• Title/Summary/Keyword: Mathematical Models

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A Review Study on Major Factors Influencing Chlorine Disappearances in Water Storage Tanks (저수조 내 잔류염소 감소에 미치는 주요 영향 인자에 관한 문헌연구)

  • Noh, Yoorae;Kim, Sang-Hyo;Choi, Sung-Uk;Park, Joonhong
    • Journal of Korean Society of Disaster and Security
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    • v.9 no.2
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    • pp.63-75
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    • 2016
  • For safe water supply, residual chlorine has to be maintained in tap-water above a certain level from drinking water treatment plants to the final tap-water end-point. However, according to the current literature, approximately 30-60% of residual chlorine is being lost during the whole water supply pathways. The losses of residual chlorine may have been attributed to the current tendency for water supply managers to reduce chlorine dosage in drinking water treatment plants, aqueous phase decomposition of residual chlorine in supply pipes, accelerated chlorine decomposition at a high temperature during summer, leakage or losses of residual chlorine from old water supply pipes, and disappearances of residual chlorine in water storage tanks. Because of these, it is difficult to rule out the possibility that residual chlorine concentrations become lower than a regulatory level. In addition, it is concerned that the regulatory satisfaction of residual chlorine in water storage tanks can not always be guaranteed by using the current design method in which only storage capacity and/or hydraulic retention time are simply used as design factors, without considering other physico-chemical processes involved in chlorine disappearances in water storage tank. To circumvent the limitations of the current design method, mathematical models for aqueous chlorine decomposition, sorption of chlorine into wall surface, and mass-transfer into air-phase via evaporation were selected from literature, and residual chlorine reduction behavior in water storage tanks was numerically simulated. The model simulation revealed that the major factors influencing residual chlorine disappearances in water storage tanks are the water quality (organic pollutant concentration) of tap-water entering into a storage tank, the hydraulic dispersion developed by inflow of tap-water into a water storage tank, and sorption capacity onto the wall of a water storage tank. The findings from his work provide useful information in developing novel design and technology for minimizing residual chlorine disappearances in water storage tanks.

Protein Requirements of the Korean Rockfish Sebastes schlegeli (조피볼락 Sebastes schlegeli의 단백질 요구량)

  • LEE Jong Yun;KANG Yong Jin;LEE Sang-Min;KIM In-Bae
    • Journal of Aquaculture
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    • v.6 no.1
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    • pp.13-27
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    • 1993
  • In order to determine the protein requirements of the Korean rockfish Sebastes schlegeli six isocaloric diets containing crude protein level from 20\%\;to\;60\%$ were fed to two groups of fish, small and large size, with the initial average body weight of 8 g and 220 g respectively. White fish meal was used as a sole protein source. Daily weight gain, daily protein retention. daily energy retention, feed efficiency, protein retention efficiency and energy retention efficiency were significantly affected by the dietary protein content (p< 0.05). The growth parameters (that is, daily weight gain, daily protein retention and daily energy retention) increased up to $44\%$ protein level with no additional response above this point. The protein requirements were determined from daily weight gain using two different mathematical models. Second order polynomial regression analysis showed that maximum daily weight gain occurred at $56.7\%\;and\;50.6\%$ protein levels for the small size group and the large size group, respectively. However the protein requirements, determined by the broken line model, appeared to be about $40\%$ for both groups. Nutrient utilization also suggested that the protein requirements of both groups were close to $40\%$. When daily protein intake was considered, daily protein requirements per 100g of fish, estimated by the broken line model, were 0.99g and 0.35g for the small and large size groups respectively. Based on these results, a $40\%$ dietary crude protein level could be recommended for the optimum growth and efficient nutrient utilization of the Korean rockfish weighing between 8g and 300g.

