• Title/Summary/Keyword: Mathematical concept

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Improvement of the Convergence Capability of a Single Loop Single Vector Approach Using Conjugate Gradient for a Concave Function (오목한 성능함수에서 공액경사도법을 이용한 단일루프 단일벡터 방법의 수렴성 개선)

  • Jeong, Seong-Beom;Lee, Se-Jung;Park, Gyung-Jin
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.36 no.7
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    • pp.805-811
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    • 2012
  • The reliability based design optimization (RBDO) approach requires high computing cost to consider uncertainties. In order to reduce the design cost, the single loop single vector (SLSV) approach has been developed for RBDO. This method can reduce the cost in calculating deign sensitivity by elimination of the nested optimization process. However, this process causes the increment of the instability or inaccuracy of the method according to the problem characteristics. Therefore, the method may not give accurate solution or the robustness of the solution is not guaranteed. Especially, when the function is concave, the process frequently diverges. In this research, the concept of the conjugate gradient method for unconstrained optimization is utilized to develop a new single loop single vector method. The conjugate gradient is calculated with gradient directions at the most probable points (MPP) of previous cycles. Mathematical examples are solved for the verification of the proposed method. The numeri cal performances of the obtained results are compared to those of other RBDO methods. The SLSV approach using conjugate gradient is not greatly influenced by the problem characteristics and improves its convergence capability.

A Study on Teaching Figures Based on van Hiele's Theory - Focused on the 4th Graders - (van Hiele의 학습단계에 따른 초등학교 4학년의 도형지도 방안연구)

  • Seo, Eun-Young;Chang, Hye-Won
    • Education of Primary School Mathematics
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    • v.13 no.2
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    • pp.85-97
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    • 2010
  • The purpose of this study is to develop a teaching program in consideration of the geometrical thinking levels of students to make a contribution to teaching figures effectively. To do this, we checked the geometrical thinking levels of fourth-graders, developed a teaching program based on van Hiele's theory, and investigated its effect on their geometrical thinking levels. The teaching program based on van Hiele's theory put emphasis on group member interaction and specific activities through offering various geometrical experiences. It contributed to actualizing activity-centered, student-oriented, inquiry-oriented and inductive instruction instead of sticking to expository, teacher-led and deductive instruction. And it consequently served to improving their geometrical thinking levels, even though some students didn't show any improvement and one student was rather degraded in that regard - but in the former case they made partial progress though there was little marked improvement, and in the latter case she needs to be considered in relation to her affective aspects above all. The findings of the study suggest that individual variances in thinking level should be recognized by teachers. Students who are at a lower level should be given easier tasks, and more challenging tasks should be assigned to those who are at an intermediate level in order for them to have a positive self-concept about mathematics learning and ultimately to foster their thinking levels.

Modeling of CO2 Emission from Soil in Greenhouse

  • Lee, Dong-Hoon;Lee, Kyou-Seung;Choi, Chang-Hyun;Cho, Yong-Jin;Choi, Jong-Myoung;Chung, Sun-Ok
    • Horticultural Science & Technology
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    • v.30 no.3
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    • pp.270-277
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    • 2012
  • Greenhouse industry has been growing in many countries due to both the advantage of stable year-round crop production and increased demand for fresh vegetables. In greenhouse cultivation, $CO_2$ concentration plays an essential role in the photosynthesis process of crops. Continuous and accurate monitoring of $CO_2$ level in the greenhouse would improve profitability and reduce environmental impact, through optimum control of greenhouse $CO_2$ enrichment and efficient crop production, as compared with the conventional management practices without monitoring and control of $CO_2$ level. In this study, a mathematical model was developed to estimate the $CO_2$ emission from soil as affected by environmental factors in greenhouses. Among various model types evaluated, a linear regression model provided the best coefficient of determination. Selected predictor variables were solar radiation and relative humidity and exponential transformation of both. As a response variable in the model, the difference between $CO_2$ concentrations at the soil surface and 5-cm depth showed are latively strong relationship with the predictor variables. Segmented regression analysis showed that better models were obtained when the entire daily dataset was divided into segments of shorter time ranges, and best models were obtained for segmented data where more variability in solar radiation and humidity were present (i.e., after sun-rise, before sun-set) than other segments. To consider time delay in the response of $CO_2$ concentration, concept of time lag was implemented in the regression analysis. As a result, there was an improvement in the performance of the models as the coefficients of determination were 0.93 and 0.87 with segmented time frames for sun-rise and sun-set periods, respectively. Validation tests of the models to predict $CO_2$ emission from soil showed that the developed empirical model would be applicable to real-time monitoring and diagnosis of significant factors for $CO_2$ enrichment in a soil-based greenhouse.

