• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.95-101
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• 1996

In this paper, we extend Ganelius' lemma in Anderson [1]. In the Ganelius' original version several of the ${\alpha}$$\sub$k/ are equal to 1, but in our extension theorem we have the ${\alpha}$$\sub$k/ distinct and all unequal to 1. Then our theorem can be used to introduce an indefinite quadrature formula for ∫$\sub$-1/$\^$1/ f($\chi$)d$\chi$, f $\in$ H$\^$p/, with p ＞ 1. We will also correct an error in the proof of Ganelius' theorem provided in Ganelius [2].(omitted)

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.17-23
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• 1993

In this paper, we will discuss on the above problem for the case that .upsilon. is a Riemannian foliation. If .upsilon. is a Riemannian foliation on (M, g), we derive some basic relations between the curvature $R^{D}$ of the normal connection D and the curvature R of the Levi-Civita connection .del. on (M, g) (see Lemma 1).).

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1391-1409
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• 2016

In this paper, we investigate a family of holomorphic functions in several complex variables concerning the total derivative (or called radial derivative), and obtain some well-known normality criteria such as the Miranda's theorem, the Marty's theorem and results on the Hayman's conjectures in several complex variables. A high-dimension version of the famous Zalcman's lemma for normal families is also given.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.791-797
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• 2021

In this corrigendum, we offer a correction to [J. Korean Math. Soc. 54 (2017), No. 2, 461-477]. We construct a counterexample for the strengthened Cauchy-Schwarz inequality used in the original paper. In addition, we provide a new proof for Lemma 5 of the original paper, an estimate for the extremal eigenvalues of the standard unpreconditioned FETI-DP dual operator.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.4
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• pp.335-343
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• 2022

We show that valleys, high peaks, and modular ascents are statistics of Fuss-Catalan paths having a distribution given by the Fuss-Narayana number. We prove the results using the Cycle Lemma and provide bijections among them. We also show that relative peaks are independent of the base path. In particular, valleys and high peaks can be obtained from relative peaks by fixing the base path in certain ways.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.577-585
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• 2022

In this work, we introduced and study vector equilibrium problems for trifunction in measurable space (for short, VEPMS). The existence of solutions of (VEPMS) are obtained by employing Aumann theorem and Fan KKM lemma. As an application, we prove an existence result for vector variational inequality problem for measurable space. Our results in this paper are new which can be considered as significant extension of previously known results in the literature.

• Advances in Computational Design
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• v.9 no.1
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• pp.53-71
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• 2024

Owing to these mechanical properties, carbon nanotubes have the potential to be employed in many future devices and nanostructured materials. As an example, high Young modulus accompanied by their low density, makes them a good choice for reinforcing material in composites. Therefore, we empathize and manually derive the results which shows the utilized lemma and criterion are believed effective and efficient for aircraft structural analysis of composite and nonlinear scenarios. To be fair, the experiment by numerical computation and calculations were explained the perfectness of the methodology we provided in the research.

• Advances in Computational Design
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• v.9 no.2
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• pp.97-113
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• 2024

In this paper, we proposed a new class of stochastic neutral neural networks with uncertain and deterministic coefficients. Made the Sigmund activation and Lipschitz activation functions less conditional. The Lyapnov-Krasovskii functional is constructed. The linear matrix inequality (LMI) is constructed using Schur's lemma, and new criteria for the global asymptotic stability and global asymptotic robust stability of neural networks are obtained. Furthermore, we have verified that the method is effective and feasible through numerical examples.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.363-447
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• 2009

The author previously defined the spectral invariants, denoted by $\rho(H;\;a)$, of a Hamiltonian function H as the mini-max value of the action functional ${\cal{A}}_H$ over the Novikov Floer cycles in the Floer homology class dual to the quantum cohomology class a. The spectrality axiom of the invariant $\rho(H;\;a)$ states that the mini-max value is a critical value of the action functional ${\cal{A}}_H$. The main purpose of the present paper is to prove this axiom for nondegenerate Hamiltonian functions in irrational symplectic manifolds (M, $\omega$). We also prove that the spectral invariant function ${\rho}_a$ : $H\;{\mapsto}\;\rho(H;\;a)$ can be pushed down to a continuous function defined on the universal (${\acute{e}}tale$) covering space $\widetilde{HAM}$(M, $\omega$) of the group Ham((M, $\omega$) of Hamiltonian diffeomorphisms on general (M, $\omega$). For a certain generic homotopy, which we call a Cerf homotopy ${\cal{H}}\;=\;\{H^s\}_{0{\leq}s{\leq}1}$ of Hamiltonians, the function ${\rho}_a\;{\circ}\;{\cal{H}}$ : $s\;{\mapsto}\;{\rho}(H^s;\;a)$ is piecewise smooth away from a countable subset of [0, 1] for each non-zero quantum cohomology class a. The proof of this nondegenerate spectrality relies on several new ingredients in the chain level Floer theory, which have their own independent interest: a structure theorem on the Cerf bifurcation diagram of the critical values of the action functionals associated to a generic one-parameter family of Hamiltonian functions, a general structure theorem and the handle sliding lemma of Novikov Floer cycles over such a family and a family version of new transversality statements involving the Floer chain map, and many others. We call this chain level Floer theory as a whole the Floer mini-max theory.

• Proceedings of the KSPS conference
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• 2006.11a
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• pp.99-108
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• 2006

Three experiments were conducted to determine the exact locus of the frequency effect in speech production. In Experiment 1. a picture naming task was used to replicate whether the word frequency effect is due to the processes involved in lexical access or not. The robust word frequency effect of 31ms was obtained. The question to be addressed in Experiment 2 is whether the word frequency effect is originated from the level where a lemma is selected. To the end, using a picture-word interference task, the significance of interactions between the effects of target frequency, distractor frequency and semantic relatedness were tested. Interaction between the distractor frequency and semantic relatedness variables was significant. And interaction between the target and distractor frequency variables showed a significant tendency. In addition, the results of Experiment 2 suggest that the mechanism underlying the word frequency effect is encoded as different resting activation level of lemmas. Experiment 3 explored whether the word frequency effect is attributed to the lexeme level where phonological information of words is represented or not. A methodological logic applied to Experiment 3 was the same as to Experiment 2. Any interaction was not significant. In conclusion, the present study obtained the evidence supporting two assumptions: (a) the locus of the word frequency effect exists in the processes involved in lemma selection, (b) the mechanism for the word frequency effect is encoded as different resting activation level of lemmas. In order to explain the word frequency effect obtained in this study, the core assumptions of current production models need to be modified.