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

  • Ahn, Jae-Moon
    • 대한수학회보
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    • 제35권1호
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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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백강잠의 멜라닌 생성 억제와 미백효과에 관한 연구 (A Study on the Melanin Synthesis Inhibition and Whitening Effect of Bombysis Corpus)

  • 오한철;임규상;황충연;윤인환;김남권
    • 한방안이비인후피부과학회지
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    • 제20권3호
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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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시엽(枾葉)의 멜라닌 생성 억제와 작용기전에 관한 연구 (Inhibitory Effect of Persimmon Leaves on Melanin Synthesis and its Action Mechanism in B16F10 cells)

  • 장두현;유동열
    • 대한한방부인과학회지
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    • 제22권2호
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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
    • 대한수학회보
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    • 제61권4호
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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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    • 제30권3호
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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.

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

  • 이경희
    • 대한가정학회지
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    • 제28권4호
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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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적하수오(赤何首烏)의 멜라닌 생성 억제와 작용기전에 관한 연구 (Inhibitory Effect of Polygonum Multiflorum on Melanin Synthesis and Its Action Mechanism in B16F10)

  • 송종석;유동열
    • 대한한방부인과학회지
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    • 제21권2호
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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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물-결합재 비와 잔골재-결합재 비에 따른 알칼리 활성화 슬래그 모르타르의 기초특성 (The Fundamental Properties of Alkali-Activated Slag Cement (AASC) Mortar with Different Water-Binder Ratios and Fine Aggregate-Binder Ratios)

  • 김태완;함형길;이성행;엄장섭
    • 한국구조물진단유지관리공학회 논문집
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    • 제17권5호
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    • pp.77-86
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    • 2013
  • 본 연구는 물-결합재 비 (W/B)와 잔골재-결합재 비 (F/B)에 따른 알칼리 활성화 슬래그 시멘트 (AASC)의 기초 특성에 관한 연구이다. W/B 비는 0.35, 0.40, 0.45, 그리고 0.50를 선정하였다. 그리고 F/B 비는 1.00에서 3.00까지 0.25 크기로 고려하였다. 알칼리 활성화제는 2M과 4M의 NaOH를 사용하였다. 실험은 플로우, 흡수율, 압축강도, 초음파 속도 그리고 건조수축을 측정하여 비교하였다. 플로우, 압축강도, 흡수율, 초음파 속도 그리고 건조수축 모두 W/B 비가 증가하면 감소하였다. 압축강도는 동일 W/B 비에서 F/B 비가 증가할수록 감소하였다. 또한 특정 F/B 비에서 강도가 증가하는 것을 볼 수 있었다. 그리고 S2 (river sand 2)는 S1 (river sand 1)보다 낮은 물리적 특성을 나타냈는데, 이는 조립률 때문으로 판단된다. 본 실험의 결과 AASC의 공학적 특성은 W/B 비와 F/B 비가 영향을 주는 것으로 판단된다. 최적의 F/B 비는 각 W/B 비에 대해 1.75~2.50 인 것으로 생각된다. 또한 W/(B+F) 비가 0.13과 0.14 사이일 때 AASC 모르타르의 배합설계가 효과적일 것으로 판단된다.

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

  • 이재영;성용준;윤석환;박찬록;이홍재;노경운
    • 핵의학기술
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    • 제21권2호
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    • pp.37-43
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    • 2017
  • PET/CT 영상 재구성시 감쇠보정맵을 사용하여 영상재구성에 적용한다. 감쇠보정 맵의 CT parameter을 변경하여 PET/CT 영상 재구성 할 때 적용하여 SUVmax에 어떤 영향을 미치는지 비교 평가해보고자 한다. 장비는 Biograph mCT 64를 사용하였고 Phantom은 NEMA IEC Body Phantom을 사용하였다. 실험을 위해 환자는 2017년 2월에서 3월까지 본원 PET/CT 검사를 시행한 환자 20명을 대상으로 Lung, Liver, Bone에 관심영역을 선택하여 기존 08f AC, 45f medium, 80f ultra sharp 방식의 CT kernel을 적용한 감쇠보정맵을 사용하여 PET/CT 영상 재구성에 도입 후 방사능 농도(kBq/mL), SUVmax, SD(standard deviation) 변화 유무를 평가하였다. Phantom 방사능 농도 측정 결과 B08f AC 대비 B45f 0.96%, B80f 6.58% 증가하였고 B08f AC 대비 B45f 0.86%, B80f 6.54%각각 증가하였고, SD의 경우 B08f AC 대비 B45f 1.27%, B80f 6.96% 증가하였다. 환자에서 부위별 SUV는 Lung에서 B08f AC 대비 B45f 1.6%, B80f 6.6%, Liver에서 B08f AC 대비 B45f 0.7%, B80f 4.7%, Bone에서 B08f AC 대비 B45f 1.3%, B80f 6.2% 증가를 보였다. 부위별 SD는 Lung에서 B08f AC 대비 B45f 6.2%, B80f 15.4%, Liver에서 B08f AC 대비 B45f 2.1%, B80f 11%, Bone에서 B08f AC 대비 B45f 를 사용할 때 2.3%, B80f 14.7% 증가를 보였다. CT Kernel변화에 따라 sharpness noise와 영상의 질은 변화를 보였으나 SUVmax와 SD는 통계적으로 유의한 차이가 없었다.(P>.05). 핵의학 영상은 정량적인 평가가 중요하다 따라서 부위에 따라 CT kernel이 적절하게 조절되고 noise level이 낮은 감쇠보정 맵을 사용하여 PET/CT 재구성시에 적용하여 정량적 평가에 오류를 줄이는 것이 중요하다고 사료되므로 따라서 같은 부위라 할지라도 sharpness noise가 인위적으로 증가된 kernel을 사용하는 것보다 noise가 낮은 kernel을 사용하는 것이 SD편차를 줄이고 정량적인 평가에 오류를 적게 하여 정확한 진단과 SUV 측정에 유용할 것으로 사료된다.

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

  • 김수민;유동열
    • 대한한방부인과학회지
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    • 제22권4호
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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.