• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.75-90
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• 2007

Huffman, Park and Skoug introduced various results for the $L_p$ analytic Fourier-Feynman transform and the convolution for functionals on classical Wiener space which belong to some Banach algebra S introduced by Cameron and Strovic. Also Chang, Kim and Yoo extended the above results to an abstract Wiener space for functionals in the Fresnel class F(B) which corresponds to S. Recently Kim, Song and Yoo investigated more generalized relationships between the Fourier-Feynman transform and the convolution product for functionals in a generalized Fresnel class $F_{A_1,A'_2}$ containing F(B). In this paper, we establish various interesting relationships and expressions involving the first variation and one or two of the concepts of the Fourier-Feynman transform and the convolution product for functionals in $F_{A_1,A_2}$.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.375-384
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• 2008

Let $k={\mathbb{F}}_q(T)$ and ${\mathbb{A}}={\mathbb{F}}_q[T]$. Fix a prime divisor ${\ell}$ q-1. In this paper, we consider a ${\ell}$-cyclic real function field $k(\sqrt[{\ell}]P)$ as a subfield of the imaginary bicyclic function field K = $k(\sqrt[{\ell}]P,\;(\sqrt[{\ell}]{-Q})$, which is a composite field of $k(\sqrt[{\ell}]P)$ wit a ${\ell}$-cyclic totally imaginary function field $k(\sqrt[{\ell}]{-Q})$ of class number one. und give various conditions for the class number of $k(\sqrt[{\ell}]{P})$ to be one by using invariants of the relatively cyclic unramified extensions $K/F_i$ over ${\ell}$-cyclic totally imaginary function field $F_i=k(\sqrt[{\ell}]{-P^iQ})$ for $1{\leq}i{\leq}{\ell}-1$.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.481-495
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• 2009

Huffman, Park and Skoug introduced various results for the $L_{p}$ analytic Fourier-Feynman transform and the convolution for functionals on classical Wiener space which belong to some Banach algebra $\mathcal{S}$ introduced by Cameron and Storvick. Also Chang, Kim and Yoo extended the above results to an abstract Wiener space for functionals in the Fresnel class $\mathcal{F}(B)$ which corresponds to $\mathcal{S}$. Moreover they introduced the $L_{p}$ analytic Fourier-Feynman transform for functionals on a product abstract Wiener space and then established the above results for functionals in the generalized Fresnel class $\mathcal{F}_{A1,A2}$ containing $\mathcal{F}(B)$. In this paper, we investigate more generalized relationships, between the Fourier-Feynman transform and the convolution product for functionals in $\mathcal{F}_{A1,A2}$, than the above results.

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.147-154
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• 1988

For a positive integer p, $A_p$ will denote the class of functions $f(z)=z^p+\sum\limits^{\infty}_{n=p+1}a_nz^n$ which are analytic in the unit disc U = {z: |z| <1}. For $0{\leq}{\alpha}{\leq}1$, 0<${\beta}{\leq}1$, $0{\leq}{\lambda}$ $S_p({\alpha},{\beta},{\lambda})$ denote the class of functions $f(z){\in}A_p$ which satisfy the condition $\left|\frac{{\frac{zf^{\prime}(z)}{f(z)}}-p}{{{\alpha}{\frac{zf^{\prime}(z)}{f(z)}}+p-{\lambda}(1+{\alpha})}}\right|$<${\beta}$ for $z{\in}U$ In this paper we obtain a representation theorem for the class $S_p({\alpha},{\beta},{\lambda})$ and also derive distortion theorem and sharp estimates for the coefficients of this class.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.123-132
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• 2014

In this paper, we investigate the following form of a certain class of quadratic functional equations and its fuzzy stability. $$f(kx+y)+f(kx-y)=f(x+y)+f(x-y)-2(1-k^2)f(x)$$ where k is a fixed rational number with $k{\neq}1$, -1, 0.

