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$L_1$ analytic fourier-feynman transform on the fresnel class of abstract wiener space

  • Ahn, Jae-Moon
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.1
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    • pp.99-117
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    • 1998
  • Let $(B, H, p_1)$ be an abstract Wiener space and $F(B)$ the Fresnel class on $(B, H, p_1)$ which consists of functionals F of the form : $$ F(x) = \int_{H} exp{i(h,x)^\sim} df(h), x \in B, $$ where $(\cdot, \cdot)^\sim$ is a stochastic inner product between H and B, and f is in $M(H)$, the space of complex Borel measures on H. We introduce an $L_1$ analytic Fourier-Feynman transforms for functionls in $F(B)$. Furthermore, we introduce a convolution on $F(B)$, and then verify the existence of the $L_1$ analytic Fourier-Feynman transform for the convolution product of two functionals in $F(B)$, and we establish the relationships between the $L_1$ analytic Fourier-Feynman tranform of the convolution product for two functionals in $F(B)$ and the $L_1$ analytic Fourier-Feynman transforms for each functional. Finally, we show that most results in [7] follows from our results in Section 3.

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A Study on the Melanin Synthesis Inhibition and Whitening Effect of Bombysis Corpus (백강잠의 멜라닌 생성 억제와 미백효과에 관한 연구)

  • Oh, Han-Cheol;Lim, Kyu-Sang;Hwang, Chung-Yeon;Youn, In-Hwan;Kim, Nam-Kwen
    • The Journal of Korean Medicine Ophthalmology and Otolaryngology and Dermatology
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    • v.20 no.3
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    • pp.1-13
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    • 2007
  • Objective : This study was performed to assess the whitening effect of Bombysis Corpus on melanin synthesis. Methods : The whitening effects of Bombysis Corpus were examined by in vitro melanin production assay. We assessed inhibitory effects of Bombysis Corpus on melanin-release from B16F10, on melanin production in B16F10, on mushroom tyrosinase activity in vitro, on tyrosinase activity in B16F10, effect of Bombysis Corpus on the expression tyrosinase, TRP-1, PKA, ERK-1 ERK-2, AKT-1, MITF in B16F10. Results : 1. Bombysis Corpus inhibited melanin-release, melanin production in B16F10. 2. Bombysis Corpus inhibited tyrosinase activity in vitro and in B16F10. 3. Bombysis Corpus suppressed the expression of tyrosinase, TRP-1 in B16F10. 4. Bombysis Corpus suppressed the expression of PKA in B16F10. 5. Bombysis Corpus suppressed the expression of ERK-1, ERK-2, AKT-1 in B16F10. 6. Bombysis Corpus suppressed the expression of MITF in B16F10. Conclusion : The study shows that Bombysis Corpus inhibited melanin production on the melanogenesis.

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Inhibitory Effect of Persimmon Leaves on Melanin Synthesis and its Action Mechanism in B16F10 cells (시엽(枾葉)의 멜라닌 생성 억제와 작용기전에 관한 연구)

  • Jang, Du-Hyun;Yoo, Dong-Youl
    • The Journal of Korean Obstetrics and Gynecology
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    • v.22 no.2
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    • pp.43-59
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    • 2009
  • Purpose: This study was performed to determine the inhibitory effect of Persimmon Leaves extract (PL) on melanin synthesis in B16F10 melanoma cells B16F10. Methods: The inhibitory effects of PL on melanin synthesis were determined by in vitro assay. To elucidate inhibitory effects of PL on melanin synthesis, we determined the melanin release and melanin production in B16F10. And to investigate the action mechanism, we assessed the gene expression of tyrosinase, TRP-1, TRP-2, PKA, PKC${\beta}$, ERK-1, ERK-2, AKT-1, MITF in B16F10. Results: 1. PL inhibited melanin release, melanin production in B16F10. 2. PL inhibited tyrosinase activity in vitro and in B16F10. 3. PL suppressed the expression of tyrosinase, TRP-1, TRP-2 in B16F10. 4. PL suppressed the expression of PKA, PKC${\beta}$ in B16F10. 5. PL increased the expression of ERK-1, ERK-2, AKT-1 in B16F10. 6. PL suppressed the expression of MITF in B16F10. Conclusion: From these results, it may be concluded that PL is possesed of the antimelanogenetic effects.

