• Title, Summary, Keyword: F&B

Search Result 5,970, Processing Time 0.047 seconds

SOME RESULTS ON UNIQUENESS OF MEROMORPHIC SOLUTIONS OF DIFFERENCE EQUATIONS

  • Gao, Zong Sheng;Wang, Xiao Ming
    • Communications of the Korean Mathematical Society
    • /
    • v.32 no.4
    • /
    • pp.959-970
    • /
    • 2017
  • In this paper, we investigate the transcendental meromorphic solutions with finite order of two different types of difference equations $${\sum\limits_{j=1}^{n}}a_jf(z+c_j)={\frac{P(z,f)}{Q(z,f)}}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ and $${\prod\limits_{j=1}^{n}}f(z+c_j)={\frac{P(z,f)}{Q(z,f)}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ that share three distinct values with another meromorphic function. Here $a_j$, $b_k$, $d_l$ are small functions of f and $a_j{\not{\equiv}}(j=1,2,{\ldots},n)$, $b_p{\not{\equiv}}0$, $d_q{\not{\equiv}}0$. $c_j{\neq}0$ are pairwise distinct constants. p, q, n are non-negative integers. P(z, f) and Q(z, f) are two mutually prime polynomials in f.

RESOLVENT INEQUALITY OF LAPLACIAN IN BESOV SPACES

  • Han, Hyuk;Pak, Hee Chul
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.22 no.1
    • /
    • pp.117-121
    • /
    • 2009
  • For $1{\leq}p$, $q{\leq}{\infty}$ and $s{\in}\mathbb{R}$, it is proved that there exists a constant C > 0 such that for any $f{\in}B^{s+2}_{p,q}(\mathbb{R}^n)$ $${\parallel}f{\parallel}_{B^{s+2}_{p,q}(\mathbb{R}^n)}{\leq}C{\parallel}f\;-\;{\Delta}f{\parallel}_{B^{s}_{p,q}(\mathbb{R}^n)}$$, which tells us that the operator $I-\Delta$ is $B^{s+2}_{p,q}$-coercive on the Besov space $B^s_{p,q}$.

  • PDF

The Normality of Meromorphic Functions with Multiple Zeros and Poles Concerning Sharing Values

  • WANG, YOU-MING
    • Kyungpook Mathematical Journal
    • /
    • v.55 no.3
    • /
    • pp.641-652
    • /
    • 2015
  • In this paper we study the problem of normal families of meromorphic functions concerning shared values. Let F be a family of meromorphic functions in the plane domain $D{\subseteq}{\mathbb{C}}$ and n, k be two positive integers such that $n{\geq}k+1$, and let a, b be two finite complex constants such that $a{\neq}0$. Suppose that (1) $f+a(f^{(k)})^n$ and $g+a(g^{(k)})^n$ share b in D for every pair of functions f, $g{\in}F$; (2) All zeros of f have multiplicity at least k + 2 and all poles of f have multiplicity at least 2 for each $f{\in}F$ in D; (3) Zeros of $f^{(k)}(z)$ are not the b points of f(z) for each $f{\in}F$ in D. Then F is normal in D. And some examples are provided to show the result is sharp.

Ginsenoside Rg3 Induces Apoptosis in B16F10 Melanoma Cells (ginsenoside Rg3에 의한 B16F10 흑색종 세포의 세포사멸 유도)

  • Lee, Seul Gi;Kim, Byung Soo;Nam, Ju-Ock
    • Journal of Life Science
    • /
    • v.24 no.9
    • /
    • pp.1001-1005
    • /
    • 2014
  • Ginsenoside Rg3 is one of the active ingredients extracted from red ginseng, and it is an effective chemical component of the human body and well known in herbal medicine as a restorative agent. Several studies have shown that Rg3 has a potent anti-tumor effect on various cancer cell lines. However, Rg3-induced apoptosis in B16F10 melanoma cancer cells is not well understood. In the present study, we tested whether ginsenoside Rg3 could induce apoptosis in B16F10 melanoma cells. We found that Rg3 could inhibit B16F10 melanoma cell viability in a dose-dependent manner, but not normal cells, such as EA.hy.926 and NIH3T3 cells. We also found that Rg3 could induce apoptosis in B16F10 melanoma cells using tunnel-staining assay in a dose-dependent manner. Rg3 treatment induces the phosphorylation of p38 and the expression of Bax, but it inhibits the expressions of the phosphorylation of focal adhesion kinase Bcl2 and pro-caspase3. Taken together, our data suggest that Rg3 could be useful as an anti-cancer agent in B16F10 melanoma cells.

