• Title/Summary/Keyword: mathematical verification

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The Macroeconomic Production Model in Business Environment - Analying with a Static and Dynamic Equations

  • Donghae LEE
    • Asian Journal of Business Environment
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    • v.14 no.1
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    • pp.23-30
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    • 2024
  • Purpose: The purpose of this research is to explore the macroeconomic model through both static and dynamic equations. The primary objective of this study is to investigate the variations in the elasticity of substitution across changing economic variables within the framework of the Allen-Uzawa production functions. Research, design, data and methodology: The data were drawn from the World Bank's annual central statistical office database from 2010 to 2021 in the United States of America. The level of expenditures and of the public finance sector, macroeconomic data like output, inflation rates, and labor are examined. Results: This study demonstrates the interaction of two equations, clarifying that the macroeconomic model is practical to determining the stability of both static and dynamic equation systems analytically. The Allen-Uzawa equations allow for the verification of macroeconomic model properties, and study results demonstrate an increase in the range of capital uses as a form of mechanization. A constant elasticity of substitution function is derived from the macroeconomic variables. Conclusion: The macroeconomic model, though the analysis of the static and dynamic Allen - Uzawa model, not only facilitates the examination of long-term trends in crucial endogenous variables but also overcomes challenges commonly associated with other mathematical methods. Overall, the analysis promotes economic growth, investment, and employment. The levels of expenditures and the public finance sector, along with macroeconomic data such as output, inflation rates, and labor, are examined.

Data Level Parallelism for H.264/AVC Decoder on a Multi-Core Processor and Performance Analysis (멀티코어 프로세서에서의 H.264/AVC 디코더를 위한 데이터 레벨 병렬화 성능 예측 및 분석)

  • Cho, Han-Wook;Jo, Song-Hyun;Song, Yong-Ho
    • Journal of the Institute of Electronics Engineers of Korea SD
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    • v.46 no.8
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    • pp.102-116
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    • 2009
  • There have been lots of researches for H.264/AVC performance enhancement on a multi-core processor. The enhancement has been performed through parallelization methods. Parallelization methods can be classified into a task-level parallelization method and a data level parallelization method. A task-level parallelization method for H.264/AVC decoder is implemented by dividing H.264/AVC decoder algorithms into pipeline stages. However, it is not suitable for complex and large bitstreams due to poor load-balancing. Considering load-balancing and performance scalability, we propose a horizontal data level parallelization method for H.264/AVC decoder in such a way that threads are assigned to macroblock lines. We develop a mathematical performance expectation model for the proposed parallelization methods. For evaluation of the mathematical performance expectation, we measured the performance with JM 13.2 reference software on ARM11 MPCore Evaluation Board. The cycle-accurate measurement with SoCDesigner Co-verification Environment showed that expected performance and performance scalability of the proposed parallelization method was accurate in relatively high level

A Study on the Development of Feedback-Based Instructional Materials for Process-Focused Assessment Classes in High School Mathematics Classes (고등학교 수학 수업에서 과정 중심 평가 수업을 위한 피드백 중심 수업 자료 개발에 관한 연구)

  • Lee, Dong Gun;Han, Chang Hun
    • Communications of Mathematical Education
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    • v.36 no.1
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    • pp.107-138
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    • 2022
  • This study is a study that developed class materials that can apply Process-Focused Assessment to classes by paying attention to feedback using teacher learning community programs centered on teachers belonging to the same school in the field. In particular, this study was conducted with the aim of developing class materials applicable to actual classes. At this time, We thought about how to provide appropriate feedback when applying course-based evaluation in school field classes. It was conducted according to the procedure of data development research by Lee & Ahn(2021). As for the procedure of data development itself, an evaluation plan was established by establishing a strategy to reconstruct achievement standards and confirm understanding based on curriculum analysis. Next, an evaluation task, a scoring standard table, and a preliminary feedback preparation table were developed. In addition, based on these development materials, a learning guidance plan that can predict scenes when applying actual classes was developed as a result. This study has value as a practical study that can contribute to providing a link between theory and field schools. It is also meaningful in that it considered how the teacher would grasp when to provide feedback in performing rocess-Focused Assessment. Likewise, in providing feedback by teachers, it is meaningful in that it reflects in the data development how to prepare in advance and take classes according to the characteristics of the subject. Finally, it seems that the possibility of field application can be improved in that the results of the 4th class developed in this study are presented in a form applicable to the class directly in the field.