THE GROWTH OF BLOCH FUNCTIONS IN SOME SPACES

  • Wenwan Yang;Junming Zhugeliu
    • Bulletin of the Korean Mathematical Society
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    • v.61 no.4
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    • pp.959-968
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    • 2024
  • Suppose f belongs to the Bloch space with f(0) = 0. For 0 < r < 1 and 0 < p < ∞, we show that $$M_p(r,\,f)\,=\,({\frac{1}{2\pi}}{\int_{0}^{2\pi}}\,{\mid}f(re^{it}){\mid}^pdt)^{1/p}\,{\leq}\,({\frac{{\Gamma}(\frac{p}{2}+1)}{{\Gamma}(\frac{p}{2}+1-k)}})^{1/p}\,{\rho}{\mathcal{B}}(log\frac{1}{1-r^2})^{1/2},$$ where ρʙ(f) = supz∈ⅅ(1 - |z|2)|f'(z)| and k is the integer satisfying 0 < p - 2k ≤ 2. Moreover, we prove that for 0 < r < 1 and p > 1, $${\parallel}f_r{\parallel}_{B_q}\,{\leq}\,r\,{\rho}{\mathcal{B}}(f)(\frac{1}{(1-r^2)(q-1)})^{1/q},$$ where fr(z) = f(rz) and ||·||ʙq is the Besov seminorm given by ║f║ʙq = (∫𝔻 |f'(z)|q(1-|z|2)q-2dA(z)). These results improve previous results of Clunie and MacGregor.

BOUNDEDNESS OF 𝓒b,c OPERATORS ON BLOCH SPACES

  • Nath, Pankaj Kumar;Naik, Sunanda
    • Korean Journal of Mathematics
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    • v.30 no.3
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    • pp.467-474
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    • 2022
  • In this article, we consider the integral operator 𝓒b,c, which is defined as follows: $${\mathcal{C}}^{b,c}(f)(z)={\displaystyle\smashmargin{2}{\int\nolimits_{0}}^z}{\frac{f(w)*F(1,1;c;w)}{w(1-w)^{b+1-c}}}dw,$$ where * denotes the Hadamard/ convolution product of power series, F(a, b; c; z) is the classical hypergeometric function with b, c > 0, b + 1 > c and f(0) = 0. We investigate the boundedness of the 𝓒b,c operators on Bloch spaces.

A Study on the Visual Effects According to the Lines in Cloth Designing (의복 디자인 선에 따른 시각적 효과에 관한 연구)

  • 이경희
    • Journal of the Korean Home Economics Association
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    • v.28 no.4
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    • pp.1.1-13
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    • 1990
  • Authors have performed the sensory evaluation tests according to each given items after selecting various lines in order to assess the visual effects by the lines in cloth designing. The evaluations were done by means of ranking tests followed by paired comparison tests. The results obtained were as follows : 1. In the item in than "Shoulder width looks wide", the design C3 showed the best visual effect, and then B1, F8, and A5 comes in order. In "Shoulder width looks narrow", they were A2, F5, F7, and B2 in order. 2. In "Bust looks big", the effect was best in F9, and then B1, F5, C3, and A5 and order. "Bust looks small" item showed A3, C1, and F1 in order. 3. In "Waist looks thick", they were B2, D1, and F7 while in "Waist looks thin", they were B3, F8, and D6 in order. 4. In the item in that "Hip looks big", the best effect was in F9, and then E3, C2, and B4 in order. In "Hip looks small", the best one was C1, and then comes. E1, F6, and F8. 5. In "Upper body looks thick", they were D2, D4, F8, C3 and A5 in order whild in "Upper body looks thin", they were A1, F5, and D7 in order. 6. In the item "Lower body lookds thick", they were F9, C2, E3, B3, and D3 in order. In "Lower body looks thin", the best one was C1, and then D1, E2, F6, and F8 comes in order. 7. In "whole body looks thick", they were F9, F3, D3, and A5, and in "Whole body looks thin", they were F5, A1, C1, and D6 in order. 8. In "Height looks tall", the effects were in order of A4, D6, E1, and F7 while in "Height looks short", they were E3, F9, B4, D2, and D1. 8. In "Height looks tall", the effects were in order of A4, D6, E1, and F7 while in "Height looks short", they were E3, F9, B4, D2, and D1. F9, B4, D2, and D1.

