• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.91-102
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• 2002

Let M and N be CR manifolds with nondegenerate Levi forms of hypersurface type of dimension 2m ＋ 1 and 2n ＋ 1, respectively, where 1 $\leq$ m $\leq$ n. Let f : M longrightarrow N be a CR mapping. Under a generic assumption we construct a complete system of finite order for the infinitesimal deformations of f. In particular, we prove the space of infinitesimal deformations of f forms a finite dimensional Lie algebra.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.133-140
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• 2002

On compact complex hyperbolic manifolds of complex dimension two, we show that the dimension of the space of infinitesimal deformations of self-dual conformal structures is smaller than that of the deformation obstruction space and that every self-dual metric with covariantly constant Ricci tensor must be a standard one upto rescalings and diffeomorphisms.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.271-291
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• 2021

Hom-Lie-Yamaguti color algebras are defined and their representation and cohomology theory is considered. The (2, 3)-cocycles of a given Hom-Lie-Yamaguti color algebra T are shown to be very useful in a study of its deformations. In particular, it is shown that any (2, 3)-cocycle of T gives rise to a Hom-Lie-Yamaguti color structure on T⊕V , where V is a T-module, and that a one-parameter infinitesimal deformation of T is equivalent to that a (2, 3)-cocycle of T (with coefficients in the adjoint representation) defines a Hom-Lie-Yamaguti color algebra of deformation type.

• Journal of the Korea Computer Graphics Society
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• v.10 no.1
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• pp.15-21
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• 2004

This paper proposes a real-time technique for simulating large rotational deformations. Modal analysis based on a linear strain tensor has been shown to be suitable for real-time simulation, but is accurate only for moderately small deformations. In the present work, we identify the rotational component of an infinitesimal deformation, and extend linear modal analysis to track that component. We then develop a procedure to integrate the small rotations occurring al the nodal points. An interesting feature of our formulation is that it can implement both position and orientation constraints in a straightforward manner. These constraints can be used to interactively manipulate the shape of a deformable solid by dragging/twisting a set of nodes, Experiments show that the proposed technique runs in real-time even for a complex model, and that it can simulate large bending and/or twisting deformations with acceptable realism.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.4
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• pp.572-582
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• 1989

Elastic deformations of an infinitely long strip and a beam loaded by uniform pressure upon their upper surfaces, with the fixed-free end dondition, are considered within the range of small strains. All local governing equations are satisfied up to first order in strains, and to take into account the higher order terms neglected in the local governing equations, the overall equilibrium is imposed exactly up to the leading order. The success of the approach relies upon the semi-inverse method and the decomposition of deformations in which the classical linear theory guides the solution. The solution bridges the gap between the two extremes-the classical solutions valid only for infinitesimal deformations and the solutions form the technical theories for deformations with large rotations. The solutions may be used to confirm the technical theories and to verify numerical solutions obtained from finite element analysis.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1079-1092
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• 2007

This paper studies the deformation theory of a holomorphic surjective map from a normal compact complex space X to a compact $K\"{a}hler$ manifold Y. We will show that when the target has non-negative Kodaira dimension, all deformations of surjective holomorphic maps $X{\rightarrow}Y$ come from automorphisms of an unramified covering of Y and the underlying reduced varieties of associated components of Hol(X, Y) are complex tori. Under the additional assumption that Y is projective algebraic, this was proved in [7]. The proof in [7] uses the algebraicity in an essential way and cannot be generalized directly to the $K\"{a}hler$ setting. A new ingredient here is a careful study of the infinitesimal deformation of orbits of an action of a complex torus. This study, combined with the result for the algebraic case, gives the proof for the $K\"{a}hler$ setting.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.4
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• pp.320-328
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• 2007

This paper presents a stiffness modeling of a low-DOF parallel robot, which takes into account of elastic deformations of joints and links, A low-DOF parallel robot is defined as a spatial parallel robot which has less than six degrees of freedom. Differently from serial chains in a full 6-DOF parallel robot, some of those in a low-DOF parallel robot may be subject to constraint forces as well as actuation forces. The reaction forces due to actuations and constraints in each serial chain can be determined by making use of the theory of reciprocal screws. It is shown that the stiffness of an F-DOF parallel robot can be modeled such that the moving platform is supported by 6 springs related to the reciprocal screws of actuations (F) and constraints (6-F). A general $6{\times}6$ stiffness matrix is derived, which is the sum of the stiffness matrices of actuations and constraints, The compliance of each spring can be precisely determined by modeling the compliance of joints and links in a serial chain as follows; a link is modeled as an Euler beam and the compliance matrix of rotational or prismatic joint is modeled as a $6{\times}6$ diagonal matrix, where one diagonal element about the rotation axis or along the sliding direction is infinite. By summing joint and link compliance matrices with respect to a reference frame and applying unit reciprocal screw to the resulting compliance matrix of a serial chain, the compliance of a spring is determined by the resulting infinitesimal displacement. In order to illustrate this methodology, the stiffness of a Tricept parallel robot has been analyzed. Finally, a numerical example of the optimal design to maximize stiffness in a specified box-shape workspace is presented.