• International Journal of Aeronautical and Space Sciences
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• v.12 no.1
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• pp.57-62
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• 2011

The effects of swirl chamber's diameter and length on injector's dynamic characteristics were investigated through an experimental study. A mechanical pulsator was installed in front of the manifold of a swirl injector which produces pressure oscillations in the feed line. Pressure in the manifold, liquid film thickness in the orifice and the pressure in the orifice were measured in order to understand the dynamic characteristic of the simplex swirl injector with varying geometry. A direct pressure measuring method (DPMM) was used to calculate the axial velocity of the propellant in the orifice and the mass flow rate through the orifice. These measured and calculated values were analyzed to observe the amplitude and phase differences between the input value in the manifold and the output values in the orifice. As a result, a phase-amplitude diagram was obtained which exhibits the injector's response to certain pressure fluctuation inputs. The mass flow rate was calculated by the DPMM and measured directly through the actual injection. The effect of mean manifold pressure change was insignificant with the frequency range of manifold pressure oscillation used in this experiment. Mass flow rate was measured with the variation of injector's geometries and amplitude of the mass flow rate was observed with geometry and pulsation frequency variation. It was confirmed that the swirl chamber diameter and length affect an injector's dynamic characteristics. Furthermore, the direction of geometry change for achieving dynamic stability in the injector was suggested.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.397-401
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• 2008

Knowledge of dynamic characteristics of structural elements often can make difference between success and failure in the design of structure due to resonance effect. In this paper an analytical model of a cantilever beam having midpoint load is considered for structural optimization. This involves creating the geometry which allows parametric study of all design variables. For that purpose optimization of cantilever beam is elaborated in order to find the optimum geometry which minimizes its volume eventually for minimum weight using ANSYS. But such geometry could be obtained by different combinations of width and height, so that it may have the same cross sectional area yet different dynamic behavior. So for optimum safe design, besides minimum volume it should have minimum vibration as well. In order to predict vibration different dynamic analyses are performed simultaneously to solve the eigenvalues problem assuming no damping initially through MATLAB simulations using state space form for modal analysis, which identifies the resonant frequencies and mode shapes belonging to the lowest three modes of vibration. And next by introducing damping effects tip displacement, bending stress and the vertical reaction force at the fixed end is evaluated under some dynamic load of varying frequency, and finally it is discussed how resonance can be avoided for particular design. Investigation of results clearly shows that only structural analysis is not enough to predict the optimum values of dimension for safe design. Potentially this technique will meet maintenance and cost goals of many organizations particularly for the application where dynamic loading is invertible and helps a lot ensuring that the proposed design will be safe for both static and dynamic conditions.

• Journal for History of Mathematics
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• v.15 no.1
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• pp.115-134
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• 2002

The increasing use of computers in mathematics and in mathematics education is strongly reflected in the teaching on Euclid geometry, in particular in the use of dynamic graphics software. This development has raised questions about the role of analytic proof in school geometry. One can sometimes find a proof which is rather more explanatory than the one commonly used. Because we, math educators are concerned with tile explanatory power of the proofs, as opposed to mere verification, we should devise ways to use dynamic software in the use of explanatory proofs.

• Research in Mathematical Education
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• v.7 no.1
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• pp.41-58
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• 2003

This study firstly examined 18 prospective secondary mathematics teachers' understanding of the nature of definitions and the use of the dynamic geometry software Sketchpad to not only improve their understanding of definitions, but also their ability to define geometric concepts themselves. Results indicated that the evaluation of definitions by accurate construction and measurement enabled students to achieve a better understanding of necessary and sufficient conditions, as well as the ability to more readily find counter-examples, and to recognize uneconomical definitions, and improve them.

• Journal of the Korean School Mathematics Society
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• v.5 no.2
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• pp.101-109
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• 2002

Among interactive dynamic geometry softwares, Cinderella has some merits on the accuracy of algorithms and compatibility with internet. In this paper we compare dynamic geometry softwares such as GSP, Cabri II, Cinderella briefly and we design a web based interactive learning materials using the exercise editor of Cinderella and some Java applets, and we propose a web based interactive teaching and learning model in which achievement test can be given by the clickings on the help icon.

• Tribology and Lubricants
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• v.17 no.2
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• pp.116-123
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• 2001

A theoretical analysis has been undertaken to show the influence of bearing geometry on the steady state characteristics of air lubricated spherical tilting pad bearings. The geometry variations considered are the number of pads, the eccentricity ratio, the direction of load, and the preloading. Dynamic characteristic equations are derived with pad assembly method.

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.89-112
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• 2017

In this study we have analyzed processes of generalization in which students have geometrically solved cubic equation $x^3+ax=b$, regarding geometrical solution of cubic equation $x^3+4x=32$ as examples. The result of this research indicate that students could especially re-interpret the geometric solution of the given cubic equation via dynamically understanding the variables in dynamic geometry environment. Furthermore, participants could simultaneously re-interpret the given geometric solution and then present a different geometric solutions of $x^3+ax=b$, so that the level of generalization could be improved. In conclusion, the study could provide useful pedagogical implications in school mathematics that the dynamic geometry environment performs significant function as a means of students-centered exploration when understanding variables and enhancing the level of generalization in problem solving.

• ETRI Journal
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• v.10 no.3
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• pp.125-140
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• 1988

Computational geometry has wide applications in pattern recognition, image processing, VLSI design, and computer graphics. Voronoi diagrams in computational geometry possess many important properites which are related to other geometric structures of a set of point. In this pater the design of systolic algorithms for the static and the dynamic Voronoi diagrams is considered. The major motivation for developing the systolic architecture is for VLSI implementation. A new systematic transform technique for designing systolic arrays, in particular, for the problem in computational geometry has been proposed. Following this procedure, a type T systolic array architecture and associated systolic algorithms have been designed for constructing Voronoi diagrams. The functions of the cells in the array are also specified. The resulting systolic array achieves the maximal throughput with O(n) computational complexity.

• Journal of ILASS-Korea
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• v.10 no.1
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• pp.24-34
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• 2005

Injection technology is one of the important technologies in a diesel engine. Many studies have done on the injection system. In this study, the fuel chamber geometry, the orifice ratio and the needle lift of the injection valve for a marine diesel engine are varied, and simulated. The result shows that the nozzle hole size has influence on the rail pressure and injection duration sensitively. The decrease of the static pressure at the nozzle hole entrance and the increase of the dynamic pressure on the outlet surface are occurred with the increase of the nozzle hole diameter. The highest dynamic pressure of the outlet was occurred at the needle lift of 0.4mm and the nozzle hole diameter of 0.328mm in this test nozzle.

• Research in Mathematical Education
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• v.14 no.3
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• pp.219-231
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• 2010

Mathematically, a proof is to create a convincing argument through logical reasoning towards a given proposition or a given statement. Mathematics educators have been working diligently to create environments that will assist students to perform proofs. One of such environments is the use of dynamic-geometry-software in the classroom. This paper reports on a case study and intends to probe into students' own thinking, patterns they used in completing certain tasks, and the extent to which they have utilized technology. Their tasks were to explore the shape-to-shape, shape-to-part, and part-to-part interrelationships of geometric objects when dealing with certain geometric problem-solving situations utilizing dissection-motion-operation (DMO).