• Kyungpook Mathematical Journal
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• 제20권1호
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• pp.37-45
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• 1980

The Riemannian space of recurrent curvature was defined and studied by Ruse [8] and Walker [10]. In 1963, $M{\acute{o}}or$ [4] generalised this idea for Finsler spaces and defined and studied Finsler spaces of recurrent curvature. These spaces for various curvature tensors have subsequently been studied by Mishra and Pande [1], Sen [9] and Misra [3] etc. The purpose of the present paper is to study Finsler space based on the recurrency of the curvature tensors derived from non-linear connections.

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.433-448
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• 2022

The Cartan's second curvature tensor Pⁱ_jkh is a positively homogeneous of degree-1 in yⁱ, where yⁱ represent a directional coordinate for the line element in Finsler space. In this paper, we discuss the decomposition of Cartan's second curvature tensor Pⁱ_jkh in two spaces, a generalized 𝔅P-recurrent space and generalized 𝔅P-birecurrent space. We obtain different tensors which satisfy the recurrence and birecurrence property under the decomposition. Also, we prove the decomposition for different tensors are non-vanishing. As an illustration of the applicability of the obtained results, we finish this work with some illustrative examples.

• 대한수학회보
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• 제54권1호
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• pp.177-186
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• 2017

In this paper, a type of Riemannian manifold (namely, pseudo semiconformally symmetric manifold) is introduced. Also the several geometric properties of such a manifold is investigated. Finally the existence of such a manifold is ensured by a proper example.

• 대한수학회논문집
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• 제36권3호
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• pp.593-607
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• 2021

The aim of the present paper is to establish an intrinsic generalization of Cartan connection in Finsler geometry. This connection is called the vertical recurrent Finsler connection. An intrinsic proof of the existence and uniqueness theorem for such connection is investigated. Moreover, it is shown that for such connection, the associated semi-spray coincides with the canonical spray and the associated nonlinear connection coincides with the Barthel connection. Explicit intrinsic expression relating this connection and Cartan connection is deduced. We also investigate some applications concerning the fundamental geometric objects associated with this connection. Finally, three important results concerning the curvature tensors associated to a special vertical recurrent Finsler connection are studied.

• 대한수학회논문집
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• 제29권2호
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• pp.319-329
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• 2014

In this paper we study the properties of conformally recurrent pseudo Riemannian manifolds admitting a proper conformal vector field with respect to the scalar field ${\sigma}$, focusing particularly on the 4-dimensional Lorentzian case. Some general properties already proven by one of the present authors for pseudo conformally symmetric manifolds endowed with a conformal vector field are proven also in the case, and some new others are stated. Moreover interesting results are pointed out; for example, it is proven that the Ricci tensor under certain conditions is Weyl compatible: this notion was recently introduced and investigated by one of the present authors. Further we study conformally recurrent 4-dimensional Lorentzian manifolds (space-times) admitting a conformal vector field: it is proven that the covector ${\sigma}_j$ is null and unique up to scaling; moreover it is shown that the same vector is an eigenvector of the Ricci tensor. Finally, it is stated that such space-time is of Petrov type N with respect to ${\sigma}_j$.

• 한국음향학회지
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• 제42권4호
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• pp.357-363
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• 2023

다양한 신호가 혼합된 수중 신호로부터 각각의 신호를 분리하는 기술은 오랫동안 연구되어왔지만, 낮은 품질의 수중 신호의 특성 상 쉽게 해결되지 않는 문제이다. 현재 주로 사용되는 방법은 Short-time Fourier transform을 사용하여 수신된 음향신호의 스펙트로그램을 얻은 뒤, 주파수의 특성을 분석하여 신호를 분리하는 기술이다. 하지만 매개변수의 최적화가 까다롭고, 스펙트로그램으로 변환하는 과정에서 위상 정보들이 손실되는 한계점이 지적되었다. 본 연구에서는 이러한 문제를 해결하기 위해 긴 시계열 신호 처리에서 좋은 성능을 보인 Dual-path Recurrent Neural Network을 기반으로, 다중 채널 센서로부터 생성된 입력신호인 3차원 텐서를 처리할 수 있도록 변형된 Tripple-path Recurrent Neural Network을 제안한다. 제안하는 기술은 먼저 다중 채널 입력 신호를 짧은 조각으로 분할하고 조각 내 신호 간, 구성된 조각간, 그리고 채널 신호 간의 각각의 관계를 고려한 3차원 텐서를 생성하여 로컬 및 글로벌 특성을 학습한다. 제안된 기법은, 기존 방법에 비해 개선된 Root Mean Square Error 값과 Scale Invariant Signal to Noise Ratio을 가짐을 확인하였다.