Linear Free Energy Relationship on the Phosphorylation of Acetylcholinesterase by Insecticidal O,O-Diethylphenylphosphate Derivatives (살충성(殺蟲性) O,O-Diethylphenylphosphate유도체(誘導體)들에 의(依)한 Acetylcholinesterase의 Phosphorylation에 미치는 자유(自由)에너지 관계(關係))

  • Sung, Nack-Do
    • Korean Journal of Agricultural Science
    • /
    • v.11 no.1
    • /
    • pp.176-181
    • /
    • 1984
  • Linear free energy relation ship(LFER) on the insecticidal activity of O,O-diethylphenylphosphate (A) and 3,5-dimethylphenyl-O,O-diethylphosphate (B) derivatives were studied by EHT MO calculation method and regression analysis method. LFER between varying substituent constants and $pI_{50}$ constants of phosphates, (A) & (B) were calculated with applying Hammett, Okamoto-Brown, Taft and Swain-Lupton's DSP equations;percent resonance effect(R) and field effect(F) of (A) were %R=33.5 & %F=66.5 and also that of (B) were %R=2 & %F=98, respectively. On the basis of above findings, the insecticidal activities were similar for both (A) and (B), but (B) have larger field and inductive contribution than (A), due to the 3,5-dimethyl group of (B).

  • PDF

KINEMATIC STRUCTURES OF CERTAIN LOOPS

  • Im, Bok-Hee
    • Communications of the Korean Mathematical Society
    • /
    • v.12 no.3
    • /
    • pp.543-551
    • /
    • 1997
  • In this paper, we call a loop F kinematic if for $a, b \in F\{0}$, the following two conditions are valid : (i) the centralizer Z(a) of a is a commutative group under the induced operation from the loop F, and (ii) Z(a) = Z(b) or $Z(a) \cap Z(b) = {0}$, where 0 is the identity of F. Some example of kinematic loops are given.

  • PDF

Inhibitory Effect of Soyosangagamhwajae on Melanin Synthesis and its Action Mechanism in B16F10 Mouse Melanoma Cell (소요산가감화제(逍遙散加減化製)의 멜라닌 생성 억제와 작용기전에 관한 연구)

  • Kim, Eun-Seop;Lim, Hyun-Jung;Shin, Sun-Mi;Kim, Soo-Min;Lee, Jung-Eun;Yoo, Dong-Youl
    • The Journal of Korean Obstetrics and Gynecology
    • /
    • v.21 no.1
    • /
    • pp.83-98
    • /
    • 2008
  • Purpose: This study was performed to determine the inhibitory effect of Soyosangagamhwajae(SYG) on melanin synthesis in B16F10 mouse melanoma cell. Methods: The Inhibitory effects of Soyosangagamhwajae(SYG) on melanin synthesis were determined by in-vitro assay. To elucidate inhibitory effects of SYG on melanin synthesis, we determined the melanin release in B16F10 cell. And to investigate the action mechanism, we assessed the gene expression of tyrosinase, TRP-1, TRP-2. PKA, $PKC{\beta}$ in B16F10 cell. Results: 1. SYG significantly inhibited melanin-release in B16F10 cell. 2. SYG significantly inhibited mushroom tyrosinase activity in vitro. 3. SYG significantly suppressed the expression of tyrosinase in B16F10 cell. 4. SYG significantly suppressed the expression of TRP-1, TRP-2 in B16F10 cell. 5. SYG significantly suppressed the expression of PKA, $PKC{\beta}$ in B16F10 cell. Conclusion: From these results, it may be concluded that SYG has the antimelanogenetic effect.