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A Study on the Optimal Limit State Design of Reinforced Concrete Flat Slab-Column Structures (한계상태설계법(限界狀態設計法)에 의한 철근(鐵筋)콘크리트 플래트 슬라브형(型) 구조체(構造體)의 최적화(最適化)에 관한 연구(研究))

  • Park, Moon Ho
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.4 no.1
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    • pp.11-26
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    • 1984
  • The aim of this study is to establish a synthetical optimal method that simultaneously analyze and design reinforced concrete flat slab-column structures involving multi-constraints and multi-design variables. The variables adopted in this mathematical models consist of design variables including sectional sizes and steel areas of frames, and analysis variable of the ratio of bending moment redistribution. The cost function is taken as the objective function in the formulation of optimal problems. A number of constraint equations, involving the ultimate limit state and the serviceability limit state, is derived in accordance with BSI CP110 requirements on the basis of limit state design theory. Both objective function and constraint equations derived from design variables and an analysis variable generally become high degree nonlinear problems. Using SLP as an analytical method of nonlinear optimal problems, an optimal algorithm is developed so as to analyze and design the structures considered in this study. The developed algorithm is directly applied to a few reinforced concrete flat slab-column structures to assure the validity of it and the possibility of optimization From the research it is found that the algorithm developed in this study is applicable to the optimization of reinforced concrete flat slab column structures and it converges to a optimal solution with 4 to 6 iterations regardless of initial variables. The result shows that an economical design can be possible when compared with conventional designs. It is also found that considering the ratio of bending moment redistribution as a variable is reasonable. It has a great effect on the composition of optimal sections and the economy of structures.

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Development of a Predictive Model Describing the Growth of Listeria Monocytogenes in Fresh Cut Vegetable (샐러드용 신선 채소에서의 Listerio monocytogenes 성장예측모델 개발)

  • Cho, Joon-Il;Lee, Soon-Ho;Lim, Ji-Su;Kwak, Hyo-Sun;Hwang, In-Gyun
    • Journal of Food Hygiene and Safety
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    • v.26 no.1
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    • pp.25-30
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    • 2011
  • In this study, predictive mathematical models were developed to predict the kinetics of Listeria monocytogenes growth in the mixed fresh-cut vegetables, which is the most popular ready-to-eat food in the world, as a function of temperature (4, 10, 20 and $30^{\circ}C$). At the specified storage temperatures, the primary growth curve fit well ($r^2$=0.916~0.981) with a Gompertz and Baranyi equation to determine the specific growth rate (SGR). The Polynomial model for natural logarithm transformation of the SGR as a function of temperature was obtained by nonlinear regression (Prism, version 4.0, GraphPad Software). As the storage temperature decreased from $30^{\circ}C$ to $4^{\circ}C$, the SGR decreased, respectively. Polynomial model was identified as appropriate secondary model for SGR on the basis of most statistical indices such as mean square error (MSE=0.002718 by Gompertz, 0.055186 by Baranyi), bias factor (Bf=1.050084 by Gompertz, 1.931472 by Baranyi) and accuracy factor (Af=1.160767 by Gompertz, 2.137181 by Baranyi). Results indicate L. monocytogenes growth was affected by temperature mainly, and equation was developed by Gompertz model (-0.1606+$0.0574^*Temp$+$0.0009^*Temp^*Temp$) was more effective than equation was developed by Baranyi model (0.3502-$0.0496^*Temp$+$0.0022^*Temp^*Temp$) for specific growth rate prediction of L.monocytogenes in the mixed fresh-cut vegetables.

Quantitative Analysis of Magnetization Transfer by Phase Sensitive Method in Knee Disorder (무릎 이상에 대한 자화전이 위상감각에 의한 정량분석법)