Numerical Verification of Hybrid Optimization Technique for Finite Element Model Updating (유한요소모델개선을 위한 하이브리드 최적화기법의 수치해석 검증)

  • Jung, Dae-Sung;Kim, Chul-Young
    • Journal of the Earthquake Engineering Society of Korea
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    • v.10 no.6 s.52
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    • pp.19-28
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    • 2006
  • Most conventional model updating methods must use mathematical objective function with experimental modal matrices and analytical system matrices or must use information about the gradient or higher derivatives of modal properties with respect to each updating parameter. Therefore, most conventional methods are not appropriate for complex structural system such as bridge structures due to stability problem in inverse analysis with ill-conditions. Sometimes, moreover, the updated model may have no physical meaning. In this paper, a new FE model updating method based on a hybrid optimization technique using genetic algorithm (GA) and Holder-Mead simplex method (NMS) is proposed. The performance of hybrid optimization technique on the nonlinear problem is demonstrated by the Goldstein-Price function with three local minima and one global minimum. The influence of the objective function is evaluated by the case study of a simulated 10-dof spring-mass model. Through simulated case studies, finally, the objective function is proposed to update mass as well as stiffness at the same time. And so, the proposed hybrid optimization technique is proved to be an efficient method for FE model updating.

Development of Stress-Strain Relationship Considering Strength and Age of Concrete (콘크리트의 강도와 재령을 고려한 응력-변형률 관계식의 개발)

  • 오태근;이성태;김진근
    • Journal of the Korea Concrete Institute
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    • v.13 no.5
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    • pp.447-456
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    • 2001
  • Many investigators have tried to represent the nonlinear behavior of stress-strain relationship of concrete using mathematical curves. Most of empirical expressions for stress-strain relationship, however, have focused on old age concrete, and were not able to represent well the behavior of concrete at an early age. Where wide understanding on the behavior of concrete from early age to old age is very important in evaluating the durability and service life of concrete structures. In this paper, effect of 5 different strength levels and ages of from 12 hours to 28 days on compressive stress-strain relationship was observed experimentally and analytically. Tests were carried out on $\phi$100${\times}$200mm cylindrical specimens water-cured at 20${\pm}$3$^{\circ}C$. An analytical expression of stress-stain relationship with strength and age was developed using regression analyses on experimental results. For the verification of the proposed model, the model was compared with present and existing experimental data and some existing models. The analysis shows that the proposed model predicts well experimental data and describes well effect of strength and age on stress-strain relationship.

The Separating Cover Using an Explosive Bolt and Spring Lever (폭발볼트 및 스프링 레버를 이용한 발사관 분리식 덮개)

  • Choi, Won-Hong;Shin, Sang-Mok
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.45 no.11
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    • pp.922-931
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    • 2017
  • This research paper describes design procedures and those verification with multi-body dynamic analysis and an experiment for the development of an unprecedented type of canister cover, named as the separating cover. In order to overcome drawbacks from the precious rupture type and actuator driven cover, the separating cover was suggested. It has the simplest structure composed of the previously developed explosive bolt and a spring-lever driven system. First of all, mechanical feasibility with proposed design parameters based on mathematical modeling was confirmed through dynamic analysis and then its results showed good agreement with the followed empirical results acquired from a high speed camera. On top of that, a parametric study was conducted to identify the effect of each design parameter on separating performance. It is highly expected that this research contributes to provide military industries with a brand new canister cover having simplicity and cost efficiency and thus it will be very useful in MLRS(Multiple Launch Rocket System).

Prediction and Verification of Hover Performance through Multi-Copter Propulsion System Test Results (멀티콥터의 추진 시스템 실험 결과를 통한 제자리 비행 성능 예측 및 검증)

  • Park, Seungho;Go, Yeong-Ju;Ryi, Jaeha;Choi, Jong-Soo
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.46 no.7
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    • pp.527-534
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    • 2018
  • The endurance of the multi-copter is one of the important variables that determine the mission performance. Therefore, accurate endurance should be defined as essential for performing effective missions. In this paper, we present the results of the study on the flight performance of the aircraft, especially the hovering of the drone(multi-copter). Unlike conventional aircraft, which consider aerodynamic performance by the fuselage, the multi-copter is mostly determined by the propulsion system. Therefore, the research method classifies the various parts constituting the drone system into functions, analyzes the performance of the unit parts and obtains the experimental data by sorting out the specifications and functions at the component level and mathematical formulation, The results of this study are as follows. In addition, the 5kg class quad copter was used to predict and verify the voltage change with endurance through analysis of in situ flight. By predicting endurance under various conditions, it can help design/build the right Multi-copter for mission.

