• Journal of Biomedical Engineering Research
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• v.16 no.2
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• pp.223-230
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• 1995

This study investigates a combined mathematical model for the quantitative estimation of regional myocardial blood flow in experimental canine coronary artery occlusion and in patients with ischemic myocardial diseases using Rb-82 dynamic myocardial positron emission tomography. The coronary thrombosis was induced using the new catheter technique by narrowing the lumen of coronary vessel gradually, which finally led to partial obstruction of coronary artery. Thirty four Rb-82 dynamic myocardial PET scans were performed sequentially for each experiment using our 5, 10 and 20 second acquisition protocol, respectively, and six to seven regions of interest were drawn on each transaxial slices, one on left ventricular chamber for input function and the others on normal and decreased perfusion myocardial segments for the flow estimation in those regions. Two compartment model and graphical analysis method have been applied to the measured sets of regional PET data, and the rate constants of influx to myocardial tissue were calculated for regional myocardial flow estimates with the two parameter fits of raw data by the Levenberg-Marquardt method. The results showed that, (I) two compartment model suggested by Kety-Schmidt, with proper modification of the measured data and volume of distribution, could be used for the simple estimation of regional myocardial blood flow, (2) the calculated regional myocardial blood flow estimates were dependent on the selection of input function, which reflected partial volume effect and left ventricular wall motion in previously used graphical analysis, and (3) mathematically fitted input and tissue time activity curves were more suitable than the direct application of the measured data in terms of convergence.

• School Mathematics
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• v.19 no.1
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• pp.95-116
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• 2017

Through the teaching experiments, we investigated a series of processes for obtaining the differential coefficient at x=0 of the exponential function $y=2^x$ based on the process of constructing the natural constant e and the understanding of it. and all of the students who participated in this study were students who had no experience of calculating the derivative of the exponential function. The purpose of this study was not to generalize the responses of students but to suggest implications for mathematical concept mapping related to calculus by analyzing various responses of students participating in experiments. It is expected that the accumulation of research data derived in this kind of research on the way of understanding and composition of learners will be an important basic data for presenting the learning model related to calculus.

• Structural Engineering and Mechanics
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• v.53 no.3
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• pp.537-573
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• 2015

Multiple-step beams carrying intermediate lumped masses with/without rotary inertias are widely used in engineering applications, but in the literature for free vibration analysis of such structural systems; Bernoulli-Euler Beam Theory (BEBT) without axial force effect is used. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass systems, Bernoulli-Euler multiple-step and multi-span beams carrying multiple spring-mass systems and multiple point masses are plenty, but that of Timoshenko multiple-step beams carrying intermediate lumped masses and/or rotary inertias with axial force effect is fewer. The purpose of this paper is to utilize Numerical Assembly Technique (NAT) and Differential Transform Method (DTM) to determine the exact natural frequencies and mode shapes of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and/or rotary inertias. The model allows analyzing the influence of the shear and axial force effects, intermediate lumped masses and rotary inertias on the free vibration analysis of the multiple-step beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate lumped mass with rotary inertia, the step change in cross-section, left-end support and right-end support of the multiple-step Timoshenko beam are derived from the analytical solution. After the derivation of the coefficient matrices, NAT is used to establish the overall coefficient matrix for the whole vibrating system. Finally, equating the overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equations of the motion. The calculated natural frequencies of Timoshenko multiple-step beam carrying intermediate lumped masses and/or rotary inertias for the different values of axial force are given in tables. The first five mode shapes are presented in graphs. The effects of axial force, intermediate lumped masses and rotary inertias on the free vibration analysis of Timoshenko multiple-step beam are investigated.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.491-504
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• 2018