  • Yoon, Moon-Hyun;Sung, Mi-Sook;Yin, Chang-Sik;Lee, Heung-Kyu;Choe, Bo-Young
    • Investigative Magnetic Resonance Imaging
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    • v.10 no.2
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    • pp.98-107
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    • 2006
  • Magnetization Transfer (MT) imaging generates contrast dependent on the phenomenon of magnetization exchange between free water proton and restricted proton in macromolecules. In biological materials in knee, MT or cross-relaxation is commonly modeled using two spin pools identified by their different T2 relaxation times. Two models for cross-relaxation emphasize the role of proton chemical exchange between protons of water and exchangeable protons on macromolecules, as well as through dipole-dipole interaction between the water and macromolecule protons. The most essential tool in medical image manipulation is the ability to adjust the contrast and intensity. Thus, it is desirable to adjust the contrast and intensity of an image interactively in the real time. The proton density (PD) and T2-weighted SE MR images allow the depiction of knee structures and can demonstrate defects and gross morphologic changes. The PD- and T2-weighted images also show the cartilage internal pathology due to the more intermediate signal of the knee joint in these sequences. Suppression of fat extends the dynamic range of tissue contrast, removes chemical shift artifacts, and decreases motion-related ghost artifacts. Like fat saturation, phase sensitive methods are also based on the difference in precession frequencies of water and fat. In this study, phase sensitive methods look at the phase difference that is accumulated in time as a result of Larmor frequency differences rather than using this difference directly. Although how MT work was given with clinical evidence that leads to quantitative model for MT in tissues, the mathematical formalism used to describe the MT effect applies to explaining to evaluate knee disorder, such as anterior cruciate ligament (ACL) tear and meniscal tear. Calculation of the effect of the effect of the MT saturation is given in the magnetization transfer ratio (MTR) which is a quantitative measure of the relative decrease in signal intensity due to the MT pulse.

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A Study of Organic Matter Fraction Method of the Wastewater by using Respirometry and Measurements of VFAs on the Filtered Wastewater and the Non-Filtered Wastewater (여과한 하수와 하수원액의 VFAs 측정과 미생물 호흡률 측정법을 이용한 하수의 유기물 분액 방법에 관한 연구)

  • Kang, Seong-wook;Cho, Wook-sang
    • Journal of the Korea Organic Resources Recycling Association
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    • v.17 no.1
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    • pp.58-72
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    • 2009
  • In this study, the organic matter and biomass was characterized by using respirometry based on ASM No.2d (Activated Sludge Model No.2d). The activated sludge models are based on the ASM No.2d model, published by the IAWQ(International Association on Water Quality) task group on mathematical modeling for design and operation of biological wastewater treatment processes. For this study, OUR(Oxygen Uptake Rate) measurements were made on filtered as well as non-filtered wastewater. Also, GC-FID and LC analysis were applied for the estimation of VFAs(Volatile Fatty Acids) COD(S_A) in slowly bio-degradable soluble substrates of the ASM No.2d. Therefore, this study was intended to clearly identify slowly bio-degradable dissolved materials(S_S) and particulate materials(X_I). In addition, a method capable of determining the accurate time to measure non-biodegradable COD(S_I), by the change of transition graphs in the process of measuring microbial OUR, was presented in this study. Influent fractionation is a critical step in the model calibrations. From the results of respirometry on filtered wastewater, the fraction of fermentable and readily biodegradable organic matter(S_F), fermentation products(S_A), inert soluble matter(S_I), slowly biodegradable matter(X_S) and inert particular matter(X_I) was 33.2%, 14.1%, 6.9%, 34.7%, 5.8%, respectively. The active heterotrophic biomass fraction(X_H) was about 5.3%.

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Estimation and Methods Estimating Daily Food Consumption of Agrammus agrammus (노래미, Agrammus agrammus의 일간섭식량 추정법과 추정)

