• Korean Journal of Mathematics
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• 제26권4호
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• pp.709-727
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• 2018

Here we have studied the ideas of $g^*$-closed sets, $g{\bigwedge}_{{\tau}^-}$ sets and ${\lambda}^*$-closed sets and investigate some of their properties in the spaces of A. D. Alexandroff [1]. We have also studied some separation axioms like $T_{\frac{\omega}{4}}$, $T_{\frac{3\omega}{8}}$, $T_{\omega}$ in Alexandroff spaces and also have introduced a new separation axiom namely $T_{\frac{5\omega}{8}}$ axiom in this space.

• 대한수학회논문집
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• 제33권4호
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• pp.1141-1158
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• 2018

Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

• 대한수학회보
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• 제49권4호
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• pp.787-797
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• 2012

In this paper the authors study the $L^p$ boundedness for parabolic Littlewood-Paley operator $${\mu}{\Phi},{\Omega}(f)(x)=\({\int}_{0}^{\infty}{\mid}F_{\Phi,t}(x){\mid}^2\frac{dt}{t^3}\)^{1/2}$$, where $$F_{\Phi,t}(x)={\int}_{p(y){\leq}t}\frac{\Omega(y)}{\rho(y)^{{\alpha}-1}}f(x-{\Phi}(y))dy$$ and ${\Omega}$ satisfies a condition introduced by Grafakos and Stefanov in [6]. The result in the paper extends some known results.

• 대한수학회보
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• 제33권4호
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• pp.631-638
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• 1996

The parabolic free boundary problem with Puschino dynamics is given by (see in [3]) $$ (1) { \upsilon_t = D\upsilon_{xx} - (c_1 + b)\upsilon + c_1 H(x - s(t)) for (x,t) \in \Omega^- \cup \Omega^+, { \upsilon_x(0,t) = 0 = \upsilon_x(1,t) for t > 0, { \upsilon(x,0) = \upsilon_0(x) for 0 \leq x \leq 1, { \tau\frac{dt}{ds} = C)\upsilon(s(t),t)) for t > 0, { s(0) = s_0, 0 < s_0 < 1, $$ where $\upsilon(x,t)$ and $\upsilon_x(x,t)$ are assumed continuous in $\Omega = (0,1) \times (0, \infty)$.

• 산업기술연구
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• 제4권
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• pp.29-35
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• 1984

Buckling is a significant behavior to be considered whenever we design steel structures. In the case of H-shape beams, the lateral buckling occured by bending moment must be considered. Because of the lateral buckling of H-shape beams, the bending strength of the beams are determined by the lateral buckling stress instead of the allowable bending stress. Lateral buckling stress equation, consisting of two terms, i. e. ${\sigma}_{cr}({\nu},{\omega})={\sqrt{[{\sigma}_{cr}({\nu})]^2+[{\sigma}_{cr}({\omega})]^2}}$ has been using, but for the practical purpose of use the following equations are using two, i. e. ${\sigma}_{cr}({\nu})={\frac{0.65E}{{\ell}_h/A_f}}$, ${\sigma}_{cr}({\omega})={\frac{{\pi}^2E}{({\ell}_b/i_b)^2}}$. When we use the above equations, the results are different according to the shape of beam section, and they a re rather complex. In this study lateral buckling stress equation is derived, and the proposed formula$({\sigma}_{cr}(t))$ is compared with above mentioned two basic and practical equations. To verify the proposed formula experimentaly, 16H-shape beams which have different slender ratios arc tested by applying pure bending momet. Through the experiments the buckling behavior of H-shape beams is clarified, and the results shows that the proposed formula$({\sigma}_{cr}(t))$ is accurate enough for practical purpose.

