• 대한수학회보
• /
• 제51권5호
• /
• pp.1453-1467
• /
• 2014

In this paper, we consider the growth and existence of solutions of differential-difference equations of certain types. We also consider the differential-difference analogues of Br$\ddot{u}$ck conjecture and give a short proof on a theorem given by Li, Yang and Yi [18]. Our additional purpose is to explore the similarity or difference on some problems in differential, difference and differential-difference fields.

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

• 충청수학회지
• /
• 제23권4호
• /
• pp.773-784
• /
• 2010

The existence of solutions in Besov spaces for nonlinear heat equations having transcendental nonlinearity: $$\frac{\partial}{{\partial}t}u-{\Delta}u=F(u)$$ is investigated. In particular, it is proved the local existence and blow-up phenomena of the solutions in Besov spaces for nonlinear heat equations corresponding to two transcendental nonlinear functions $F(u){\equiv}{\mid}u{\mid}e^{u^2}$ and $F(u){\equiv}e^u$ of rapid growth.

• 수산해양기술연구
• /
• 제53권4호
• /
• pp.471-475
• /
• 2017

This study aims to suggest the methodology to improve to estimate back-calculated fish growth parameters using weighted average. It is to contribute to correct errors in the calculation of back-calculated growth equation with unequal numbers of sample by age. If the numbers of sample were evenly collected by age, each back-calculated length at age was equal between arithmetic and weighted averages. However, most samples cannot be evenly collected by age in reality because of different catchability by fishing gear and limitation of environment condition. Therefore, the estimation of back-calculated length by weighted average method is essential to calculate growth parameters. There were some published growth equations from back-calculated length using a simple arithmetic average with different numbers of samples by age when searching for back-calculated growth equations from 91 relevant papers. In this study, the process of deriving growth equation was investigated and two different average calculations were applied to a fish growth equation, for example of Acheilognathus signifer. Growth parameters, such as $L_{\infty}$, k and $t_0$, were estimated from two different back-calculated averages and the growth equations were compared with growth performance index. Based on the correction of back-calculated length using weighted average by age, the changes by female and male were -14.19% and -5.23% for $L_{\infty}$, and 59.28% and 18.91% for k, respectively. The corrected growth performance index by weighted average improved at 7.05% and 2.46% by female and male, respectively, compared to the arithmetic averages.

• 공업화학
• /
• 제32권4호
• /
• pp.417-422
• /
• 2021

본 연구에서는 유기 단열재인 poly isocyanurate foam (PIR), poly urethane foam (PUR), phenol foam (PF)을 선정하여 ISO 5660-1의 기준에 따라 콘칼로리미터(cone calorimeter)를 이용하여 측정하였다. 화재위험성 평가를 표준화하기 위하여 기준물질(PMMA)을 사용하여 Chung's equations-III와 Chung's equation-IV에 의한 화재위험성을 등급화하여 평가하였다. Chung's equations-II의 화재성능지수-II 값은 PF가 14.77 s²/kW로 화재성능지수-II가 가장 높았고, PUR이 0.08 s²/kW로 화재성능지수-II가 가장 낮았다. 화재성장지수-II 값은 PF가 0.01 kW/s²로 화재성장지수-II가 가장 낮았고, PUR이 1.14 kW/s²로 화재성장지수-II가 가장 높았다. Chung's equations-III의 화재성능지수-III에서 PUR이 0.11로 화재성능지수-III가 가장 낮게 나타났고, PF가 20.23으로 화재성능지수-III가 가장 높았다. FGI-III에서는 PUR이 14.25로 화재성장지수-III가 가장 높게 나타났고, PF가 0.13으로 가장 안전한 물질로 판단하였다. 그리고 Chung's equation-IV의 화재위험성지수-IV는 PUR (130.03) >> PIR (19.13) > PMMA (1.00) > PF (0.01)의 순서로 나타났다. 따라서 PF가 화재위험성이 가장 낮고, PUR이 가장 높은 것으로 판단하였다.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 1998년도 추계 학술대회논문집
• /
• pp.121-126
• /
• 1998

A numerical optimization procedure is developed to find the inlet velocity profile that yields the most uniform epitaxial layer in a vertical MOCVD reactor. It involves the solution of fully elliptic equations of motion, temperature, and concentration; the finite volume method based on SIMPLE algorithm has been adopted to solve the Navier-Stokes equations. The overall optimization process is highly nonlinear and has been efficiently treated by the sequential linear programming technique that breaks the non-linear problem into a series of linear ones. The optimal profile approximated by a 6th-degree Chebyshev polynomial is very successful in reducing the spatial non-uniformity of the growth rate. The optimization is particularly effective to the high Reynolds number flow. It is also found that a properly constructed inlet velocity profile can suppress the buoyancy driven secondary flow and improve the growth-rate uniformity.

