• International Journal of CAD/CAM
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• v.9 no.1
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• pp.61-69
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• 2010

Based on the equivalence principles of physical properties, geometric properties and externally applied forces between a surface and the corresponding curves, we present a fast physics and example based skin deformation method for character animation in this paper. The main idea is to represent the skin surface and its deformations with a group of curves whose computation incurs much less computing overheads than the direct surface-based approach. The geometric and physical properties together with externally applied forces of the curves are determined from those of the surface defined by these curves according to the equivalence principles between the surface and the curves. This ensures the curve-based approach is equivalent to the original problem. A fourth order ordinary differential equation is introduced to describe the deformations of the curves between two example skin shapes which relates geometric and physical properties and externally applied forces to shape changes of the curves. The skin deformation is determined from these deformed curves. Several examples are given in this paper to demonstrate the application of the method.

• Transactions of the Korean Society of Automotive Engineers
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• v.1 no.1
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• pp.66-79
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• 1993

To construct the design back data for a lean-burn gas engine, we have designed a constant volume combustion chamber with sub-chamber. With constant volume ratio of main-sub combustion chamber and constant equivalence ratio of methane-air mixture, the influence of geometric configurations(diameter, injection angle, number, length) of passagehole upon combustion characteristics were studied. It was found that combustion characteristics in the main combustion chamber were greatly influenced by the injection angle and length of passagehole.

• Journal of the Korean School Mathematics Society
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• v.24 no.2
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• pp.173-190
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• 2021

This study analyzed the proof of the inverse square law, which is said to be the core of Newton's , in relation to the geometric limit. Newton, conscious of the debate over infinitely small, solved the dynamics problem with the traditional Euclid geometry. Newton reduced mechanics to a problem of geometry by expressing force, time, and the degree of inertia orbital deviation as a geometric line segment. Newton was able to take Euclid's geometry to a new level encompassing dynamics, especially by introducing geometric limits such as parabolic approximation, polygon approximation, and the limit of the ratio of the line segments. Based on this analysis, we proposed to use Newton's geometric limit as a tool to show the usefulness of mathematics, and to use it as a means to break the conventional notion that the area of the curve can only be obtained using the definite integral. In addition, to help the desirable use of geometric limits in school mathematics, we suggested the following efforts are required. It is necessary to emphasize the expansion of equivalence in the micro-world, use some questions that lead to use as heuristics, and help to recognize that the approach of ratio is useful for grasping the equivalence of line segments in the micro-world.

• Communications for Statistical Applications and Methods
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• v.13 no.3
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• pp.777-786
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• 2006

Two factorial designs with quantitative factors are called geometrically equivalent if the design matrix of one can be transformed into the design matrix of the other by row and column permutations, and reversal of symbol order in one or more columns. Clark and Dean (2001) gave a sufficient and necessary condition (which we call the 'gCD condition') for two symmetric factorial designs with quantitative factors to be geometrically equivalent. This condition is based on the absolute value of the Euclidean(or Hamming) distance between pairs of design points. In this paper we extend the gCD condition to asymmetric designs. In addition, a modified algorithm is applied for checking the equivalence of two designs.

• International Journal of Control, Automation, and Systems
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• v.4 no.6
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• pp.769-774
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• 2006

In this paper, we discuss the problem of non-mutual detectability using the invariant zero. We propose a representation method for excess spaces by linear equation based on the Rosenbrock system matrix. As an alternative to the system enlargement method proposed by White[1], we propose an appropriate form of an enlarged system to make a set of faults mutually detectable by assigning sufficient geometric multiplicity of invariant zeros. We show the equivalence between the two methods and a necessary condition for the system enlargement in terms of the geometric and algebraic multiplicities of invariant zeros.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.5
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• pp.846-855
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• 1987

The experimental study was carried out to investigate the performance characteristics of the aero-valved pulsating combustor designed to increase the practical applications of the system. The geometric effect on the stable condition and the dynamic behavior of the system is identified. The equivalence ratio, the inflammability limit, the operating frequency, and thrust were also measured when the system oscillated stably. It is found that while the operating condition is sensitive to the diameter of the inlet pipe and the length of the tailpipe, the maximum value of the turn down ratio was obtained up to 3.2. The measured air flow rate shows that the equivalence ratio increases monotonously with the increasing fuel flow rate and decreasing air inlet diameter and tailpipe length. The measured operating frequency can be approximated by the simple linear equation and the discrepancy is within five percent. The system produced the maximum total thrust of 14N and the minimum specific fuel consumption of 0.155 Nm$^{3}$/h.N when the total thrust was 13N.

• 한국연소학회:학술대회논문집
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• 2012.04a
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• pp.199-200
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• 2012

An experimental study on geometric optimization was conducted to develop a hybrid/dual swirl jet combustor for a micro-gas turbine. A hybrid concept indicating a combination of swirling jet partially premixed and premixed flames were adopted to achieve high flame stability as well as clean combustion. Location of pilot nozzle, angle and direction of swirl vane were varied as main parameters with a constant fuel flow rate for each nozzle. The results showed that the variation in location of pilot nozzle resulted in significant change in swirl intensity due to the change in flow area near burner exit, and thus, optimized nozzle location was determined on the basis of CO and NOx emissions under conditions of co-swirl flow and swirl $angle=30^{\circ}$. The increase in swirl angle (from $30^{\circ}$ to $45^{\circ}$) enhanced the emission performances, in particular, with a significant reduction of CO emission near lean-flammability limit. It was observed that the CO emission near lean-flammability limit was further reduced through the counter-swirl flow. However, there was not significant change in the NOx emission in the operating conditions (i.e. equivalence ratio of 0.6~0.7) between the co- and the counter-swirl flow.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.18 no.8
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• pp.664-671
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• 2006

We propose the correlation to predict the spreading thermal resistance on a plate with symmetrical four heat sources. The correlation transforms four heat sources to a single equivalent heat source and then the spreading thermal resistance can be obtained with the existing equation for a single heat source. When the four heat sources are mounted on a square base plate, the correlation is expressed as a function of the heat source size, the length of base plate, the plate thermal conductivity and the distance between heat sources. Compared to the results of three-dimensional numerical analysis, the spreading thermal resistance by the proposed correlation is in good agreement within 10 percent accuracy.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.625-639
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• 1996

A convex $RP^n$-structure on a smooth anifold M is a representation of M as a quotient of a convex domain $\Omega \subset RP^n$ by a discrete group $\Gamma$ of collineations of $RP^n$ acting properly on $\Omega$. When M is a closed surface of genus g > 1, then the equivalence classes of such structures form a moduli space $B(M)$ homeomorphic to an open cell of dimension 16(g-1) (Goldman [2]). This cell contains the Teichmuller space $T(M)$ of M and it is of interest to know what of the rich geometric structure extends to $B(M)$. In [3], a symplectic structure on $B(M)$ is defined, which extends the symplectic structure on $T(M)$ defined by the Weil-Petersson Kahler form.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.351-361
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• 1995

Let M be a complete open Riemannian manifold. When the sectional curvature $K_M$ of M is nonpositive, Gromov has defined, in his lectures [3], the ideal boundary of M, and used it to study the geometric structure of M. In a Hadamard manifold, a simply connected manifold with nonpositive sectional curvature, a point at infinity can be defined as an equivalence class of rays. He proved many interesting theorems using this definition of ideal boundary and the so-called Tit's metric on it. He also suggested a counterpart to this for nonnegative curvature case. This idea has been taken up by Kasue to study the structure of complete open manifolds with asympttically nonnegative curvature [14]. Motivated by these works, we will define an idela boundary of a general noncompact manifold M, and study its structure.