• Journal of Ecology and Environment
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• 제43권4호
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• pp.376-384
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• 2019

Background: Nutrient release during litter decomposition was investigated in Vitex doniana, Terminalia avecinioides, Sarcocephallus latifolius, and Parinari curatellifolius in Makurdi, Benue State Nigeria (January 10 to March 10 and from June 10 to August 10, 2016). Leaf decomposition was measured as loss in mass of litter over time using the decay model W_t/W₀ = e-^{kd t}, while $Kd=-{\frac{1}{t}}In({\frac{Wt}{W0}})$ was used to evaluate decomposition rate. Time taken for half of litter to decompose was measured using T₅₀ = ln ²/k; while nutrient accumulation index was evaluated as $NAI=(\frac{{\omega}t\;Xt}{{\omega}oXo})$. Results: Average mass of litter remaining after exposure ranged from 96.15 g, (V. doniana) to 78.11 g, (S. lafolius) in dry (November to March) and wet (April to October) seasons. Decomposition rate was averagely faster in the wet season (0.0030) than in the dry season (0.0022) with P. curatellifolius (0.0028) and T. avecinioides (0.0039) having the fastest decomposition rates in dry and wet seasons. Mean residence time (days) ranged from 929 to 356, while the time (days) for half the original mass to decompose ranged from 622 to 201 (dry and wet seasons). ANOVA revealed highly significant differences (p < 0.01) in decomposition rates and exposure time (days) and a significant interaction (p < 0.05) between species and exposure time in both seasons. Conclusion: Slow decomposition in the plant leaves implied carbon retention in the ecosystem and slow release of CO₂ back to the atmosphere, while nitrogen was mineralized in both seasons. The plants therefore showed effectiveness in nutrient cycling and support productivity in the ecosystem.

• Journal of Biosystems Engineering
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• 제37권3호
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• pp.155-165
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• 2012

This study was performed to offer the data for design of the seedling bed transfer equipment to make the automation of working process in a plant factory. The seedling bed transfer equipment pushing the seedling bed with bearing wheels on the rail for interconnecting each working process by a pneumatic cylinder was made and examined. The examined transfer force to push the seedling bed with a weight of 178.9 N by the pneumatic cylinder with length of 60 cm and section area of 5 $cm^2$ was measured by experiments. The examined transfer forces was compared with theoretical ones calculated by the theoretical formula derived from dynamic system analysis according to the number of the seedling bed and pushing speed of the pneumatic cylinder head at no load. The transfer function of the equipment with the input variable as the pushing speed $V_{h0}$(m/s) and the output variable as the transfer force f(t)(N) was represented as $F(s)=(V_{h0}/k)(s+B/M)/(s(s^2+Bs/M+1/(kM))$ where M(kg), k(m/N) and B(Ns/m) are the mass of the bed, the compression coefficient of the pneumatic cylinder and the dynamic friction coefficient between the seedling bed and the rail, respectively. The examined transfer force curves and the theoretical ones were represented similar wave forms as to use the theoretical formular to design the device for the seedling bed transfer. The condition of no vibration of the transfer force curve was $kB^2>4M$. The condition of transferring the bed by the repeatable impact and vibration force according to difference of transfer distance of the pneumatic cylinder head from that of the bed was as $Ce^{-\frac{3{\pi}D}{2\omega}}<-1$, where ${\omega}=\sqrt{\frac{1}{kM}-\frac{B^2}{4M^2}}$, $C=\{\frac{\frac{B}{2M}-\frac{1}{kB}}{\omega}\}$, $D=\frac{B}{2M}$. The examined mean peak transfer force represented 4 times of the stead state transfer force. Therefore it seemed that the transfer force of the pneumatic cylinder required for design of the push device was 4Bv where v is the pushing speed.

• 대한수학회지
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• 제60권1호
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• pp.167-193
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• 2023

Let f be a self-dual primitive Maass or modular forms for level 4. For such a form f, we define N^s_f(T):=|{ρ ∈ ℂ : |𝕵(ρ)| ≤ T, ρ is a non-trivial simple zero of L_f(s)}|.. We establish an omega result for N^s_f(T), which is $N^s_f(T) = \Omega(T^{\frac{1}{6}-{\epsilon}})$ for any ∊ > 0. For this purpose, we need to establish the Weyl-type subconvexity for L-functions attached to primitive Maass forms by following a recent work of Aggarwal, Holowinsky, Lin, and Qi.

