• 대한수학회보
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• 제60권6호
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• pp.1651-1672
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• 2023

In 2010, Li-Ye [13, Theorem 0.1] proved that P(ζ(z), ζ'(z), . . . , ζ^(m)(z), Γ(z), Γ'(z), Γ"(z)) ≢ 0 in ℂ, where m is a non-negative integer, and P(u₀, u₁, . . . , u_m, v₀, v₁, v₂) is any non-trivial polynomial in its arguments with coefficients in the field ℂ. Later on, Li-Ye [15, Theorem 1] proved that P(z, Γ(z), Γ'(z), . . . , Γ⁽ⁿ⁾(z), ζ(z)) ≢ 0 in z ∈ ℂ for any non-trivial distinguished polynomial P(z, u₀, u₁, . . ., u_n, v) with coefficients in a set L_δ of the zero function and a class of nonzero functions f from ℂ to ℂ ∪ {∞} (cf. [15, Definition 1]). In this paper, we prove that P(z, ζ(z), ζ'(z), . . . , ζ^(m)(z), Γ(z), Γ'(z), . . . , Γ⁽ⁿ⁾(z)) ≢ 0 in z ∈ ℂ, where m and n are two non-negative integers, and P(z, u₀, u₁, . . . , u_m, v₀, v₁, . . . , v_n) is any non-trivial polynomial in the m + n + 2 variables u₀, u₁, . . . , u_m, v₀, v₁, . . . , v_n with coefficients being meromorphic functions of order less than one, and the polynomial P(z, u₀, u₁, . . . , u_m, v₀, v₁, . . . , v_n) is a distinguished polynomial in the n + 1 variables v₀, v₁, . . . , v_n. The question studied in this paper is concerning the conjecture of Markus from [16]. The main results obtained in this paper also extend the corresponding results from Li-Ye [12] and improve the corresponding results from Chen-Wang [5] and Wang-Li-Liu-Li [23], respectively.

• 방사성폐기물학회지
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• 제2권2호
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• pp.135-143
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• 2004

국산화강암에 대한U(VI) 수착에 대한 실험적 연구를 지화학적 매개변수들인 접촉시간, pH, 이온강도, 탄산염 농도 등의 함수로 회분식으로 수행하였다. 국산 화강암에 대한 U(VI)의 수착의 분배계수 $K_{d}$ 는 실험 조건에 따라 약 1-200 mL/g의 값의 범위를 가지는 것으로 나타났다. 화강암 입자에 대한 U(VI)의 수착은 접촉시간, pH 및 탄산염 농도 등에는 크게 의존하였으나 이온강도에는 크게 의존하지 않는 것으로 나타났다. 화강암 입자들에 대한U(VI)의 수착은 용액에서 pH와 탄산염의 농도에 의존하는 우라늄 화학종과 밀집한 관계가 있음을 알 수 있었다. 또한 속도론적 수착 실험에 의하여 2 단계 일차식 속도론적 거동이 화강암 입자들에 대한 우라늄의 속도론적 수착을 지배할 수 있는 것으로 유추되었다. pH 7 이상의 알칼리 영역에서 화강암에 대한 우라늄의 수착이 크게 감소되었는데 이는 화학종 계산에 의해 예측된 바에 따라 음이온의 U(VI)-탄산염 복합체 형성에 기인하였을 것이다.

• 대한수학회보
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• 제53권6호
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• pp.1805-1821
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• 2016

In this paper, we are concerned with the nonlinear elliptic equations of the p(x)-Laplace type $$\{\begin{array}{lll}-div(a(x,{\nabla}u))+{\mid}u{\mid}^{p(x)-2}u={\lambda}f(x,u) && in\;{\Omega}\\(a(x,{\nabla}u)\frac{{\partial}u}{{\partial}n}={\lambda}{\theta}g(x,u) && on\;{\partial}{\Omega},\end{array}$$ which is subject to nonlinear Neumann boundary condition. Here the function a(x, v) is of type${\mid}v{\mid}^{p(x)-2}v$ with continuous function $p:{\bar{\Omega}}{\rightarrow}(1,{\infty})$ and the functions f, g satisfy a $Carath{\acute{e}}odory$ condition. The main purpose of this paper is to establish the existence of at least three solutions for the above problem by applying three critical points theory due to Ricceri. Furthermore, we localize three critical points interval for the given problem as applications of the theorem introduced by Arcoya and Carmona.