  • KIM Chong-Kwan;KANG Yong-Joo
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.25 no.4
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    • pp.241-250
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    • 1992
  • This study was covered the amount of food consumed per day as well as methods estimating the daily food consumption per fish of Agrammus agrammus in natural population to understand flow of food organisms among trophic levels in bio-community of the coastal waters, Shinsudo, Samchonpo. The estimating formulas were induced from the mathematical models that representing the diurnal fluctuation of the stomach fullness of the fish. The daily food consumption could be estimated by both feeding rates and gastric evacuation rates, but it was more reasonable method that based on gastric evacuation rates than feeding rates. The daily food consumption in wet weight per fish by gastric evacuation rates were 1.9856g/day, 3.4725g/day, 4.4418g/day, 5.8168g/day, and 7.2113g/day in the order of age groups from 0 to 4. The daily rations as percentage of body weight were $9.35\%,\;6.65\%,\;5.76\%,\;4.72\%\;and\;5.31\%$ in the order of ages. The daily food consumption was proportional to the body weight of fish, but the daily food consumption per specific body weight was reciprocal to the body weight. Annual food consumption in wet weight. per fish by gastric evacuation rates were 529.98g from the age of 0.25 to 1.0, 1,269.28g from the age of 1.0 to 2.0, 1,622.76g from the age of 2.0 to 3.0, 2,125.57g from the age of 3.0 to 4.0, 1,316.09g from the age of 4.0 to 4.5 The amount of food consumed per fish during 4.25 years, from the age of 0.25 to 4.5, was 6,863.68g in wet weight. the relationships between the daily food consumption(Dr) by gastric evacuation rates and the total length(L, cm) or the body weight(W, g) were as follows: $$Dr=0.036L^{1.702}$$ $$Dr=0.254W^{0.664}$$

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Development of a predictive model describing the growth of Staphylococcus aureus in processed meat product galbitang (식육추출가공품 중 갈비탕에서의 Staphylococcus aureus 성장예측모델 개발)

  • Son, Na-Ry;Kim, An-Na;Choi, Won-Seok;Yoon, Sang-Hyun;Suh, Soo-Hwan;Joo, In-Sun;Kim, Soon-Han;Kwak, Hyo-Sun;Cho, Joon-Il
    • Korean Journal of Food Science and Technology
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    • v.49 no.3
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    • pp.274-278
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    • 2017
  • In this study, predictive mathematical models were developed to estimate the kinetics of Staphylococcus aureus growth in processed meat product galbitang. Processed meat product galbitang was inoculated with 0.1 mL of S. aureus culture and stored at 4, 10, 20, $37^{\circ}C$. The ${\mu}_{max}$ (maximum specific growth rate) and LPD (lag phase duration) values were calculated. The primary model was used to develop a response surface secondary model. The growth parameters were analyzed using the square root model as a function of storage temperature. The developed model was confirmed by calculating RMSE (Root Mean Square Error) values as statistic parameters. The LPD decreased, but ${\mu}_{max}$ increased with an increase in the storage temperature. At 4, 10, 20 and $37^{\circ}C$, $R^2$ was 0.99, 0.98, 0.99 and 0.99, respectively; RMSE was 0.39. The developed predictive growth model can be used to predict the risk of S. aureus contamination in processed meat product galbitang; hence, it has potential as an input model for the risk assessment.

Corporate Bond Rating Using Various Multiclass Support Vector Machines (다양한 다분류 SVM을 적용한 기업채권평가)

