• Kyungpook Mathematical Journal
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• 제54권4호
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• pp.685-697
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• 2014

In this paper, we prove that there are no pseudo null Bertrand curve with curvature functions $k_1(s)=1$, $k_2(s){\neq}0$ and $k_3(s)$ other than itself in Minkowski spacetime ${\mathbb{E}}_1^4$ and by using the similar idea of Matsuda and Yorozu [13], we define a new kind of Bertrand curve and called it pseudo null (1,3)-Bertrand curve. Also we give some characterizations and an example of pseudo null (1,3)-Bertrand curves in Minkowski spacetime.

• 대한수학회보
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• 제52권6호
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• pp.2071-2093
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• 2015

In this paper, we investigate the similarity transformations in the Minkowski n-space. We study the geometric invariants of non-null curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null curve according to a similarity motion of ${\mathbb{E}}_1^n$. We determine the parametrizations of non-null self-similar curves in ${\mathbb{E}}_1^n$.

• 대한수학회논문집
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• 제20권1호
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• pp.15-21
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• 2005

Null designs on the poset of dual polar spaces are considered. A poset of dual polar spaces is the set of isotropic subspaces of a finite vector space equipped with a nondegenerate bilinear form, ordered by inclusion. We show that the minimum number of isotropic subspaces to construct a nonzero null t-design is ${\prod}^{t}_{i=0}(1+q^{i})$ for the types $B_N,\;D_N$, whereas for the case of type $C_N$, more isotropic subspaces are needed.

• East Asian mathematical journal
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• 제37권5호
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• pp.591-598
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• 2021

In this paper we study the Cauchy problem for the Chern-Simons gauged O(3) sigma model. We prove the local existence of solutions with low regularity initial data, observing null forms of the system and applying bilinear estimates for wave-Sobolev space H^{s, b}.

• 대한수학회보
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• 제50권2호
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• pp.441-444
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• 2013

It is shown that any two-dimensional globally hyperbolic spacetime with noncompact Cauchy surfaces has no null cut points.

• 전자공학회논문지B
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• 제33B권11호
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• pp.11-21
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• 1996

Robot manipulators constituing multi-robot system must exert the desired motion force on an object to preserve tghe fine motion of it. The forces exerte on an object by the end-effectors of multi-inducing force and the internal force. Here, motion-inducing force effects the motion of an object, but internal force as lies in the null space of an object coordinate can't effect it. The motion of an object can't track exactly the desired motion by the effect of an object, but internal force as lies in the null space of the effect of internal force component, therefore internal force component must be considered. In this paper, first, under assumption that we can estimate exactly the parameter of dynamics, we constitute paper, first, under assumption that we can estimate exactly the parameter of dynamics, we constitute the controller concerning internal force. And we obtain the internal force as projecting force sensor readings onto the space spanned by null basis set of jacobian matrix. Using the resolved acceleration control method and the fact that internal force lies in the null space of jacobian matrix, we construct the robust control law to preserve the robustness with respect to the uncertainty of mainpulator parameters.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 22-24 Oct. 1991
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• pp.1664-1670
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• 1991

For kinematically redundant manipulators, conventional dynamic control methods of local torque optimization showed the instability which resulted in physically unachievable torque requirements. In order to guarantee stability of the null space vector method which resolves redundancy at the acceleration level, Maciejewski[1] analyzed the kinetic behavior of homogeneous solution component and proposed the condition to identify regions of stability and instability for this method. 'In this paper, a modified null space vector method is first presented based on the Maciejewski's condition which is a function of a manipulator's configuration. Secondly, a new control method which is based on the concept of aspects is proposed. It was shown by computer simulations that the modified null space vector method and the proposed method have a common property that a preferred aspect is preserved during the execution of a task. It was also illustrated that both methods demonstrate a drastic reduction of torque loadings at the joints in the tracking motion of a long trajectory when compared with the null space vector method, and thus guarantee the stability of joint torque.

• 대한수학회보
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• 제60권5호
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• pp.1299-1320
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• 2023

In the present paper, firstly we obtain the general expression of the canal hypersurfaces that are formed as the envelope of a family of pseudo hyperspheres, pseudo hyperbolic hyperspheres and null hyper-cones whose centers lie on a non-null curve with non-null Frenet vector fields in E⁴₁ and give their some geometric invariants such as unit normal vector fields, Gaussian curvatures, mean curvatures and principal curvatures. Also, we give some results about their flatness and minimality conditions and Weingarten canal hypersurfaces. Also, we obtain these characterizations for tubular hypersurfaces in E⁴₁ by taking constant radius function and finally, we construct some examples and visualize them with the aid of Mathematica.

• 대한수학회보
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• 제59권4호
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• pp.869-877
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• 2022

In this paper, we consider the knot complement problem for not null-homologous knots in homology lens spaces. Let M be a homology lens space with H₁(M; ℤ) ≅ ℤ_p and K a not null-homologous knot in M. We show that, K is determined by its complement if M is non-hyperbolic, K is hyperbolic, and p is a prime greater than 7, or, if M is actually a lens space L(p, q) and K represents a generator of H₁(L(p, q)).

• 전력전자학회:학술대회논문집
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• 전력전자학회 2017년도 추계학술대회
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• pp.41-42
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• 2017

기존의 다중 코일을 이용한 소형 자성체를 제어하는 시스템에서 전류 벡터 지령은 구동 매트릭스의 pseudo-inverse를 사용하여 계산되었다. 본 논문에서는 기존의 전류 지령에 null space 전류 벡터 지령을 더하는 방법을 이용하여 현재 전류 벡터값과 목표 전류 벡터 지령 사이의 전류 변화량이 최소화 되는 전류 지령 수정 방식을 제안한다. 제한된 전압 정격 내에서 제안된 방식을 적용할 경우 전류 지령 벡터값에 도달하는 시간이 짧아짐으로, 기존 방식에 비해 빠른 반응성을 얻을 수 있다. 제안된 방법은 Matlab(R) Simulink(R)를 통해 검증하였다.