Prediction of the behavior of heavy metals over time is important to evaluate the heavy metal toxicity in algae species. Various modeling studies have been well established, but there is a need for an improved model for predicting the chronic effects of metals on algae species to combine the metal kinetics and biological response of algal cells. In this study, a kinetic dynamics model was developed to predict the copper behavior (5 μg L-1, 10 μg L-1, and 15 μg L-1) for two freshwater algae (Pseudokirchneriella subcapitata and Chlorella vulgaris) in the chronic exposure experiments (8 d and 21 d). In the experimental observations, the rapid change in copper mass between the solutions, extracellular and intracellular sites occurred within initial exposure periods, and then it was slower although the algal density changed with time. Our model showed a good agreement with the measured copper mass in each part for all tested conditions with an elapsed time (R 2 for P. subcapitata: 0.928, R 2 for C. vulgaris: 0.943). This study provides a novel kinetic dynamics model that is compromised between practical simplicity and realistic complexity, and it can be used to investigate the chronic effects of heavy metals on the algal population.

Todarodes pacificus is an important marine resource commercialized in South Korea, Japan, and China. The objective of this work is to investigate the effectiveness of different mathematical models (diffusive model, Newton's model, Henderson-pabis's model, Page's model, and Weibull's model) in precisely explaining the moisture gain/loss and salt gain of the squid slices immersed in saline solutions. Brine concentrations of immersion used were 2.5, 5, 10, and 15% (w/w) for various durations (0-360 min). The effective diffusion coefficients of salt ranged from 0.549×10−9 to 0.841×10−9 m2/s, while the moisture values ranged from -0.077×10−9 to 0.374×10−9 m2/s. The experimental results of moisture and salt transfer fitted well into the Henderson-Pabis and Page models, respectively. The results presented in this study support the potential to predict the mass transfer of squid using mathematical modeling.

저자는 자신의 작업을 중심으로 수학과 미술의 연결고리, 즉 정상분배의 수행성을 탐구하는 수단으로서 수학적 모델의 원리를 고찰한다. 본 논문은 자신의 작업과 제작과정 에 대한 기술과 작업과 제작과정 모두에 작용하는 수학적 측면에 대한 분석으로 구성되어 있다. 분석의 부분은 작가 자신과 가상의 질의자 간의 문답 형식으로 제시되고, 작가의 동기와 수학이 작업과정에 작용하는 상이한 면들을 포괄하여 진행된다. 행위자 연결망 이론가인 미셀 칼론의 이론에 따라 제작과정은 ‘번역’의 연쇄망으로 기술될 것이며, 예술작품이 점점 수학적 공식의 대변인이 되지만 결국 전복하는 과정을 보여준다. 이 분석 부분은 수학을 사용하는 작가들의 간략한 토론으로 마무리된다.

Even if there are no causing factors such as car crash and road works, traffic congestion come from traffic growth on the road. In this case, estimation of traffic flow helps find the solution of traffic congestion problem. In this paper, we present a optimization model which used on traffic equilibrium problem and studied the problem of inverting shortest path sets for complex traffic system. And we also develop pivotal decomposition algorithm for reliability function of complex traffic system. Several examples are illustrated.

자전고온합성반응법을 이용하여 이규화 몰리브덴-텅스텐(Mo1-z , Wz)Si2을 합성하였다. 조성 (z)을 변화시켜 성형한 원통형 시편에 합성반응 중 전달되는 온도변화를 예측하기 위하여 시편의 중앙에 열전대를 삽입하였다. 반응 선단면이 열전대를 통과할 때 가장 높은 반응온도를 보이고 이것을 단열반응 온도라 간주하였다. 따라서 본 연구에서는 이러한 온도변화를 예측하기 위하여 자전조온합성반응의 모델링을 계시하고자 하였으며, 실험을 통하여 측정한 반응온도 분포곡선의 거동을 비교하였다. 각각의 시료에 대한 실험결과 측정된 반응속도는 약 2.14~1.35mm/sec, 반응온도는 1883K~1507K의 간을 보였다. 두 항 모두 텅스텐의 함량이 증가함에 따라 감소하는 경향을 나타냈으며, 수치해석을 통하여 거의 유사한 반응온도를 얻었다. 시료의 초기온도를 증가시킬 경우 반응온도는 증가함이 예측되었고, z=0.5인 시료에 대하여 반응온도가 1900k 이상이 되기 위해서는 약 800K-900K의 예열이 필요하였다.

This study was designed to predict the risk of a hazard chemical, vinyl chloride, by applying dose-response assessment that are one of the major process in practicing risk assessment. After extrapolating from the high dose exposure of vinyl chloride based upon animal carcinogenic data to the low dose exposed to human using several mathematical models, we calculated the cancer potency factors as well as virtually safe dose and the resulted values were compared. This process will provide the new insight to assess the risk of a chemical accurately imposed to human in the future.

This study was conducted to develop a predictive model for the growth of Escherichia coli strain RC-4-D isolated from red kohlrabi sprout seeds. We collected E. coli kinetic growth data during red kohlrabi seed sprouting under isothermal conditions (10, 15, 20, 25, and 30°C). Baranyi model was used as a primary order model for growth data. The maximum growth rate (μmax) and lag-phase duration (LPD) for each temperature (except for 10°C LPD) were determined. Three kinds of secondary models (suboptimal Ratkowsky square-root, Huang model, and Arrhenius-type model) were compared to elucidate the influence of temperature on E. coli growth rate. The model performance measures for three secondary models showed that the suboptimal Huang square-root model was more suitable in the accuracy (1.223) and the suboptimal Ratkowsky square-root model was less in the bias (0.999), respectively. Among three secondary order model used in this study, the suboptimal Ratkowsky square-root model showed best fit for the secondary model for describing the effect of temperature. This model can be utilized to predict E. coli behavior in red kohlrabi sprout production and to conduct microbial risk assessments.

This paper presents a mathematical model on the longitudinal mid-span extension of the Tamar Bridge, UK by using 6 months data of temperatures and an extension starting from July 2010. Linear models of temperature input-extension output were identified for all the combinations of input temperatures. The model using two temperatures, one temperature on the top of the mid-span section and the other on the bottom, was found to be the best with the fitness value 95.9% while single-temperature input models had maximum fitness 80%. This observation might be explained by the temperature gradient at the section: in the existence of the temperature gradient, two temperatures in the section may represent the temperature distribution of the section well while a single temperature can't. A further study needs to be carried out to verify it by a thermal simulation on a Finite Element model of the bridge.