Prediction Models of Residual Chlorine in Sediment Basin to Control Pre-chlorination in Water Treatment Plant (정수장 전염소 공정 제어를 위한 침전지 잔류 염소 농도 예측모델 개발)

  • Lee, Kyung-Hyuk;Kim, Ju-Hwan;Lim, Jae-Lim;Chae, Seon Ha
    • Journal of Korean Society of Water and Wastewater
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    • v.21 no.5
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    • pp.601-607
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    • 2007
  • In order to maintain constant residual chlorine in sedimentation basin, It is necessary to develop real time prediction model of residual chlorine considering water treatment plant data such as water qualities, weather, and plant operation conditions. Based on the operation data acquired from K water treatment plant, prediction models of residual chlorine in sediment basin were accomplished. The input parameters applied in the models were water temperature, turbidity, pH, conductivity, flow rate, alkalinity and pre-chlorination dosage. The multiple regression models were established with linear and non-linear model with 5,448 data set. The corelation coefficient (R) for the linear and non-linear model were 0.39 and 0.374, respectively. It shows low correlation coefficient, that is, these multiple regression models can not represent the residual chlorine with the input parameters which varies independently with time changes related to weather condition. Artificial neural network models are applied with three different conditions. Input parameters are consisted of water quality data observed in water treatment process based on the structure of auto-regressive model type, considering a time lag. The artificial neural network models have better ability to predict residual chlorine at sediment basin than conventional linear and nonlinear multi-regression models. The determination coefficients of each model in verification process were shown as 0.742, 0.754, and 0.869, respectively. Consequently, comparing the results of each model, neural network can simulate the residual chlorine in sedimentation basin better than mathematical regression models in terms of prediction performance. This results are expected to contribute into automation control of water treatment processes.

Robust Optimization Using Supremum of the Objective Function for Nonlinear Programming Problems (비선형계획법에서 목적함수의 상한함수를 이용한 강건최적설계)

  • Lee, Se Jung;Park, Gyung Jin
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.38 no.5
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    • pp.535-543
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    • 2014
  • In the robust optimization field, the robustness of the objective function emphasizes an insensitive design. In general, the robustness of the objective function can be achieved by reducing the change of the objective function with respect to the variation of the design variables and parameters. However, in conventional methods, when an insensitive design is emphasized, the performance of the objective function can be deteriorated. Besides, if the numbers of the design variables are increased, the numerical cost is quite high in robust optimization for nonlinear programming problems. In this research, the robustness index for the objective function and a process of robust optimization are proposed. Moreover, a method using the supremum of linearized functions is also proposed to reduce the computational cost. Mathematical examples are solved for the verification of the proposed method and the results are compared with those from the conventional methods. The proposed approach improves the performance of the objective function and its efficiency.

Performance and Thermal Design Validation for FM STEP Cube Lab. (큐브위성 STEP Cube Lab. 비행 모델의 열진공시험을 통한 성능 및 열제어계 설계 검증)

  • Kang, Soo-Jin;Jung, Hyun-Mo;Seo, Joung-Ki;Oh, Hyun-Ung
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.43 no.9
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    • pp.814-821
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    • 2015
  • The STEP Cube Lab. classified as a pico-class satellite has been successfully developed as a flight model(FM) to be launched in 2015. Its mission objective is to perform the on-orbit verification of fundamental space core-technologies. In this study, a thermal design concept based on the passive method to achieve the mission objective is introduced. The effectiveness of the thermal design and performance of the satellite has been verified through the acceptance level thermal vacuum test. In addition, to improve the reliability of thermal mathematical model, correlation was performed using the results of thermal balance test. This paper describes a series of process for the thermal vacuum test on the STEP Cube Lab. FM.