  • Ahn, Hyun-Chul;Kim, Kyoung-Jae
    • Asia pacific journal of information systems
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    • v.19 no.2
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    • pp.157-178
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    • 2009
  • Corporate credit rating is a very important factor in the market for corporate debt. Information concerning corporate operations is often disseminated to market participants through the changes in credit ratings that are published by professional rating agencies, such as Standard and Poor's (S&P) and Moody's Investor Service. Since these agencies generally require a large fee for the service, and the periodically provided ratings sometimes do not reflect the default risk of the company at the time, it may be advantageous for bond-market participants to be able to classify credit ratings before the agencies actually publish them. As a result, it is very important for companies (especially, financial companies) to develop a proper model of credit rating. From a technical perspective, the credit rating constitutes a typical, multiclass, classification problem because rating agencies generally have ten or more categories of ratings. For example, S&P's ratings range from AAA for the highest-quality bonds to D for the lowest-quality bonds. The professional rating agencies emphasize the importance of analysts' subjective judgments in the determination of credit ratings. However, in practice, a mathematical model that uses the financial variables of companies plays an important role in determining credit ratings, since it is convenient to apply and cost efficient. These financial variables include the ratios that represent a company's leverage status, liquidity status, and profitability status. Several statistical and artificial intelligence (AI) techniques have been applied as tools for predicting credit ratings. Among them, artificial neural networks are most prevalent in the area of finance because of their broad applicability to many business problems and their preeminent ability to adapt. However, artificial neural networks also have many defects, including the difficulty in determining the values of the control parameters and the number of processing elements in the layer as well as the risk of over-fitting. Of late, because of their robustness and high accuracy, support vector machines (SVMs) have become popular as a solution for problems with generating accurate prediction. An SVM's solution may be globally optimal because SVMs seek to minimize structural risk. On the other hand, artificial neural network models may tend to find locally optimal solutions because they seek to minimize empirical risk. In addition, no parameters need to be tuned in SVMs, barring the upper bound for non-separable cases in linear SVMs. Since SVMs were originally devised for binary classification, however they are not intrinsically geared for multiclass classifications as in credit ratings. Thus, researchers have tried to extend the original SVM to multiclass classification. Hitherto, a variety of techniques to extend standard SVMs to multiclass SVMs (MSVMs) has been proposed in the literature Only a few types of MSVM are, however, tested using prior studies that apply MSVMs to credit ratings studies. In this study, we examined six different techniques of MSVMs: (1) One-Against-One, (2) One-Against-AIL (3) DAGSVM, (4) ECOC, (5) Method of Weston and Watkins, and (6) Method of Crammer and Singer. In addition, we examined the prediction accuracy of some modified version of conventional MSVM techniques. To find the most appropriate technique of MSVMs for corporate bond rating, we applied all the techniques of MSVMs to a real-world case of credit rating in Korea. The best application is in corporate bond rating, which is the most frequently studied area of credit rating for specific debt issues or other financial obligations. For our study the research data were collected from National Information and Credit Evaluation, Inc., a major bond-rating company in Korea. The data set is comprised of the bond-ratings for the year 2002 and various financial variables for 1,295 companies from the manufacturing industry in Korea. We compared the results of these techniques with one another, and with those of traditional methods for credit ratings, such as multiple discriminant analysis (MDA), multinomial logistic regression (MLOGIT), and artificial neural networks (ANNs). As a result, we found that DAGSVM with an ordered list was the best approach for the prediction of bond rating. In addition, we found that the modified version of ECOC approach can yield higher prediction accuracy for the cases showing clear patterns.

Study on Tumor Control Probability and Normal Tissue Complication Probability in 3D Conformal Radiotherapy (방사선 입체조형치료에 대한 종양치유확율과 정상조직손상확율에 관한 연구)

  • 추성실
    • Progress in Medical Physics
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    • v.9 no.4
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    • pp.227-245
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    • 1998
  • A most appropriate model of 3-D conformal radiotherapy has been induced by clinical evaluation and animal study, and therapeutic gains were evaluated by numerical equation of tumor control probability(TCP) and normal tissue complication probability (NTCP). The radiation dose to the tumor and the adjacent normal organs was accurately evaluated and compared using the dose volume histogram(DVH). The TCP and NTCP was derived from the distribution of given dosage and irradiated volume, and these numbers were used as the biological index for the assessment of the treatment effects. Ten patients with liver disease have been evaluated and 3 dogs were sacrificed for this study. Based on the 3-D images of the tumor and adjacent organs, the optimum radiation dose and the projection direction which could maximize the radiation effect while minimizing the effects to the adjacent organs could be decided. 3). The most effective collimation for the normal adjacent organs was made through the beams eye view with the use of multileaf collimator. When the dose was increased from 50Gy to 70Gy, the TCP for the conventional 2-port radiation and the 5-port multidimensional therapy was 0.982 and 0.995 respectively, while the NTCP was 0.725 and 0.142 respectively, suggesting that the 3-D conformal radiotherapy might be the appropriate therapy to apply sufficient radiation dose to the tumor while minimizing the damages to the normal areas of the liver. Positive correlation was observed between the NTCP and the actual complication of the normal liver in the animal study. The present study suggest that the use of 3-D conformal radiotherapy and the application of the mathematical models of TCP and NTCP may provide the improvements in the treatment of hepatoma with enhanced results.

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