• Korean Journal of Mathematics
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• 제25권3호
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• pp.303-321
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• 2017

In this paper we use the Krasnoselskii-Burton's fixed point theorem to obtain asymptotic stability and stability results about the zero solution for the following nonlinear neutral Levin-Nohel integro-differential equation $$x^{\prime}(t)+{\displaystyle\smashmargin{2}{\int\nolimits_{t-{\tau}(t)}}^t}a(t,s)g(x(s))ds+c(t)x^{\prime}(t-{\tau}(t))=0$$. The results obtained here extend the work of Mesmouli, Ardjouni and Djoudi [20].

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.173-183
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• 2003

In this paper, we give a classification of nonoscillatory solution of a second-order neutral delay difference equation of the form △²(x/sub n/-c/sub n/x/sub n-r/)=f(n, x/sub g1(n)/, …, x/sub gm(n)/). Some existence results for each kind of nonoscillatory solutions we also established.

• Journal of applied mathematics & informatics
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• 제37권1_2호
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• pp.53-63
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• 2019

In this paper, we show the existence of solution of the neutral stochastic functional differential equations under non-Lipschitz condition, a weakened linear growth condition and a contractive condition. Furthermore, in order to obtain the existence of solution to the equation we used the Picard sequence.

• Journal of the Korean Mathematical Society
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• 제56권6호
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• pp.1641-1654
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• 2019

In this paper we study the quasi-neutral limit of the compressible magnetohydrodynamic flows in the periodic domain ${\mathbb{T}}^3$ with the well-prepared initial data. We prove that the weak solution of the compressible magnetohydrodynamic flows governed by the Poisson equation converges to the strong solution of the compressible flow of magnetohydrodynamic flows as long as the latter exists.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 한국전산응용수학회 2002년도 학술발표대회
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• pp.11-11
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• 2002

• Microbiology and Biotechnology Letters
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• 제8권2호
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• pp.77-85
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• 1980

This experiment was conducted to investigate the conditions for production and the characteristics of pretenses. Aspergillus oryzae KC-15, which is selected as a superior strain for the production of the protease, was used in this study. The results obtained were as follows: 1. The optimum culture time for the production of acid, neutral and alkaline protease on wheat bran medium were about 48, 48 and 72hr, respectively. The protease-produced by the strain were mainly alkaline and neutral one, but the production of acid protease was feeble extremely. 2. The addition of NaH$_2$PO$_4$, Na$_2$HPO$_4$, glucose, rice powder and Na-glutamate respectively to wheat bran media were effective for the production of alkaline and neutral protease, and the addition of (NH$_4$)$_2$HPO$_4$, glucose and rice powder respectively were effective for the production of acid protease. 3. Characteristics of professes(equation omitted) 4. As a heat resistance agent, NaH$_2$PO$_4$was the most effective one. The optimum amount of NaH$_2$PO$_4$was 10mg for alkaline and neutral protease, and 5mg for acid protease. 5. The heat resistance of the Protease by NaH$_2$PO$_4$was not recognized mostly above 6$0^{\circ}C$. 6. After the treatment of enzyme solution with 10mg of NaH$_2$PO$_4$for 30 minutes at 55$^{\circ}C$, the residual activities measured for alkaline, neutral and acid protease were 58, 57 and 55％ respectively.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.199-209
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• 2013

In this paper, we study the oscillation problem of the following higher-order neutral differential equation with positive and negative coefficients and mixed arguments $$z^{(n)}(t)+q_1(t)|x(t-{\sigma}_1)|^{\alpha-1}x(t-{\sigma}_1)+q_2(t)|x(t-{\sigma}_2)|^{\beta-1}x(t-{\sigma}_2)=e(t)$$, where $t{\geq}t_0$, $z(t)=x(t)-p(t)x(t-{\tau})$ with $p(t)$ > 0, ${\beta}>1>{\alpha}>0$, ${\tau}$, ${\sigma}_1$ and ${\sigma}_2$ are real numbers. Without imposing any restriction on ${\tau}$, we establish several oscillation criteria for the above equation in two cases: (i) $q_1(t){\leq}0$, $q_2(t)>0$, ${\sigma}_1{\geq}0$ and ${\sigma}_2{\leq}{\tau}$; (ii) $q_1(t){\geq}0$, $q_2(t)<0$, ${\sigma}_1{\geq}{\tau}$ and ${\sigma}_2{\leq}0$. As an interesting application, our results can also be applied to the following higher-order differential equation with positive and negative coefficients and mixed arguments $$x^{(n)}(t)+q_1(t)|x(t-{\sigma}_1)|^{\alpha-1}x(t-{\sigma}_1)+q_2(t)|x(t-{\sigma}_2)|^{\beta-1}x(t-{\sigma}_2)=e(t)$$. Two numerical examples are also given to illustrate the main results.

• Honam Mathematical Journal
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• 제45권3호
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• pp.433-456
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• 2023

This paper deals with differentiability of solutions of neutral stochastic differential equations with respect to the initial data in the G-framework. Since the initial data belongs to the space BC ([-r, 0] ; ℝⁿ) of bounded continuous ℝⁿ-valued functions defined on [-r, 0] (r > 0), the derivative belongs to the Banach space 𝓛_BC (ℝⁿ) of linear bounded operators from BC ([-r, 0] ; ℝⁿ) to ℝⁿ. We give the neutral stochastic differential equation of the derivative. In addition, we exhibit two examples confirming the accuracy of the obtained results.

• Journal of Ocean Engineering and Technology
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• 제16권5호
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• pp.41-48
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• 2002

Numerical experiments are conducted using a three-dimensional baroclinic equation model and a Lagrangian method for clarifying the effect of th settling velocity on the suspended solids diffusion caused by the dredging and the reclamination works. Diffusion characteristics of the neutral particles and the weighting particles is experimented by the Lagrangian particles trajectory model, The results show that the diffusion characteristics of the suspended solids is effected by the settling velocity classified by the particles size in the density layered semi-closed bay. To estimate exactly the diffusion characteristics of the suspended solids and the contaminant with weight the three-dimensional baroclinic equation model and the three-dimensional Lagrangian particles trajectory model considering the settling velocity of the particle in the density layered semi-closed bay must be used.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.305-314
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• 2006

In this paper, we consider the oscillation of first order sublinear difference equation with positive neutral term $\Delta(\chi(n)+p(n)\chi(\tau(n)))+f(n,\chi(g1(n)),\cdots,\chi(gm(n)))=0$. We obtain necessary and sufficient conditions for the solutions of this equation to be oscillatory.