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Inhibitory Effect of Polygonum Multiflorum on Melanin Synthesis and Its Action Mechanism in B16F10 (적하수오(赤何首烏)의 멜라닌 생성 억제와 작용기전에 관한 연구)

  • Song, Jong-Sek;Yoo, Dong-Youl
    • The Journal of Korean Obstetrics and Gynecology
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    • v.21 no.2
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    • pp.59-75
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    • 2008
  • Purpose: This study was performed to determine the inhibitory effect of Polygonum multiflorum(PM) on melanin synthesis in B16F10. Methods: The Inhibitory effects of Polygonum multiflorum(PM) on melanin synthesis were determined by in-vitro assay. To elucidate inhibitory effects of Polygonum multiflorum on melanin synthesis, we determined the melanin release and melanin production in B16F10. And to investigate the action mechanism, we assessed the gene expression of tyrosinase, TRP-1, TRP-2, MMP-2, PKA, PKC, ERK-1 ERK-2, AKT-1, MITF in B16F10. Results: 1. PM inhibited melanin-release, melanin production in B16F10. 2. PM inhibited tyrosinase activity in vitro and in B16F10. 3. PM suppressed the expression of tyrosinase, TRP-1 in B16F10. 4. PM suppressed the expression of PKA in B16F10. 5. PM suppressed the expression of ERK-1, ERK-2, AKT-1 in B16F10. 6. PM suppressed the expression of MITF in B16F10. Conclusion: From these results, it may be concluded that PM possesses the antimelanogenetic effects.

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The Fundamental Properties of Alkali-Activated Slag Cement (AASC) Mortar with Different Water-Binder Ratios and Fine Aggregate-Binder Ratios (물-결합재 비와 잔골재-결합재 비에 따른 알칼리 활성화 슬래그 모르타르의 기초특성)

  • Kim, Tae-Wan;Hahm, Hyung-Gil;Lee, Seong-Haeng;Eom, Jang-Sub
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.17 no.5
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    • pp.77-86
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    • 2013
  • This study investigates the fundamental properties of the water-binder (W/B) ratio and fine aggregate-binder (F/B) ratio in the alkali-activated slag cement (AASC) mortar. The W/B ratios are 0.35, 0.40, 0.45, and 0.50, respectively. And then the F/B ratios varied between 1.00 and 3.00 at a constant increment of 0.25. The alkali activator was an 2M and 4M NaOH. The measured mechanical properties were compared, flow, compressive strength, absorption, ultra sonic velocity, and dry shrinkage. The flow, compressive strength, absorption, ultra sonic velocity and dry shrinkage decreased with increases W/B ratio. The compressive strength decreases with increase F/B ratio at same W/B ratio. Also, at certain value of F/B ratio significant increase in strength is observed. And S2 (river sand 2) had lower physical properties than S1 (river sand 1) due to the fineness modulus. The results of experiments indicated that the mechanical properties of AASC depended on the W/B ratio and F/B ratio. The optimum range for W/B ratios and F/B ratios of AASC is suggested that the F/B ratios by 1.75~2.50 at each W/B ratios. Moreover, the W/(B+F) ratios between 0.13 and 0.14 had a beneficial effect on the design of AASC mortar.