Because of sandwich structures with low weight and high stiffness have much usage in various industries such as civil and aerospace engineering, in this article, buckling and free vibration analyses of coupled micro composite sandwich plates are investigated based on sinusoidal shear deformation (SSDT) and most general strain gradient theories (MGSGT). It is assumed that the sandwich structure rested on an orthotropic elastic foundation and make of four composite face sheets with temperature-dependent material properties that they reinforced by carbon and boron nitride nanotubes and two flexible transversely orthotropic cores. Mathematical formulation is presented using Hamilton's principle and governing equations of motions are derived based on energy approach and applying variation method for simply supported edges under electro-magneto-thermo-mechanical, axial buckling and pre-stresses loadings. In order to predict the effects of various parameters such as material length scale parameter, length to width ratio, length to thickness ratio, thickness of face sheets to core thickness ratio, nanotubes volume fraction, pre-stress load and orthotropic elastic medium on the natural frequencies and critical buckling load of double-bonded micro composite sandwich plates. It is found that orthotropic elastic medium has a special role on the system stability and increasing Winkler and Pasternak constants lead to enhance the natural frequency and critical buckling load of micro plates, while decrease natural frequency and critical buckling load with increasing temperature changes. Also, it is showed that pre-stresses due to help the axial buckling load causes that delay the buckling phenomenon. Moreover, it is concluded that the sandwich structures with orthotropic cores have high stiffness, but because they are not economical, thus it is necessary the sandwich plates reinforce by carbon or boron nitride nanotubes specially, because these nanotubes have important thermal and mechanical properties in comparison of the other reinforcement.

• Korean Journal of Food Science and Technology
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• v.19 no.6
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• pp.463-470
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• 1987

In order to develop a rapid predicting method of the shelf-life of moisture sensitive foods and establish their proper packaging methods, the qualify changes and shelf-life of dired laver as a model food were studied by the computer simulation. A mathematical model of the relationship between the rate constants of chlorophyll a and water activity was established at $10^{\circ}C,\;25^{\circ}C$ and $40^{\circ}C$. Computer simulation to predict water activity and chlorophyll a was developed by considering the simultaneous influence of storage conditions such as water content of products, storage temperature and relative humidity, packaging materials. Simulated quality changes of dried laver was in good agreement with the experiment data. Chlorophyll a and sensory score decreased as the water activity increased. And correlation coefficient between the sensory scores and the contents of chlorophyll a was very high as 0.991. The critical water activity by sensory evaluation was around 0.55. The shelf-life of dried laver packaged with plastic films could be predicted from the above results in various storage conditions.

• Structural Engineering and Mechanics
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• v.21 no.6
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• pp.713-735
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• 2005

Due to the complexity of mathematical expressions, the literature concerning the free vibration analysis of plates carrying multiple three-degree-of-freedom (dof) spring-mass systems is rare. In this paper, the three degrees of freedom (dof's) for a spring-mass system refer to the translational motion of its lumped mass in the vertical ($\bar{z}$) direction and the two pitching motions of its lumped mass about the two horizontal ($\bar{x}$ and $\bar{y}$) axes. The basic concept of this paper is to replace each three-dof spring-mass system by a set of equivalent springs, so that the free vibration characteristics of a rectangular plate carrying any number of three-dof spring-mass systems can be obtained from those of the same plate supported by the same number of sets of equivalent springs. Since the three dof's of the lumped mass for each three-dof spring-mass system are eliminated to yield a set of equivalent springs, the total dof of the entire vibrating system is not affected by the total number of the spring-mass systems attached to the rectangular plate. However, this is not true in the conventional finite element method (FEM), where the total dof of the entire vibrating system increases three if one more three-dof spring-mass system is attached to the rectangular plate. Hence, the computer storage memory required by using the presented equivalent spring method (ESM) is less than that required by the conventional FEM, and the more the total number of the three-dof spring-mass systems attached to the plate, the more the advantage of the ESM. In addition, since manufacturing a spring with the specified stiffness is much easier than making a three-dof spring-mass system with the specified spring constants and mass magnitude, the presented theory of replacing a three-dof spring-mass system by a set of equivalent springs will be also significant from this viewpoint.