• 대한수학회논문집
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• 제21권2호
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• pp.261-272
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• 2006

In this paper, we define the sequence spaces: $[V,{\lambda},f,p]_0({\Delta}^r,E,u),\;[V,{\lambda},f,p]_1({\Delta}^r,E,u),\;[V,{\lambda},f,p]_{\infty}({\Delta}^r,E,u),\;S_{\lambda}({\Delta}^r,E,u),\;and\;S_{{\lambda}0}({\Delta}^r,E,u)$, where E is any Banach space, and u = ($u_k$) be any sequence such that $u_k\;{\neq}\;0$ for any k , examine them and give various properties and inclusion relations on these spaces. We also show that the space $S_{\lambda}({\Delta}^r, E, u)$ may be represented as a $[V,{\lambda}, f, p]_1({\Delta}^r, E, u)$ space. These are generalizations of those defined and studied by M. Et., Y. Altin and H. Altinok [7].

• 음성과학
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• 제9권4호
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• pp.59-75
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• 2002

Aerodynamic analysis study was performed on 14 normal subjects (2 males, 12 females) with nonsense syllables composed of Korean bilabial stops (/p, p', $p^{h}$) and their preceding and/or following vowels, /i, a, u/. That is, [pi, p'i, $p^{h}i$, pa, p'a, $p^{h}a$, pu, p'u, $p^{h}u$, ipi, apa, upu, $ip^{h}i$, $ap^{h}a$, $up^{h}u$, ip'i, ap'a, up'u]. All measures were taken and analysed using Aerophone II voice function analyzer and included peak air pressure, mean air pressure, maximum flow rate, volume, mean SPL and phonatory SPL. A t-test and one-way ANOVA were employed for analysis. A post-hoc analysis was performed with Scheffe and Bonferroni. The results were as follows: First, MSPL. and MAP of /p, p', $p^{h}$/ were significantly different in different positions (initial and medial position). In addition, different vowel environment also produced significantly different aerodynamic characteristics those consonants. Especially the lax consonant /p/ was significantly different /i, a, u/ vowel environments. The tense consonant /p'/ was significantly different only /i/ vowel environment.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.137-152
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• 2014

In this paper, we prove, in the spirit of [3, 12, 20, 22, 23], the existence of infinitely many small solutions to the following quasilinear elliptic equation $-{\Delta}_{p(x)}u+{\mid}u{\mid}^{p(x)-2}u={\mid}u{\mid}^{q(x)-2}u+{\lambda}f(x,u)$ in a smooth bounded domain ${\Omega}$ of ${\mathbb{R}}^N$. We also assume that $\{q(x)=p^*(x)\}{\neq}{\emptyset}$, where $p^*(x)$ = Np(x)/(N - p(x)) is the critical Sobolev exponent for variable exponents. The proof is based on a new version of the symmetric mountainpass lemma due to Kajikiya [22], and property of these solutions are also obtained.

• Journal of applied mathematics & informatics
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• 제36권3_4호
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• pp.173-179
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• 2018

In this paper, we investigate the stability of positive weak solution for the singular p-Laplacian nonlinear system $-div[{\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^{p-2}{\nabla}u]+m(x){\mid}u{\mid}^{p-2}u={\lambda}{\mid}x{\mid}^{-(a+1)p+c}b(x)f(u)$ in ${\Omega}$, Bu = 0 on ${\partial}{\Omega}$, where ${\Omega}{\subset}R^n$ is a bounded domain with smooth boundary $Bu={\delta}h(x)u+(1-{\delta})\frac{{\partial}u}{{\partial}n}$ where ${\delta}{\in}[0,1]$, $h:{\partial}{\Omega}{\rightarrow}R^+$ with h = 1 when ${\delta}=1$, $0{\in}{\Omega}$, 1 < p < n, 0 ${\leq}$ a < ${\frac{n-p}{p}}$, m(x) is a weight function, the continuous function $b(x):{\Omega}{\rightarrow}R$ satisfies either b(x) > 0 or b(x) < 0 for all $x{\in}{\Omega}$, ${\lambda}$ is a positive parameter and $f:[0,{\infty}){\rightarrow}R$ is a continuous function. We provide a simple proof to establish that every positive solution is unstable under certain conditions.