The evaluate the usefulness of various CT kernel applications by PET/CT attenuation correction (PET/CT 감쇠보정시 다양한 CT Kernel 적용에 따른 유용성 평가)

  • Lee, Jae-Young;Seong, Yong-Jun;Yoon, Seok-Hwan;Park, Chan-Rok;Lee, Hong-Jae;Noh, Kyung-Wun
    • The Korean Journal of Nuclear Medicine Technology
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    • v.21 no.2
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    • pp.37-43
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    • 2017
  • Purpose Recently PET/CT image's attenuation correction is used CTAC(Computed Tomgraphy Attenuation Correction). it can quantitative evaluation by SUV(Standard Uptake Value). This study's purpose is to evaluate SUV and to find proper CT kernel using CTAC with applied various CT kernel to PET/CT construction. Materials and Methods Biograph mCT 64 was used for the equipment. We were performed on 20 patients who had examed at our hospital from february through March 2017. Using NEMA IEC Body Phantom, The data was reconstructed PET/CT images with CTAC appiled various CT kernel. ANOVA was used to evaluated the significant difference in the result. Results The result of measuring the radioactivity concentration of Phantom was B45F 96% and B80F 6.58% against B08F CT kernel, each respectively. the SUVmax increased to B45F 0.86% and B80F 6.54% against B08F CT kernel, In case of patient's parts data, the Lung SUVmax increased to B45F 1.6% and B80F 6.6%, Liver SUVmax increased to B45F 0.7% and B80F 4.7%, and Bone SUVmax increased to B45F 1.3% and B80F 6.2%, respectively. As for parts of patient's about Standard Deviation(SD), the Lung SD increased to B45F 4.2% and B80F 15.4%, Liver SD increased to B45F 2.1% and B80F 11%, and Bone SD increased to B45F 2.3% and B80F 14.7%, respectively. There was no significant difference discovered in three CT kernel (P >.05). Conclusion When using increased noise CT kernel for PET/CT reconstruction, It tends to change both SUVmax and SD in ROI(region of interest), Due to the increase the CT kernel number, Sharp noise increased in ROI. so SUVmax and SD were highly measured, but there was no statistically significant difference. Therefore Using CT kernel of low variation of SD occur less variation of SUV.

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The Effect of Mibaeksan(MB) on Melanin Synthesis and Gene Expression (미백산(美白散)이 멜라닌 생성 및 유전자 발현에 미치는 영향)

  • Kim, Soo-Min;Yoo, Dong-Youl
    • The Journal of Korean Obstetrics and Gynecology
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    • v.22 no.4
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    • pp.1-18
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    • 2009
  • Purpose: This study was performed to elucidate the inhibitory effect of Mibaeksan (MB) on melanin synthesis in B16F10 mouse melanoma cell. Methods: To demonstrate the inhibitory effects of MB on melanin synthesis, we measured the amount of released and produced melanin in B16F10 melanoma cell. Also, we evaluated tyrosinase-activity in vitro as well as in B16F10 melanoma cell. And to investigate the action mechanism, we assessed the gene expression of tyrosinase, TRP-1, TRP-2, MMP-2, PKA, $PKC{\beta}$, ERK-1 ERK-2, AKT-1 and MITF in B16F10 melanoma cells. Results: 1. MB decreased the release and production of melanin in B16F10 melanoma cells. 2. MB decreased tyrosinase activity in vitro and in B16F10 melanoma cells. 3. MB decreased the expression of tyrosinase, TRP-1, TRP-2, PKA, $PKC{\beta}$ and MMP-2 in B16F10 melanoma cells. 4. MB increased the expression of ERK-1, ERK-2 and AKT-1 in B16F10 melanoma cells. 5. MB decreased the expression of MITF in B16F10 melanoma cells. Conclusion: From these results, it may be concluded that MB has the antimelanogenetic effects.