• Journal of the korean academy of Pediatric Dentistry
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• v.24 no.1
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• pp.95-111
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• 1997

The human speech organ consists of respiration system (lung, larynx), phonation system (vocal cord), articulation system (esophagus, pharynx, uvula, teeth, gingiva, palate, tongue, lip) and resonating system(oral cavity, nasal cavity, paranasal sinus). Because teeth are components of the articulation system, it has been reported that the persons with abnormally positioned teeth generally have abnormal occlusion and pronunciation. In this study, using /ㅅ(s)/, the most commonly mispronunced consonant in children with malocclusion, and the seven single vowels, /사(sa), 서($s\delta$), 소(so), 수(su), 스($s\omega$), 시(si), 세(se)/ and / ㅏ(a), ㅓ($\delta$), ㅗ(o), ㅜ(u), ㅡ($\omega$), 1(i), ㅔ(e)/ were recorded and analyzed using speech analysis program on computer by measuring formants and compared them for investigating the differences in pronunciation in children with Angle's class I occlusions and those with Angle's class II div.1 malocclusion. The result were as follows: 1. In the Angle's Class II div.1 group, there were no significant differences in F1 of all recorded sounds as compared with Angle's Class I group(p>0.05). 2. In the consonants, there were significant differences in F2 of /스($s\omega$)/ and F2/F1 ratio of /사(sa), 서($s\delta$), 시(si)/ between the two group(p<0.05). 3. In the vowels, there were significant differences F2/F1 ratio of /ㅓ($\delta$)/(p<0.05) and no significant differences in F2/F1 ratio between two group(p>0.05). 4. In the consonants, there were significant differences in F2 and F2/F1 ratio when succeeding vowels were high or low, and F2/F1 ratio when front in accordance with tongue position (p<0.05). 5. In the vowels, there were no significant differences in formant in accordance with tongue position(p>0.05)

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.47 no.4
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• pp.31-37
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• 2010

In this paper, highly efficient dual-band class-F power amplifiers(PAs) for cellular and WLAN bands are suggested and implemented. For the first step, single-band class-F amplifiers at 840MHz, 2.4GHz are designed using commercial E-pHEMT FETs. The performance of two single band PAs are as much as 81.2% of efficiency with the output power of 24.4dBm with 840MHz PA and 93.5% of efficiency with 22.4dBm from the 2.4GHz. For the dual-band class-F PA, the harmonic controlling circuit with ideal SPDT switch was suggested. The length of transmission line is variable by a SPDT switch. As a results, the operation in 840MHz showed the peak efficiency of 60.5% with 23.5dBm, while in 2.4GHz mode the efficiency was 50.9% with the output power of 19.62dBm. Besides, it is shown that the harmonic controller of class-F above 2Ghz could be implemented on the low cost FR-4 substrate.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• v.35 no.4
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• pp.221-228
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• 2009

The purpose of the study was to investigate the characteristics of the pronunciation of Korean vowels in patients with class III malocclusion. 11 adult male patients with class III malocclusion(mean ages 22.3 years) and four adult males with normal occlusion(mean ages 26.5 years) were selected for the analysis of eight Korean monophthongs /ㅣ, ㅔ, ㅐ, ㅏ, ㅓ, ㅗ, ㅡ, ㅜ/. The values and relationships of F1, F2 and F3 were derived from the stable section of target vowel in each sentence, and the analysis using formant plots and vowel triangles' distance and area was conducted to find the features of two groups' vowel distributions. Consequently, it was identified that the pronunciation of males patients with class III malocclusion showed high values of F1 in the low vowels, high values of F2 in the back vowels, and remarkably low position of /ㅏ/. The vowel triangle suggested that the triangle areas of male patients with class III malocclusion were shown wider vertically and narrower horizontally than those of males with normal occlusion. These characteristics could reflect the structural features of class III malocclusion such as the prognathic mandible, low tongue position, and advancement of back position of the tongue.

• The Pure and Applied Mathematics
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• v.12 no.1
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• pp.57-63
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• 2005

Let ∑(p)(p ∈ N) be the class of functions f(z) = z/sup -p/ + α/sub 1-p/ z/sup 1-p/ + α/sub 2-p/z/sup 2-p/ + ... analytic in 0 < ｜z｜ < 1 and let M(p, λ, μ)(0 < λ≤ 2 and 2λ(λ - 1) ≤ μ ≤ λ²) denote the class of functions f(z) ∈ ∑(p) which satisfy (equation omitted). The object of the present paper is to derive some properties of functions in the class M(p, λ, μ).

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1185-1196
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• 2016

We show a class of homogeneous polynomials of Fermat-Waring type such that for a polynomial P of this class, if $P(f_1,{\ldots},f_{N+1})=P(g_1,{\ldots},g_{N+1})$, where $f_1,{\ldots},f_{N+1}$; $g_1,{\ldots},g_{N+1}$ are two families of linearly independent entire functions, then $f_i=cg_i$, $i=1,2,{\ldots},N+1$, where c is a root of unity. As a consequence, we prove that if X is a hypersurface defined by a homogeneous polynomial in this class, then X is a unique range set for linearly non-degenerate non-Archimedean holomorphic curves.