• 대한수학회지
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• 제58권6호
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• pp.1385-1405
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• 2021

Let A be a positive bounded linear operator acting on a complex Hilbert space (𝓗, ⟨·,·⟩). Let ω_A(T) and ║T║_A denote the A-numerical radius and the A-operator seminorm of an operator T acting on the semi-Hilbert space (𝓗, ⟨·,·⟩_A), respectively, where ⟨x, y⟩_A := ⟨Ax, y⟩ for all x, y ∈ 𝓗. In this paper, we show with different techniques from that used by Kittaneh in [24] that $$\frac{1}{4}{\parallel}T^{{\sharp}_A}T+TT^{{\sharp}_A}{\parallel}_A{\leq}{\omega}^2_A(T){\leq}\frac{1}{2}{\parallel}T^{{\sharp}_A}T+TT^{{\sharp}_A}{\parallel}_A.$$ Here T^#_A denotes a distinguished A-adjoint operator of T. Moreover, a considerable improvement of the above inequalities is proved. This allows us to compute the 𝔸-numerical radius of the operator matrix $\(\array{I&T\\0&-I}\)$ where 𝔸 = diag(A, A). In addition, several A-numerical radius inequalities for semi-Hilbert space operators are also established.

• 한국농공학회지
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• 제12권3호
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• pp.2019-2028
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• 1970

1. 트랙터에 의(依)한 효율적(效率的) 경기방법(耕起方法)을 실험(實驗) 고찰(考察)하여 다음과 같은 결과(結果)를 얻었다. 가. 포장내측경기(圃場內側耕起)에 있어서 선회소요시간(旋回所要時間)을 최소(最少)하는 효율적(效率的) 선회법(旋回法)은 선회간격(旋回間隔)이 zr(r=최소선회반경(最少旋回半徑))보다 작을때는 Q 자형(字型), 클때는 U 자형(字型)이다. 나. 포장내측경기(圃場內側耕起)의 단위선회구(單位旋回區) 건(巾) w는 2.5r 시(時) 가장 효율적(效率的)이다. 다. 포장주변부(圃場周邊部) 경기(耕起)에 있어서는 W>-0.0345L + 35.84 시(時)는 혼합경법(混合耕法)이 능률적(能率的)이고 W<-0.0345 + 35.84 시(時)는 반접속경법(半接續耕法)이 능률적(能率的)이다. 라. 포장주변부(圃場周邊部)의 건(巾)l는 내측경기시(內側 耕起時)와 주변경기시(周邊耕起時)에 있어서 모두 적을수록 효과적임으로 최소치(最少値)인 2r가 가장 적합(適合)하다. 2. 트랙터에 의(依)한 단위포장(單位圃場)과 경기능률(耕起能率)과의 관계(關係)를 고찰(考察)하여 다음과 같은 결과(結果)를 얻었다. 가. 종횡비(縱橫比)$\frac{L}{W}$ 및 면적(面積) A가 크면 일반적(一般的)으로 경기능률(耕起能率)은 증가(增加)한다. 나. 경기능률(耕起能率)의 증가율(增加率)은 종횡비(縱橫比) 및 면적(面積)이 크면 클수록 증가율(增加率)이 점차적으로 감소(減少)한다. 다. $\frac{L}{W}-T$ 곡선(曲線)에서 $\frac{L}{W}$에 대(對)한 T의 변화(變化)가 큰 범위(範圍)는 대략(大略) 20a에서 6, 30a에서 5, 50a에서 4, 80a에서 3, 100a에서 2.5 이내(以內)이다. 라. T-A 곡선(曲線)의 변화율(變化率)은 $\frac{L}{W}$의 영향(影響)을 받으나 대략(大略) $T=A^{-\frac{2}{3}}$ 곡선(曲線)의 변화율(變化率)과 같다. 마. 종횡비(縱橫比)가 3이상(以上)일때는 면적(面積)의 크기에 상관(相關)없이 경기능률(耕起能率)에 미치는 10a 면적증가(面積增加)의 효과는 약(約) 5 정도(程度)의 종횡비(縱橫比) 증가효과와 같다. 바. 종횡비(縱橫比)가 $2{\sim}3$일때는 면적(面積)의 크기에 상관(相關)없이 경기능률(耕起能率)에 미치는 10a 면적증가(面積增加)의 효과는 약(約) $4{\sim}2$ 정도(程度)의 종횡비(縱橫比) 증가효과와 같으면 이는 종횡비(縱橫比)가 적을수록, 면적(面積)이 클수록 차차(次次) 감소(減少)한다.