• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.307-314
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• 2010

By introducing a homogeneous kernel of 0-degree with an independent parameter and estimating the weight coefficient, a bilateral form of the Hilbert-type series inequality with a best constant factor is established.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.411-423
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• 2007

This paper deals with a reverse Hardy-Hilbert's inequality with a best constant factor by introducing two parameters ${\lambda}$ and ${\alpha}$. We also consider the equivalent form and the analogue integral inequalities. Some particular results are given.

• Korean Journal of Mathematics
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• v.26 no.2
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• pp.293-297
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• 2018

In the paper [4], we constructed 3-part of the Hilbert class field of imaginary quadratic fields whose class number is divisible exactly by 3. In this paper, we extend the result for any odd prime p.

• Journal for History of Mathematics
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• v.16 no.4
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• pp.33-44
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• 2003

This article shows Hilbert's Paris address within the context of his career and the mathematics of his day. And the text of Hilbert's speech will be considered in some detail, particularly those parts of it that reflects his vision of mathematics most clearly. At the end it is attempted to show the limitations of the standard view of Hilbert as an advocate of a formalist approach to mathematics.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.111-123
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• 2005

Here, the Fredholm integral equation with Hilbert kernel is solved numerically, using two different methods. Also the error, in each case, is estimated.

• Honam Mathematical Journal
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• v.29 no.3
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• pp.403-413
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• 2007

In this paper, we introduce the notion of a norm in Hilbert algebras, and discuss some properties of Cauchy sequences.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.161-166
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• 2013

In this paper we study the infiniteness of the Hilbert 3-class field tower of imaginary cubic function fields.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.393-401
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• 2009

By introducing a parameter and estimating the weight coefficient, we obtain a new Hilbert-type integral inequality with a composite kernel and a best constant factor. As applications, we also consider its equivalent forms and reverse forms.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.747-756
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• 2007

In this paper we give an example of imaginary quadratic number field k such that every ideal of k becomes principal in some proper subfields of the Hilbert class field of k.

• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.405-411
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• 2005

We use a congruence relation on deductive systems of a Hilbert algebra H, to define a uniform structure on H and investigate the corresponding topology.