• Title, Summary, Keyword: deformation space

### Compensation On-line of Errors Caused by Rotor Centrifugal Deformation for a Magnetically Suspended Sensitive Gyroscope

• Xin, Chao-Jun;Cai, Yuan-Wen;Ren, Yuan;Fan, Ya-Hong
• Journal of Electrical Engineering and Technology
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• v.13 no.2
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• pp.1030-1041
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• 2018
• The aim of this paper is to design a centrifugal deformation error compensation method with guaranteed performance that allows angular velocity measurement of the magnetically suspended sensitive gyroscopes (MSSGs). The angular velocity measurement principle and the structure of the MSSG are described, and the analytical model of errors caused by MSSG rotor centrifugal deformation is established. Then, an on-line rotor centrifugal deformation error compensation method based on measurement of rotor spinning speed in real-time has been designed. The common issues caused by centrifugal deformation of spinning rotors can be effectively resolved by the proposed method. Comparative experimental results before and after compensation demonstrate the validity and superiority of the error compensation method.

### Space Deformation of Parametric Surface Based on Extension Function

• Wang, Xiaoping;Ye, Zhenglin;Meng, Yaqin;Li, Hongda
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• v.1 no.1
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• pp.23-32
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• 2002
• In this paper, a new technique of space deformation for parametric surfaces with so-called extension function (EF) is presented. Firstly, a special extension function is introduced. Then an operator matrix is constructed on the basis of EF. Finally the deformation of a surface is achieved through multiplying the equation of the surface by an operator matrix or adding the multiplication of some vector and the operator matrix to the equation. Interactively modifying control parameters, ideal deformation effect can be got. The implementation shows that the method is simple, intuitive and easy to control. It can be used in such fields as geometric modeling and computer animation.

### A Modified Domain Deformation Theory for Signal Classification (함수의 정의역 변형에 의한 신호간의 거리 측정 방법)

• Kim, Sung-Soo
• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.3
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• pp.342-349
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• 1999
• The metric defined on the domain deformation space better measures the similarity between bounded and continuous signals for the purpose of classification via the metric distances between signals. In this paper, a modified domain deformation theory is introduced for one-dimensional signal classification. A new metric defined on a modified domain deformation for measuring the distance between signals is employed. By introducing a newly defined metric space via the newly defined Integra-Normalizer, the assumption that domain deformation is applicable only to continuous signals is removed such that any kind of integrable signal can be classified. The metric on the modified domain deformation has an advantage over the $L^2$ metric as well as the previously introduced domain deformation does.

### GEOMETRY ON EXOTIC HYPERBOLIC SPACES

• Kim, In-Kang
• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.621-631
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• 1999
• In this paper we briefly describe the geometry of the Cayley hyperbolic plane and we show that every uniform lattice in quaternionic space cannot be deformed in the Cayley hyperbolic 2-plane. We also describe the nongeometric bending deformation by developing the theory of the Cartan angular invariant for quaternionic hyperbolic space.

### REMARKS ON SIMPLY k-CONNECTIVITY AND k-DEFORMATION RETRACT IN DIGITAL TOPOLOGY

• Han, Sang-Eon
• Honam Mathematical Journal
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• v.36 no.3
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• pp.519-530
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• 2014
• To study a deformation of a digital space from the viewpoint of digital homotopy theory, we have often used the notions of a weak k-deformation retract [20] and a strong k-deformation retract [10, 12, 13]. Thus the papers [10, 12, 13, 16] firstly developed the notion of a strong k-deformation retract which can play an important role in studying a homotopic thinning of a digital space. Besides, the paper [3] deals with a k-deformation retract and its homotopic property related to a digital fundamental group. Thus, as a survey article, comparing among a k-deformation retract in [3], a strong k-deformation retract in [10, 12, 13], a weak deformation k-retract in [20] and a digital k-homotopy equivalence [5, 24], we observe some relationships among them from the viewpoint of digital homotopy theory. Furthermore, the present paper deals with some parts of the preprint [10] which were not published in a journal (see Proposition 3.1). Finally, the present paper corrects Boxer's paper [3] as follows: even though the paper [3] referred to the notion of a digital homotopy equivalence (or a same k-homotopy type) which is a special kind of a k-deformation retract, we need to point out that the notion was already developed in [5] instead of [3] and further corrects the proof of Theorem 4.5 of Boxer's paper [3] (see the proof of Theorem 4.1 in the present paper). While the paper [4] refers some properties of a deck transformation group (or an automorphism group) of digital covering space without any citation, the study was early done by Han in his paper (see the paper [14]).

