• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.13-23
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• 2009

Some strong convergence theorems of explicit iteration scheme for asymptotically nonexpansive semi-groups in Banach spaces are established. The results presented in this paper extend and improve some recent results in [T. Suzuki. On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces, Proc. Amer. Math. Soc. 131(2002)2133-2136; H. K. Xu. A strong convergence theorem for contraction semigroups in Banach spaces, Bull. Aust. Math. Soc. 72(2005)371-379; N. Shioji and W. Takahashi. Strong convergence theorems for continuous semigroups in Banach spaces, Math. Japonica. 1(1999)57-66; T. Shimizu and W. Takahashi. Strong convergence to common fixed points of families of nonexpansive mappings, J. Math. Anal. Appl. 211(1997)71-83; N. Shioji and W. Takahashi. Strong convergence theorems for asymptotically nonexpansive mappings in Hilbert spaces, Nonlinear Anal. TMA, 34(1998)87-99; H. K. Xu. Approximations to fixed points of contraction semigroups in Hilbert space, Numer. Funct. Anal. Optim. 19(1998), 157-163.]

• 제어로봇시스템학회논문지
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• 제12권3호
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• pp.233-240
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• 2006

This paper presents the robust control method using a self recurrent wavelet neural network (SRWNN) via adaptive backstepping design technique for stable walking of biped robots with unknown model uncertainties. The SRWNN, which has the properties such as fast convergence and simple structure, is used as the uncertainty observer of the biped robots. The adaptation laws for weights of the SRWNN and reconstruction error compensator are induced from the Lyapunov stability theorem, which are used for on-line controlling biped robots. Computer simulations of a five-link biped robot with unknown model uncertainties verify the validity of the proposed control system.

• 대한수학회지
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• 제43권5호
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• pp.1019-1045
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• 2006

As a natural generalization of a Sasakian space form, we define a contact strongly pseudo-convex CR-space form (of constant pseudo-holomorphic sectional curvature) by using the Tanaka-Webster connection, which is a canonical affine connection on a contact strongly pseudo-convex CR-manifold. In particular, we classify a contact strongly pseudo-convex CR-space form $(M,\;\eta,\;\varphi)$ with the pseudo-parallel structure operator $h(=1/2L\xi\varphi)$, and then we obtain the nice form of their curvature tensors in proving Schurtype theorem, where $L\xi$ denote the Lie derivative in the characteristic direction $\xi$.

• 대한수학회보
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• 제55권3호
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• pp.763-776
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• 2018

In this paper we consider the element-wise (Hadamard) product (or sum) of elliptic divisibility sequences and study the periodic structure of these sequences. We obtain that the element-wise product (or sum) of elliptic divisibility sequences are periodic modulo a prime p like linear recurrence sequences. Then we study periodicity properties of product sequences. We generalize our results to the case of modulo $p^l$ for some prime p > 3 and positive integer l. Finally we consider the p-adic behavior of product sequences and give a generalization of [9, Theorem 4].

• Korean Journal of Mathematics
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• 제20권2호
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• pp.161-176
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• 2012

The authors [6] introduced the concept of a complete matrix of grade $g$ > 3 to describe a structure theorem for complete intersections of grade $g$ > 3. We show that a complete matrix can be used to construct the Eagon-Northcott complex [7]. Moreover, we prove that it is the minimal free resolution $\mathbb{F}$ of a class of determinantal ideals of $n{\times}(n+2)$ matrices $X=(x_{ij})$ such that entries of each row of $X=(x_{ij})$ form a regular sequence and the second differential map of $\mathbb{F}$ is a matrix $f$ defined by the complete matrices of grade $n+2$.

• 대한수학회보
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• 제50권4호
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• pp.1201-1207
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• 2013

Let N be a complete Riemannian manifold with nonnegative Ricci curvature and let M be a complete noncompact oriented stable minimal hypersurface in N. We prove that if M has at least two ends and ${\int}_M{\mid}A{\mid}^2\;dv={\infty}$, then M admits a nonconstant harmonic function with finite Dirichlet integral, where A is the second fundamental form of M. We also show that the space of $L^2$ harmonic 1-forms on such a stable minimal hypersurface is not trivial. Our result is a generalization of one of main results in [12] because if N has nonnegative sectional curvature, then M admits no nonconstant harmonic functions with finite Dirichlet integral. And our result recovers a main theorem in [3] as a corollary.

• 대한수학회논문집
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• 제35권2호
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• pp.401-415
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• 2020

It is well-known that if char𝕜 = 0, then an Artinian monomial complete intersection quotient 𝕜[x₁, …, x_n]/(x₁^a₁, …, x_n^a_n) has the strong Lefschetz property in the narrow sense, and it is decomposed by the direct sum of irreducible 𝖘𝖑₂-modules. For an Artinian ring A = 𝕜[x₁, x₂, x₃]/(x₁⁶, x₂⁶, x₃⁶), by the Schur-Weyl duality theorem, there exist 56 trivial representations, 70 standard representations, and 20 sign representations inside A. In this paper we find an explicit basis for A, which is compatible with the S₃-module structure.

• 제어로봇시스템학회논문지
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• 제13권5호
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• pp.406-413
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• 2007

This paper proposes a self-recurrent wavelet neural network(SRWNN) based adaptive backstepping control technique for the robust steering control of autonomous underwater vehicles(AUVs) with unknown model uncertainties and external disturbance. The SRWNN, which has the properties such as fast convergence and simple structure, is used as the uncertainty observer of the steering model of AUV. The adaptation laws for the weights of SRWNN and reconstruction error compensator are induced from the Lyapunov stability theorem, which are used for the on-line control of AUV. Finally, simulation results for steering control of an AUV with unknown model uncertainties and external disturbance are included to illustrate the effectiveness of the proposed method.

• 전기전자학회논문지
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• 제2권1호
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• pp.108-113
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• 1998

Floquet의 정리와 이등분의 원리 (bisection principle)에 기초한 등가 전송선로 해석법을 이용하여 평면 DFB 구조의 반사특성을 해석하고, 격자주기 (grating petiod)에 따른 분산특성과 전력반사도를 계산하였다. 수치해석 결과 등가 전송선로 해석법은 DFB 전송구조의 광학적 특성을 분석하기 위한 간편하고 유용한 알고리즘으로 사용될 수 있음을 보여 주었다.

• 호남수학학술지
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• 제30권4호
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• pp.589-602
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• 2008

As a survey-type article, the paper reviews various digital topological utilities from digital covering theory. Digital covering theory has strongly contributed to the calculation of the digital k-fundamental group of both a digital space(a set with k-adjacency or digital k-graph) and a digital product. Furthermore, it has been used in classifying digital spaces, establishing almost Van Kampen theory which is the digital version of van Kampen theorem in algebrate topology, developing the generalized universal covering property, and so forth. Finally, we remark on the digital k-surface structure of a Cartesian product of two simple closed $k_i$-curves in ${\mathbf{Z}}^n$, $i{\in}{1,2}$.