• Food Engineering Progress
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• v.15 no.3
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• pp.214-220
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• 2011

$\beta$-Glucosidase enzyme reaction under high hydrostatic pressure was investigated in terms of physical chemistry. A model substrate (p-nitrophenyl-${\beta}$-D-glucopyranoside(pNPG)) was used, and the pressure effects on the enzymatic hydrolysis (pNPG${\rightarrow}$pNP) at 25 MPa, 50 MPa, 75 MPa, and 100 MPa were analyzed. Two parts of the reaction such as kinetic and equilibrium stages were considered for mathematical modelling, and their physicochemical parameters such as forward and inverse reaction constants, equilibrium constant, volume change by pressure, etc. were mathematically modeled. The product concentration increased with pressure, and the two stages of reaction were observed. Prediction models were derived to numerically compute the product concentrations according to reaction time over kinetic to equilibrium stages under high pressure condition. Conclusively, the $\beta$-Glucosidase enzyme reaction could be activated by pressurization within 100 MPa, and the developed models were very successful in their prediction.

• Journal of the Microelectronics and Packaging Society
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• v.31 no.1
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• pp.23-28
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• 2024

Electronic products utilizing flexible devices experience harsh mechanical deformations in real-use environments. As a result, researches on the mechanical reliability of these flexible devices have attracted considerable interest among researchers. This study employed previous bending strain models and finite element analysis to predict the maximum bending strain of metal films deposited on flexible substrates. Bending experiments were simulated using finite element analysis with variations in the material and thickness of the thin films, and the substrate thickness. The results were compared with the strains predicted by existing models. The distribution of strain on the surface of film was observed, and the error rate of the existing model was analyzed during bending. Additionally, a modified model was proposed, providing mathematical constants for each case.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.12 no.3
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• pp.167-173
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• 1979

It is preented the removable moving screen media-activated sludge (REMSMAS) process by using the biological fixed-film systems. The substrate removal kinetic difference between the aeration-only completed mixing activated sludge (CMAS) process and REMSMAS process were observed. The substrate removal kinetics were developed based on the attached and suspended microbial growths. The units of the aeration-only CMAS process were continously operated with the normal detention time of 4.5, 6, 9.5 and 12 flours studies after steady-state condition and the operating of the REMSMAS units conducted with the normal detention time of 6 and 12 hours studies in nonsteady-state condition. The feed solution was diluted 18 times to the raw starch wastewater in of order to maintain the proper COD (950mg/l) and BOD (450mg/l) concentration. Design parameters related to the suspended microbial growths were caculated by the equations used in the aeration-only CMAS model and these parameters used to evalute the kinetic constants in the REMSMAS process. The kinetic constant values of $Y_2,\;K_d,(\mu_{max})_s\;and\;K_s$ from Monod equations were respectively 0.78, 0.027/hr, 1.1/hr and 95mg/l in the aeration-only CMAS process. The value of the aera capacity (F) appeared to be $9.1\;mg/cm^2-day$ and the mean value of the saturation constant $(K_g)$ appeared to be 53.5 mg/l in the REMSMAs process. Also, the substrate removal .ate of the REMSMAS process was higher than that of the normal activated sludge process when this system was operated in steady-state condition. However, the rate was reduced as the critical operating day was approached.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.1 no.1
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• pp.43-51
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• 1981

A model of substrate utilization witbin bacterial films has been developed and simulated for a better understanding of fixed film treatment processes. The model consists of two parts, a deep biofilm and a thin biofilm, which are classified based on substrate penetration into the biofilm. Substrate concentration and flux within a biofilm can be computed from the model. Three dimensionless parameters, ${\phi}_1$, ${\phi}_2$ and $\bar{S}_b$ were obtained during model construction, and the substrate concentration and flux can be expressed in terms of these parameters. It has been found that an. increase of ${\phi}_1$ or a decrease of ${\phi}_2$ results in an increase of treatment efficiencies. It has also been found that systems maintaining high efficiencies belong to a deep biofilm. Among the constants involved, the mass transfer coefficient is the only controllable term and it depends Largely on fluid velocity near the biofilm surface. Substrate removal efficiency may be increased with an increase of fluid velocity for a biofilm of fixed depth. However, film depth is decreased due to sloughing with increasing velocity, and the system reaches a new steady state. Because changes in film depth are not well defined quantitatively yet, the efficiency can not be clearly described at a new steady state.