• Applied Biological Chemistry
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• 제9권
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• pp.91-96
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• 1968

내산성(耐酸性) Amylase를 강력(强力)히 생산(生産)하는 2개(個)의 균주(菌株)를 분리(分離)하고 정치배양(靜置培養)에 있어서의 배양(培養) pH의 영향에 관(關)하여 실험(實驗)했다. 1. 두 균주(菌株)는 모두 Asp. usamii의 tan type mutant와 유사(類似)했다. 2. $u^{-1}$ 균(菌)은 초발(初發)에 pH를 4로, $u^{-2}$ 균(菌)은 초발(初發)에 pH를 2로 할때 효소생성(酵素生成)이 가장 좋았는데 이것은 저(低) pH의 일시적(一時的)인 영향에 의(依)하는 것이 아니며 초발(初發) pH를 비교적(比較的) 낮게 할 때 배양기간중(培養基間中)의 pH 경과(經過)가 적합(適合)했기 때문이다. 3. $u^{-2}$ 균(菌)보다 $u^{-1}$ 균효소(菌酵素)의 내산성(耐酸性)이 컸으며 $u^{-2}$ 균(菌)은 초발(初發)에 pH를 낮게 하여(pH 2) 배양(培養)할 때 생성효소(生成酵素)의 내산성(耐酸性)이 컸다.

• 대한수학회보
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• 제56권5호
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• pp.1297-1314
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• 2019

In this work, we investigate the following fractional boundary value problems $$\{_tD^{\alpha}_T({\mid}_0D^{\alpha}_t(u(t)){\mid}^{p-2}_0D^{\alpha}_tu(t))\\={\nabla}W(t,u(t))+{\lambda}g(t){\mid}u(t){\mid}^{q-2}u(t),\;t{\in}(0,T),\\u(0)=u(T)=0,$$ where ${\nabla}W(t,u)$ is the gradient of W(t, u) at u and $W{\in}C([0,T]{\times}{\mathbb{R}}^n,{\mathbb{R}})$ is homogeneous of degree r, ${\lambda}$ is a positive parameter, $g{\in}C([0,T])$, 1 < r < p < q and ${\frac{1}{p}}<{\alpha}<1$. Using the Fibering map and Nehari manifold, for some positive constant ${\lambda}_0$ such that $0<{\lambda}<{\lambda}_0$, we prove the existence of at least two non-trivial solutions

• BMB Reports
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• 제47권10호
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• pp.575-580
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• 2014

In this study, we investigate whether arsenite-induced DNA damage leads to p53-dependent premature senescence using human glioblastoma cells with p53-wild type (U87MG-neo) and p53 deficient (U87MG-E6). A dose dependent relationship between arsenite and reduced cell growth is demonstrated, as well as induced ${\gamma}H2AX$ foci formation in both U87MG-neo and U87MG-E6 cells at low concentrations of arsenite. Senescence was induced by arsenite with senescence-associated ${\beta}$-galactosidase staining. Dimethyl- and trimethyl-lysine 9 of histone H3 (H3DMK9 and H3TMK9) foci formation was accompanied by p21 accumulation only in U87MG-neo but not in U87MG-E6 cells. This suggests that arsenite induces premature senescence as a result of DNA damage with heterochromatin forming through a p53/p21 dependent pathway. p21 and p53 siRNA consistently decreased H3TMK9 foci formation in U87M G-neo but not in U87MG-E6 cells after arsenite treatment. Taken together, arsenite reduces cell growth independently of p53 and induces premature senescence via p53/p21-dependent pathway following DNA damage.