### Improved kinematic mount design for bar type reference mirror for profilometric measurement large optical surface

• Jung, Kil-Jae;Yang, Ho-Soon;Rhee, Hyug-Gyo;Jyun, Byoung-Hyug;Lee, Yun-Woo;Kim, Sug-Whan
• Bulletin of the Korean Space Science Society
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• pp.25.3-25.3
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• 2010
• Our previous study used a bar-type reference mirror to measure the relative distance to the target surface. The target measurement accuracy was required to $1{\mu}m$ PV for aspheric optical surface up to 1m in diameter. Earlier system suffers from the reference surface deformation when the measuring part moves. In order to reduce the deformation, measuring part and the reference part separated from each order in the new design. This system utilizes a kinematic support assembly using invar flexure to minimize the reference surface deformation under gravity and vibration. The surface deformation requirement of reference mirror is defined as of $0.2{\mu}m$ under gravity and 40Hz vibration. The finite element results, shows reference mirror deformation of $0.164{\mu}m$. The first resonance mode was computed to analysis 46.05Hz for reference part and 43.44Hz for measuring part. Thesis satisfies the frequency requirement.

### ANALYTIC CONSTRUCTION OF VERSAL DEFORMATION OF RESOLUTION OF NORMAL ISOLATED SINGULARITIES

• Miyajima, Kimio
• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.125-150
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• 2009
• We analytically construct the versal deformation space of resolution of normal isolated singularities based on the formalism in [9].

### The deformation space of real projective structures on the $(^*n_1n_2n_3n_4)$-orbifold

• Lee, Jungkeun
• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.549-560
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• 1997
• For positive integers $n_i \geq 2, i = 1, 2, 3, 4$, such that $\Sigma \frac{n_i}{1} < 2$, there exists a quadrilateral $P = P_1 P_2 P_3 P_4$ in the hyperbolic plane $H^2$ with the interior angle $\frac{n_i}{\pi}$ at $P_i$. Let $\Gamma \subset Isom(H^2)$ be the (discrete) group generated by reflections in each side of $P$. Then the quotient space $H^2/\gamma$ is a differentiable orbifold of type $(^* n_1 n_2 n_3 n_4)$. It will be shown that the deformation space of $Rp^2$-structures on this orbifold can be mapped continuously and bijectively onto the cell of dimension 4 - \left$\mid$ {i$\mid$n_i = 2} \right$\mid$\$.

### DEFORMATION OF LOCALLY FREE SHEAVES AND HITCHIN PAIRS OVER NODAL CURVE

• Sun, Hao
• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.809-823
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• 2020
• In this article, we study the deformation theory of locally free sheaves and Hitchin pairs over a nodal curve. As a special case, the infinitesimal deformation of these objects gives the tangent space of the corresponding moduli spaces, which can be used to calculate the dimension of the corresponding moduli space. The deformation theory of locally free sheaves and Hitchin pairs over a nodal curve can be interpreted as the deformation theory of generalized parabolic bundles and generalized parabolic Hitchin pairs over the normalization of the nodal curve, respectively. This interpretation is given by the correspondence between locally free sheaves over a nodal curve and generalized parabolic bundles over its normalization.

### Deformation Characteristics and Determination of Deformation Modulus of Rocks around the Lower Gangway during Coal Mining Operation (석탄층 하반갱도 주위암반의 변형특성 및 변형계수 결정연구)

• 이현주
• Tunnel and Underground Space
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• v.2 no.2
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• pp.237-250
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• 1992
• The cavities formed by the excavation of coal seam cause unstable within rock body, leading to large displacement around adjacent roadway. This displacement brings the closure of roadway and deformation of support. Therefore, it is necessary to understand and predict the deformation characteristics of roadway while coal seam is under excavation. In this study, the observed displacements are compared with the calculated ones through the analysis using Linear Boundary Element Mothod under the elastostatic conditions, in order to determine the virgin stress state and deformation modulus which affect the deformation characteristices.