  • PDF

T-NEIGHBORHOODS IN VARIOUS CLASSES OF ANALYTIC FUNCTIONS

  • Shams, Saeid;Ebadian, Ali;Sayadiazar, Mahta;Sokol, Janusz
    • Bulletin of the Korean Mathematical Society
    • /
    • v.51 no.3
    • /
    • pp.659-666
    • /
    • 2014
  • Let $\mathcal{A}$ be the class of analytic functions f in the open unit disk $\mathbb{U}$={z : ${\mid}z{\mid}$ < 1} with the normalization conditions $f(0)=f^{\prime}(0)-1=0$. If $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ and ${\delta}$ > 0 are given, then the $T_{\delta}$-neighborhood of the function f is defined as $$TN_{\delta}(f)\{g(z)=z+\sum_{n=2}^{\infty}b_nz^n{\in}\mathcal{A}:\sum_{n=2}^{\infty}T_n{\mid}a_n-b_n{\mid}{\leq}{\delta}\}$$, where $T=\{T_n\}_{n=2}^{\infty}$ is a sequence of positive numbers. In the present paper we investigate some problems concerning $T_{\delta}$-neighborhoods of function in various classes of analytic functions with $T=\{2^{-n}/n^2\}_{n=2}^{\infty}$. We also find bounds for $^{\delta}^*_T(A,B)$ defined by $$^{\delta}^*_T(A,B)=jnf\{{\delta}&gt;0:B{\subset}TN_{\delta}(f)\;for\;all\;f{\in}A\}$$ where A, B are given subsets of $\mathcal{A}$.

A Study on the Melanin Synthesis Inhibition and Whitening Effect of Schizandrae Fructus (오미자(五味子)의 멜라닌 생성 억제와 미백효과에 관한 연구)

  • Doo, In-Sun;Lim, Kyu-Sang;Hwang, Chung-Yeon;Park, Min-Cheol;Kim, Nam-Kwen
    • The Journal of Korean Medicine Ophthalmology and Otolaryngology and Dermatology
    • /
    • v.20 no.3
    • /
    • pp.51-62
    • /
    • 2007
  • Objective : The aim of this study is to assess the effect of Schizandrae Fructus on melanin synthesis inhibition and whitening effect. Methods : We assessed inhibitory effects of Schizandrae Fructus on melanin-release from B16F10, on melanin production in B16F10, on mushroom tyrosinase activity in vitro, on tyrosinase activity in B16F10 and effect of Schizandrae Fructus on the expression tyrosinase, TRP-1, TRP-2, PKA, ERK-1 ERK-2, AKT-1, MITF in B16F10. Results and Conclusion : 1. Schizandrae Fructus inhibited melanin-release, melanin production in B16F10. 2. Schizandrae Fructus inhibited tyrosinase activity in vitro and in B16F10. 3. Schizandrae Fructus suppressed the expression of tyrosinase, TRP-1, TRP-2, PKA, ERK-2 in B16F10.

  • PDF

A NOTE ON CONTINUED FRACTIONS WITH SEQUENCES OF PARTIAL QUOTIENTS OVER THE FIELD OF FORMAL POWER SERIES

  • Hu, Xuehai;Shen, Luming
    • Bulletin of the Korean Mathematical Society
    • /
    • v.49 no.4
    • /
    • pp.875-883
    • /
    • 2012
  • Let $\mathbb{F}_q$ be a finite field with q elements and $\mathbb{F}_q((X^{-1}))$ be the field of all formal Laurent series with coefficients lying in $\mathbb{F}_q$. This paper concerns with the size of the set of points $x{\in}\mathbb{F}_q((X^{-1}))$ with their partial quotients $A_n(x)$ both lying in a given subset $\mathbb{B}$ of polynomials in $\mathbb{F}_q[X]$ ($\mathbb{F}_q[X]$ denotes the ring of polynomials with coefficients in $\mathbb{F}_q$) and deg $A_n(x)$ tends to infinity at least with some given speed. Write $E_{\mathbb{B}}=\{x:A_n(x){\in}\mathbb{B},\;deg\;A_n(x){\rightarrow}{\infty}\;as\;n{\rightarrow}{\infty}\}$. It was shown in [8] that the Hausdorff dimension of $E_{\mathbb{B}}$ is inf{$s:{\sum}_{b{\in}\mathbb{B}}(q^{-2\;deg\;b})^s$ < ${\infty}$}. In this note, we will show that the above result is sharp. Moreover, we also attempt to give conditions under which the above dimensional formula still valid if we require the given speed of deg $A_n(x)$ tends to infinity.