2003

LCP(Life Cycle Profiles) of bridge structures are indispensable for the LCC(Life Cycle Cost) evaluations of bridge system. The bridge under considerations may be newly-designed one or one in service. Thus, a systematic study of LCP is essential for both reliable LCC evaluation and strategic bridge management. LCP is mainly influenced by the structural environment in nature. However, in Korea, LCC evaluation has been performed with the LCP of foreign research results or only with the pieces of professional engineers' opinion. Therefore, to alleviate the drawbacks of foreign LCP and to enhance the reliability of current LCP, LCP should be established using the available data in bridge management system(BMS). In this study, LCP along with a subset of the BMS data was investigated and several mathematical expressions were proposed and evaluated. The condition ratings of a bridge were trasformed into the numerical indices through fuzzy logics with real field data. From the numerical results, it is concluded that the mathematical LCP model of $y=\sqrt{y^2_0-at}$ is shown to be the fittest one (R=0.815) to express the condition rating varied with the age. This has been drawn from the case study of slab bridges under the similar conditions.

• Wind and Structures
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• 제34권1호
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• pp.59-72
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• 2022

In this work the numerical results of the flow around a 5:1 rectangular cylinder at Reynolds numbers 3 000 and 40 000, zero angle of attack and smooth incoming flow condition are presented. Implicit Large Eddy Simulations (ILES) have been performed with a high-order accurate spatial scheme and an implicit high-order accurate time integration method. The spatial approximation is based on a discontinuous Galerkin (dG) method, while the time integration exploits a linearly-implicit Rosenbrock-type Runge-Kutta scheme. The aim of this work is to show the feasibility of high-fidelity flow simulations with a moderate number of DOFs and large time step sizes. Moreover, the effect of different parameters, i.e., dimension of the computational domain, mesh type, grid resolution, boundary conditions, time step size and polynomial approximation, on the results accuracy is investigated. Our best dG result at Re=3 000 perfectly agrees with a reference DNS obtained using Nek5000 and about 40 times more degrees of freedom. The Re=40 000 computations, which are strongly under-resolved, show a reasonable correspondence with the experimental data of Mannini et al. (2017) and the LES of Zhang and Xu (2020).