• 한국수학교육학회지시리즈A:수학교육
• /
• 제30권1호
• /
• pp.43-45
• /
• 1991

• 대한수학회논문집
• /
• 제15권2호
• /
• pp.331-338
• /
• 2000

In the present paper, we investigate a problem in a sym-metric Finsler space, which is a special space. First we prove that if a symmetric space remains to be a symmetric one under the Z-projective change, then the space is of zero curvature. Further we will study W-recurrent space and D-recurrent space under the pro-jective change.

• Kyungpook Mathematical Journal
• /
• 제60권4호
• /
• pp.805-819
• /
• 2020

The objective of this study is to investigate 𝜂-Einstein solitons on (𝜀)-Kenmotsu manifolds when the Weyl-conformal curvature tensor satisfies some geometric properties such as being flat, semi-symmetric and Einstein semi-symmetric. Here, we discuss the properties of 𝜂-Einstein solitons on 𝜑-symmetric (𝜀)-Kenmotsu manifolds.

• 대한수학회논문집
• /
• 제38권1호
• /
• pp.47-53
• /
• 2023

The Terracini t-locus of an embedded variety X ⊂ ℙ^r is the set of all cardinality t subsets of the smooth part of X at which a certain differential drops rank, i.e., the union of the associated double points is linearly dependent. We give an easy to check criterion to exclude some sets from the Terracini loci. This criterion applies to tensors and partially symmetric tensors. We discuss the non-existence of codimension 1 Terracini t-loci when t is the generic X-rank.

• 대한수학회논문집
• /
• 제25권4호
• /
• pp.615-621
• /
• 2010

We study pseudo symmetric (briefly $(PS)_n$) and pseudo Ricci symmetric (briefly $(PRS)_n$) warped product manifolds $M{\times}_FN$. If M is $(PS)_n$, then we give a condition on the warping function that M is a pseudosymmetric space and N is a space of constant curvature. If M is $(PRS)_n$, then we show that (i) N is Ricci symmetric and (ii) M is $(PRS)_n$ if and only if the tensor T defined by (2.6) satisfies a certain condition.

• 정보처리학회논문지B
• /
• 제15B권3호
• /
• pp.205-210
• /
• 2008

본 논문에서는 잡음에 의해 손상된 텍스트 영상으로부터 복원 및 분할을 위한 새로운 접근 방법을 제안한다. 제안된 방법은 손상된 영역의 복원을 위하여 색상 및 비색상 성분을 2차 대칭 스틱 텐서로 표현하고 보팅 기반의 손상된 영역을 복원하였으며, 마지막으로 클러스터링 방법에 의해 분할을 수행한다. 먼저 우리는 제안된 색상 선택함수에 의해 잡음에 강건한 색상과 비색상 성분을 선택한다. 두 번째 단계에서는 각각의 선택된 특징 벡터들은 스틱 텐서로 표현하였으며 제한된 보팅 커널의 필드내에서 이웃하는 보터들과 통신을 통하여 새롭게 정의된다. 따라서 2차 보팅 후 각각의 스틱 텐서는 이웃하는 텐서와 같은 특성을 가지며 손상된 영역들을 복원할 수 있다. 마지막으로 복원된 영상의 성능을 평가하기 위하여 적응적 평균 이동 알고리즘과 클러스터링 알고리즘을 이용하여 영상 분할을 수행하였다. 실험에서 제안된 방법은 전체적인 처리과정을 자동적으로 수행 가능하였으며 배경 및 객체의 영역에서 효율적인 복원 및 분할을 수행할 수 있었다.

• 호남수학학술지
• /
• 제45권3호
• /
• pp.471-490
• /
• 2023

In this present paper, we study QSM-connection (quarter-symmetric metric connection) on Sasakian statistical manifolds. Firstly, we express the relation between the QSM-connection ${\tilde{\nabla}}$ and the torsion-free connection ∇ and obtain the relation between the curvature tensors ${\tilde{R}}$ of ${\tilde{\nabla}}$ and R of ∇. After then we obtain these relations for ${\tilde{\nabla}}$ and the dual connection ∇^* of ∇. Also, we give the relations between the curvature tensor ${\tilde{R}}$ of QSM-connection ${\tilde{\nabla}}$ and the curvature tensors R and R^* of the connections ∇ and ∇^* on Sasakian statistical manifolds. We obtain the relations between the Ricci tensor of QSM-connection ${\tilde{\nabla}}$ and the Ricci tensors of the connections ∇ and ∇^*. After these, we construct an example of a 3-dimensional Sasakian manifold admitting the QSM-connection in order to verify our results. Finally, we study the submanifolds with the induced connection with respect to QSM-connection of statistical manifolds.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제27권1호
• /
• pp.1-22
• /
• 2023

In this paper we settle some polynomial identity which provides a family of explicit Waring decompositions of any monomial Xa00 Xa11··· Xann over a field k. This gives an upper bound for the Waring rank of a given monomial and naturally leads to an explicit Waring decomposition of any homogeneous form and, eventually, of any polynomial via (de)homogenization. Note that such decomposition is very useful in many applications dealing with polynomial computations, symmetric tensor problems and so on. We discuss some computational aspect of our result as comparing with other known methods and also present a computer implementation for potential use in the end.

• 대한수학회지
• /
• 제61권2호
• /
• pp.309-339
• /
• 2024

Let M be a real hypersurface in the complex hyperbolic quadric Q^m*, m ≥ 3. The Riemannian curvature tensor field R of M allows us to define a symmetric Jacobi operator with respect to the Reeb vector field ξ, which is called the structure Jacobi operator R_ξ = R( · , ξ)ξ ∈ End(TM). On the other hand, in [20], Semmelmann showed that the cyclic parallelism is equivalent to the Killing property regarding any symmetric tensor. Motivated by his result above, in this paper we consider the cyclic parallelism of the structure Jacobi operator R_ξ for a real hypersurface M in the complex hyperbolic quadric Q^m*. Furthermore, we give a complete classification of Hopf real hypersurfaces in Q^m* with such a property.

• 대한수학회논문집
• /
• 제24권2호
• /
• pp.265-275
• /
• 2009

The object of the present paper is to study 3-dimensional normal almost contact metric manifolds satisfying certain curvature conditions. Among others it is proved that a parallel symmetric (0, 2) tensor field in a 3-dimensional non-cosympletic normal almost contact metric manifold is a constant multiple of the associated metric tensor and there does not exist a non-zero parallel 2-form. Also we obtain some equivalent conditions on a 3-dimensional normal almost contact metric manifold and we prove that if a 3-dimensional normal almost contact metric manifold which is not a ${\beta}$-Sasakian manifold satisfies cyclic parallel Ricci tensor, then the manifold is a manifold of constant curvature. Finally we prove the existence of such a manifold by a concrete example.