• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.27-41
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• 2019

We determine explicit formulas for the number of representations of a positive integer n by quaternary quadratic forms with coefficients 1, 2, 5 or 10. We use a modular forms approach.

• Journal of Advanced Research in Ocean Engineering
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• v.4 no.3
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• pp.124-134
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• 2018

In this study, when the stability of the structure against the ocean wave is considered for designing the offshore structures in the Pacific, Indian ocean and Atlantic regions where the cyclone is largely generated, the ocean wave caused by the cyclone as well as the storm surge which called wind induced wave shall be predicted accurately for the purpose of judgment. The predicted wind induced wave was evaluated by comparing the outcome results the model test of Nobuhiro Matsunaga (1996) and Conventional Experiment forms such as Jonswap spectral forms(Carter, 1982), Simplified Donelan / Jonswap forms(Wilson 1965), Donelan spectral forms(Donelan 1980), Revised SPM forms(Schafer Lake 2005, 2007, 2008), SPM forms(CERC 1977), the CEM forms(Kazeminezhad et al., 2005), SMB forms(Sverdrup Munk and Bretschneider 1947,1954, 1970), and Revised Wilson forms(Wilson 1965, Goda 2003). Most of these conventional experiment forms confirmed a good match when the fetch length is less than 10 km. However, normal cyclone fetch length is more than 100km, With this fetch length, the comparison result is 10.4% of deviation when used Jonswap spectral forms(Carter, 1982) but the deviation of the other forms is around 74% due to boundary limit of fetch and wind duration. Therefore, in this study, we proposed the revised forms after comparing these results with the model results. We confirmed that the deviation range is around 10% based on revisited experiment forms. Since the model test was carried out in the small water tank, the scale up factor was applied to the mode test results in order to obtain similar results to the actual environment from revisited forms.

• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.525-542
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• 2002

In this article, we prove a certain local-global principle for representation of binary forms by an infinite family of quinary positive integral quadratic forms.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.237-255
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• 2023

In this article, we find bases for the spaces of modular forms $M_2({\Gamma}_0(88),\;({\frac{d}{\cdot}}))$ for d = 1, 8, 44 and 88. We then derive formulas for the number of representations of a positive integer by the diagonal quaternary quadratic forms with coefficients 1, 2, 11 and 22.

• Korean Journal of English Language and Linguistics
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• v.1 no.2
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• pp.295-309
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• 2001

The simple forms in English have mostly been investigated in terms of tense, especially by those who do not distinguish between tense and aspect in English. However, we often find some usages of the simple forms that do not seem to fit in any of the meanings of tense. The purpose of this paper is to find aspectual meanings out of the simple present and past forms by re-analyzing their meanings in terms of aspect. It turns out that they represent the perfective aspect seeing a situation as a whole with no beginning. middle and end. As for the controversial stative situations in the simple forms, they have been proven to show the perfective aspect, too, if we agree to see both the part and whole in state as having the same features. And syntactic evidences from the simple forms and their corresponding progressive forms compared also show that the habitual dynamic situations represent the same aspect in the simple forms.

• BMB Reports
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• v.29 no.1
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• pp.1-10
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• 1996

The binding interaction of ethidium to a series of synthetic deoxyoligonucleotides containing a B-Z junction between left-handed Z-DNA and right-handed B-DNA, was studied. The series of deoxyoligonucleotides was designed so as to vary a dinucleotide step immediately adjacent to a B-Z junction region. Ethidium binds to the right-handed DNA forms and hybrid B-Z forms which contain a B-Z junction, in a highly cooperative manner. In a series of deoxyoligonucleotides, the binding affinity of ethidium with DNA forms which were initially hybrid B-Z forms shows over an order of magnitude higher than that with any other DNA forms, which were entirely in B-form DNA The cooperativity of binding isotherms were described by an allosteric binding model and by a neighbor exclusion model. The binding data were statistically compared for two models. The conformation of allosterically converted DNA forms under binding with ethidium is found to be different from that of the initial B-form DNA as examined by CD spectra. The ratio of the binding constant was interestingly correlated to the free energy of base unstacking and the conformational conversion of the dinucleotide. The more the base stacking of the dinucleotide is unstable, or the harder the conversion of B to A conformation, the higher the ratio of the binding constant of ethidium with the allosterically converted DNA forms and with the initial B-Z hybrid forms. DNA sequence around a B-Z junction region affects the binding affinity of ethidium. The results in this study demonstrate that ethidium could preferentially interact with unusual DNA structures.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.809-824
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• 1997

With the primitive orders in quaternion algebra, theta series associated with these orders are constructed. Here, we studied the space of modular forms generated by these theta series.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.559-581
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• 2013

This paper is motivated by a 2001 paper of Choie and Kim and a 2006 paper of Bump and Choie. The paper of Choie and Kim extends an earlier result of Bol for elliptic modular forms to the setting of Siegel and Jacobi forms. The paper of Bump and Choie provides a representation theoretic interpretation of the phenomenon, and shows how a natural generalization of Choie and Kim's result on Siegel modular forms follows from a natural conjecture regarding ($g$, K)-modules. In this paper, it is shown that the conjecture of Bump and Choie follows from work of Boe. A second proof which is along the lines of the proof given by Bump and Choie in the genus 2 case is also included, as is a similar treatment of the result of Choie and Kim on Jacobi forms.

• Journal of Korean Library and Information Science Society
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• v.30 no.4
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• pp.351-370
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• 1999

This paper aims to study on bibliographic reference forms, especially focused on the forms of korean sources. Although bibliographic reference is one of the critical elements in academic works, it seems every work has it's own forms in Korea. The fact that the bibliographic reference forms in korean works are made up by option causes the present state of diversity which makes difficulty in bibliographic control. The results of this search into internal academic journals show the diversity in the entry of title and significant gap of bibliographic reference forms among disciplines.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.333-347
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• 2015

In this paper, by using the modular forms of weight nk ($2{\leq}n{\in}\mathbb{N}$ and $k{\in}\mathbb{Z}$), we construct a formula which generates modular forms of weight 2nk+4. This formula consist of some known results in [14] and [4]. Moreover, we obtain Fourier expansion of these modular forms. We also give some properties of an operator related to the derivative formula. Finally, by using the function $j_4$, we obtain the Fourier coefficients of modular forms with weight 4.