• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.923-935
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• 2023

In this paper, we will discuss existence of solution of square-mean pseudo almost automorphic solution for fractional stochastic evolution equations driven by G-Brownian motion which is given as ^c₀D^𝛼_𝜌 Ψ_𝜌 = 𝒜(𝜌)Ψ_𝜌d𝜌 + 𝚽(𝜌, Ψ_𝜌)d𝜌 + ϒ(𝜌, Ψ_𝜌)d ⟨ℵ⟩_𝜌 + χ(𝜌, Ψ_𝜌)dℵ_𝜌, 𝜌 ∈ R. Furthermore, we also prove that solution of the above equation is unique by using Lipschitz conditions and Cauchy-Schwartz inequality. Moreover, examples demonstrate the validity of the obtained main result and we obtain the solution for an equation, and proved that this solution is unique.

• Explosives and Blasting
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• v.16 no.3
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• pp.16-24
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• 1998

Methods of Rock fragmentation are used rock of housing repair development at KU-SAN DONG area in seoul Youn-Pyong Ku. So, Theorical analyses of the effect of vibration and frequency on structural damage around old housed also discussed. The results can be summarized as follows: 1. A area(Rock area not more than 15m Ku-San Mention) Some Empirical equations were obtained $V=K\{{\frac{D}{W}}1/3\}^{-n}$ where the values for n and K are estimated to be -1.64 and 94 respectively, this values were obtained only theorical analyses. If we have 125g charge this area is impossible blasting operation, so this area must be worked by SRS(Super Rock Splitter) method. 2. B area(Rock area from 15m to 25m in a boundary line from Ku-San Mention) This area charge is about 125g in a delay time by some empirical equation s. So, this area can be blasting operations by small charge. 3. C area(Rock area from 25m to 35m in a boundary line from Ku-San Mention) This area charge is about 500g in delay time by some empirical equation s. So, this area can be blasting operations by middle charge. 4. D area(Rock area more then 35m in a boundary line from Ku-San Mention) This area charge is about 1000g in a delay time by some empirical equation s. So, this area can be blasting operations by middle charge.

• Journal of Korea Soil Environment Society
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• v.1 no.2
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• pp.43-50
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• 1996

The adsorption charateristics of lead(II) ions on Aspergillus niger and Rhizopus arrhizus were investigated. Adsorption amount of A. niger and R. arrhizus was about 95 mg/g and 25 mg/g, respectively. These biomass was approached to adsorption equilibrium within reaction time of 1hr because of their high reactivity. The uptake of lead ion by A. niger was less sensitivity than it by R. arrhizus on the inhibition effect of alkali metals and the decreasing ratio of uptake of lead ion of A. niger and R. arrhizus by inhibition effect of alkali metals was 37% and 50%, respectively. In pre-treatment on these biomass, NaOH treatment was contributed high adsorption capacity to these biomass. Then, adsorption amount of A. niger and R. allhizus was increased about 25 mg/g and 10 mg/g, respectively. In isotherm for the adsorption of lead ion based on Freundlich equation, 1/n value of A. niger and R. ar고izus was calculated the range of 0.28-0.56 and 0.44-0.67, respectively.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.2
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• pp.73-84
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• 2003

In this paper, we investigate the new quadratic type functional equation f(2x + y) - f(x + 2y) = 3f(x) - 3f(y) and prove the stablility of this equation in the spirit of Hyers, Ulam, Rassias and G$\breve{a}$vruţa.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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• pp.377-384
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• 2008

In this paper, we prove the stability of the functional equation $$\sum\limits_{i=0}^{3}3Ci(-1)^{3-i}f(ix+y)-3!f(x)=0$$ in the sense of P. $G{\breve{a}}vruta$ on the punctured domain. Also, we investigate the superstability of the functional equation.

• Bulletin of the Korean Chemical Society
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• v.32 no.12
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• pp.4233-4238
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• 2011

Based on the exact quantization rule for the nonrelativistic Schrodinger equation, the exact quantization rule for the relativistic one-dimensional Klein-Gordon equation is suggested. Using the new quantization rule, the exact relativistic energies for exactly solvable potentials, e.g. harmonic oscillator, Morse, and Rosen-Morse II type potentials, are obtained. Consequently the new quantization rule is found to be exact for one-dimensional spinless relativistic quantum systems. Though the physical meanings of the new quantization rule have not been fully understood yet, the present formal derivation scheme may shed light on understanding relativistic quantum systems more deeply.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.455-463
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• 2012

In this paper, by using degree theory, we consider a kind of higher-order Li$\acute{e}$enard type $p$-Laplacian differential equation as follows $$({\phi}_p(x^{(m)}))^{(m)}+f(x)x^{\prime}+g(t,x)=e(t)$$. Some new results on the existence of anti-periodic solutions for above equation are obtained.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.571-579
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• 2007

Finite difference schemes are considered for a generalization of the Cahn-Hilliard equation with Neumann boundary conditions and the Kuramoto-Sivashinsky equation with a periodic boundary condition, which is of the type $ut+\frac{{\partial}^2} {{\partial}x^2}\;g\;(u,\;u_x,\;u_{xx})=f(u,\;u_x,\;u_{xx})$. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.185-195
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• 2010

In the unified field theory(UFT), in order to find a solution of the Einstein's equation it is necessary and sufficient to study the torsion tensor. The main goal in the present paper is to obtain, using a given torsion tensor (3.1), the complete representation of a particular solution of the Einstein's equation in terms of the basic tensor $g_{{\lambda}{\nu}}$ in even-dimensional UFT $X_n$.

• Asian-Australasian Journal of Animal Sciences
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• v.33 no.12
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• pp.2039-2049
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• 2020

Objective: This study was conducted to provide models to accurately predict nitrogen (N) and phosphorus (P) excretion of dairy cows on smallholder farms in Indonesia based on readily available farm data. Methods: The generic model in this study is based on the principles of the Lucas equation, describing the relation between dry matter intake (DMI) and faecal N excretion to predict the quantity of faecal N (Q_FN). Excretion of urinary N and faecal P were calculated based on National Research Council recommendations for dairy cows. A farm survey was conducted to collect input parameters for the models. The data set was used to calibrate the model to predict Q_FN for the specific case. The model was validated by comparing the predicted quantity of faecal N with the actual quantity of faecal N (Q_FNACT) based on measurements, and the calibrated model was compared to the Lucas equation. The models were used to predict N and P excretion of all 144 dairy cows in the data set. Results: Our estimate of true N digestibility equalled the standard value of 92% in the original Lucas equation, whereas our estimate of metabolic faecal N was -0.60 g/100 g DMI, with the standard value being -0.61 g/100 g DMI. Results of the model validation showed that the R² was 0.63, the MAE was 15 g/animal/d (17% from Q_FNACT), and the RMSE was 20 g/animal/d (22% from Q_FNACT). We predicted that the total N excretion of dairy cows in Indonesia was on average 197 g/animal/d, whereas P excretion was on average 56 g/animal/d. Conclusion: The proposed models can be used with reasonable accuracy to predict N and P excretion of dairy cattle on smallholder farms in Indonesia, which can contribute to improving manure management and reduce environmental issues related to nutrient losses.