• Korean Journal of Mathematics
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• v.26 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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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 ${\theta}$.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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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 $\Omega = (0,1) \times (0, \infty)$.

• Journal of Industrial Technology
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• v.4
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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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• v.43 no.4
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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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• v.37 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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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.

• Magazine of the Korean Society of Agricultural Engineers
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• v.12 no.3
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• pp.2019-2028
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• 1970

1. Experiments were made for the efficient plowing method by the 4 wheel tractor, the results are as follow; 1) In case of plowing of inner side of the field, the efficient turning method to be the smallest turning time is the $\Omega$-shaped turning method in the turning distance less than 2r (r is the minimum turning radius of the tractor), and also, it is the U-shaped turning method in the turning distance larger than 2r. 2) 2.5r is most efficient in the unit turning section 'w' on plowing of the inner side of the field. 3) In case of plowing of outer side of the field, intermitted plowing method is efficient in case of W>-0.0345 L + 35.84, and also, semi-followed plowing method is efficient in case of W<-0.0345 L + 35.84. 4) The smaller the width of outer side of outer side of the field 'I' is, the higher is the plowing efficiency, and it is estimated that the minimum value 2r is suitable to 'I' in plowing of inner side and outer side of the field. 2. Study on the correlation between the unit field and plowing efficiencies obtained the following results; 1) plowing efficienies increase generally according as length-width ratio L/W and area A increase. 2) Percent of increase of plowing efficiencies decreases generally according as length-width ratio and area enlarge. 3) The limit that change of T is large owing to L/W is 6 for 20 a, 5 for 30 a, 4 for 50 a, 3 for 80 a, less than 2.5 for 100 a, generally, in L/W-T curve. 4) Rate of change of T-A curve is similar to rate of change of $T=A-\frac{2}{3}$ curve in spite of influence of L/W. 5) In case that length-width ratio is more than 3, effects of increase of 10 a area influenced upon plowing efficiencies are as much as effects of about 5 increase of length width ratio without correlation of size of the field. 6) In case that length-width ratio is 2 to 3, effects of increase of 10 a area influenced upon plowing efficiencies are as much as effects of about 4 to 2 increase of length-width ratio without correlation of size of the field, and the effects decrease according as not only length-width ratio decreases but also area increases, generally.