• Ocean and Polar Research
• /
• 제28권3호
• /
• pp.237-243
• /
• 2006

The ages of sandfish, Arctoscopus japoninis sampled from the eastern sea of Korea, were determined by the transverse section method of otoliths. Ages were assigned to every individual according to the number of opaque zones, and then fitted to the von Bertalanffy growth equation. Estimated equations were $L_t=25.90(1-e^{-0.2976(t+0.4447)})$ for females and $L_t=21.38(1-e^{-0.2917(t+1.2087)})$ for males, where t is age (year) and $L_t$, is body length (mm) at age t. These two equations were significantly different and the body length of females calculated from the equation was larger than that of males except at 1 year old.

• Food Science and Biotechnology
• /
• 제17권6호
• /
• pp.1352-1356
• /
• 2008

Bootstrap method, a computer-intensive statistical technique to estimate the distribution of a statistic was applied to deal with uncertainty and variability of the experimental data in stochastic prediction modeling of microbial growth on a chill-stored food. Three different bootstrapping methods for the curve-fitting to the microbial count data were compared in determining the parameters of Baranyi and Roberts growth model: nonlinear regression to static version function with resampling residuals onto all the experimental microbial count data; static version regression onto mean counts at sampling times; dynamic version fitting of differential equations onto the bootstrapped mean counts. All the methods outputted almost same mean values of the parameters with difference in their distribution. Parameter search according to the dynamic form of differential equations resulted in the largest distribution of the model parameters but produced the confidence interval of the predicted microbial count close to those of nonlinear regression of static equation.

• 대한수학회논문집
• /
• 제37권1호
• /
• pp.137-161
• /
• 2022

In this article, we study the existence and multiplicity of homoclinic solutions for the following fourth-order differential equation (1) u⁽⁴⁾(x) + ωu''(x) + a(x)u(x) = f(x, u(x)), ∀x ∈ ℝ where a(x) is not required to be either positive or coercive, and F(x, u) = ∫^u₀ f(x, v)dv is of subquadratic or superquadratic growth as |u| → ∞, or satisfies only local conditions near the origin (i.e., it can be subquadratic, superquadratic or asymptotically quadratic as |u| → ∞). To the best of our knowledge, there is no result published concerning the existence and multiplicity of homoclinic solutions for (1) with our conditions. The proof is based on variational methods and critical point theory.

• 소성∙가공
• /
• 제14권4호
• /
• pp.384-391
• /
• 2005

The nickel-based alloy Nimonic 80A possesses the excellent strength, and the resistance against corrosion, creep and oxidation at high temperature. Its products are used in aerospace engineering, marine engineering and power generation, etc. Control of forging parameters such as strain, strain rate, temperature and holding time is important because change of the microstructure in hot working affects the mechanical properties. Change of the microstructure evolves by recovery, recrystallization and grain growth phenomena. The dynamic recrystallization evolution has been studied in the temperature range of $950\~1250^{\circ}C$ and strain rate range of $0.05\~5s^{-1}$ using hot compression tests. The metadynamic recrystallization and grain growth evolution has been studied in the temperature range of $950\~1250^{\circ}C$ and strain rate range $0.05,\;5s^{-1}$, holding time range of 5, 10, 100, 600 sec using hot compression tests. Modeling equations are proposed to represent the flow curve, recrystallized grain size, recrystallized fraction and grain growth phenomena by various tests. Parameters in modeling equations are expressed as a function of the Zener-Hollomon parameter. The modeling equation for grain growth is expressed as a function of the initial grain size and holding time. The modeling equations developed were combined with thermo-viscoplastic finite element modeling to predict the microstructure change evolution during hot forging process. The grain size predicted from FE simulation results is compared with results obtained in field product.