• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.563-572
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• 2009

In this paper, by introducing some parameters and using the way of weight function, a new integral inequality with a best constant factor is given, which is a relation between Hilbert's integral inequality and a Hilbert-type inequality. As applications, the equivalent form, the reverse forms and some particular inequalities are considered.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.595-600
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• 1996

We give a characterization of a deductive system. We introduce the concept of maximal deductive systems and show that every bounded Hilbert algebra with at least two elements contains at least one maximal deductive system. Moreover, we introduce the notion of radical and semisimple in a Hilbert algebra and prove that if H is a bounded Hilbert algebra in which every element is an involution, then H is semisimple.

• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.169-177
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• 2003

Recently, K. Watanabe Showed that the Hilbert-Kunz multiplicity of a toric ring is a rational number. In this paper we give an explicit formula to compute the Hilbert-Kunz multiplicity of two-dimensional toric rings. This formula also shows that the Hilbert-Kunz multiplicity of a two-dimensional non-regular toric ring is at least 3/2.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1211-1226
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• 2021

The study of reducible Hilbert curves of conic fibrations over a smooth surface is carried on in this paper and the question of when the main component is itself the Hilbert curve of some ℚ-polarized surface is dealt with. Special attention is paid to the polynomial defining the canonical equation of the Hilbert curve.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.445-453
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• 2012

In this paper, we introduce the concept of multiplier in a Hilbert algebra and obtained some properties of multipliers. Also, we introduce the simple multiplier and characterized the kernel of multipliers in Hilbert algebras.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.3
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• pp.343-352
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• 2018

We study the complete convergence for sequences of dependent random variables in Hilbert spaces. Results are obtained for negatively associated random variables and ${\phi}$-mixing random variables in Hilbert spaces.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2011.10a
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• pp.106-106
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• 2011

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1299-1309
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• 2021

Demeter [1] and Kuk and Lee [5] proved the unboundedness of the trilinear Hilbert transforms H_a,b,c under the critical index 1/2 for some parameters a, b and c. We show the unboundedness of H_a,b,c for any parameters.

• Journal of Advanced Marine Engineering and Technology
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• v.36 no.2
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• pp.258-266
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• 2012

Recently, Acoustic Emission (AE) technique is widely applied to develop the early fault detection system, and the problem about a signal processing method for AE signal is mainly focused on. In the signal processing method, envelope analysis is a useful method to evaluate the rolling element bearing problems and Wavelet transform is a powerful method to detect faults occurred on gearboxes. However, exact method for AE signal is not developed yet. Therefore, in this paper, two methods, which is Hilbert transforms (HT) and Hilbert-Huang transforms (HHT), will be compared for development a signal processing method for early fault detection system by using AE. AE signals were measured through a fatigue test. HHT has better advantages than HT because HHT can show the time-frequency domain result. But, HHT needs long time to process a signal, which has a lot of data, and has a disadvantage in de-noising filter.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.905-909
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• 1997

A characterization of Hilbert spaces is given in terms of four boundary points and two interior points of the unit sphere.