Design and Performance Evaluation of Low-Temperature Vacuum Blackbody System (저온-진공 흑체시스템의 설계 및 성능 평가)

  • Kim, Ghiseok;Chang, Ki Soo;Lee, Sang-Yong;Kim, Geon-Hee;Kim, Dong-Ik
    • Journal of the Korean Society for Nondestructive Testing
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    • v.33 no.4
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    • pp.336-341
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    • 2013
  • In this paper, the design concept of a low-temperature vacuum blackbody was described, and thermophysical model of the blackbody was numerically evaluated. Also the working performance of low-temperature vacuum blackbody was evaluated using infrared camera system. The blackbody system was constructed to operate under high-vacuum conditions ($2.67{\times}10^{-2}$ Pa) to reduce temperature uncertainty, which is caused by vapor condensation at low temperatures usually below 273 K. In addition, both heat sink and heat shield including cold shield were installed around radiator to prevent heat loss from the blackbody. Simplified mathematical model of blackbody radiator was analyzed using modified Stefan-Boltzmann's rule. The infrared radiant performance of the blackbody was evaluated using infrared camera. Based on the results of measurements, and simulation, temperature stability of the low-temperature vacuum blackbody demonstrated that the blackbody system can serve as a highly stable reference source for the calibration of an infrared optical system.

Comparative Analyses of Mass Marketing and Target Marketing Based on Price Elasticity and Production Cost (가격탄력성과 생산비용에 기초한 대량 마케팅과 표적시장 마케팅의 비교 분석)

  • Won, Jee Sung
    • Journal of Distribution Science
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    • v.11 no.4
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    • pp.61-72
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    • 2013
  • Purpose - It is widely accepted that the process of developing marketing strategy is composed of three steps: market segmentation, target market selection and positioning. However, mass marketing strategy based on cost reduction through economies of scale and standardized products, can be also an effective strategic option. Many marketing scholars including Theodore Levitt emphasize the importance of applying the mass production concept to various industries including service industries. Especially, in times of economic downturn, the capability of providing consumers with low-priced, value products can be an important source of competitive advantage, as well as the ability of providing high-priced premium products. Marketers should decide whether they will implement mass marketing strategy or target marketing strategy. The present study theoretically shows that firms should understand the target customers' price elasticity as well as the firm's cost structure in order to make such a strategic decision. Research design, data, and methodology - Instead of implementing an empirical study, this study provides a theoretical(mathematical) investigation on the effect of consumers' price elasticity on a firm's optimal price level, profit, sales volume, revenue, and cost. The results are mostly deduced from derivative calculations and several graphs are utilized to represent the results on the relationships between the variables under study. Results - The analytical results suggest that it is more profitable for a firm to adopt the segment/target marketing strategy (more specifically the differentiation strategy) when the degree of consumers' heterogeneity is high and the proportion of the fixed cost in the total cost is low. On the other hand, if the degree of consumers' heterogeneity is low and the fixed cost is high, it is better to adopt the mass marketing strategy or the cost leadership strategy. The strategy of concentrating on a single target market will be effective when consumers' needs are highly heterogeneous but the fixed cost is high. Any of the three types of generic strategies proposed my Porter(1980, 1985) can be applied when both the consumers' heterogeneity and the fixed cost are low. This study also proposes the contribution-margin-based method for developing the optimal pricing strategy. Conclusions - One of the primary roles of marketers is to find a proper compromise between the two conflicting goals of maximizing customer satisfaction and minimizing cost. In order to do so, he or she should understand the characteristics of the target customers as well as the cost structure of the firm. In addition to the theoretical analyses, this study discusses several business cases and explains how superior companies find the optimal compromise position between these two goals and dominate the market. One of the radical changes recently taking place in business arena is the reduction of production and distribution costs of both physical goods and information due to the advancement and the wide diffusion of information technology. The cost reduction combined with lowered priced elasticity incurred by customized products and services, will enable many firms to adopt the mass customization strategy.

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A Comparative Study of Elementary School Mathematics Textbooks between Korea and Japan - Focused on the 4th Grade - (한국과 일본의 초등학교 수학교과서 비교 연구 - 4학년을 중심으로 -)

  • Lee, Jae-Chun;Kim, Seon-Yu;Kang, Hong-Jae
    • Journal of Elementary Mathematics Education in Korea
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    • v.13 no.1
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    • pp.1-15
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    • 2009
  • This research is to provide a useful reference for the future revision of textbook by comparative analysis with the textbook in the 4th grade of elementary school in Japan. The results from this research is same as follows: First, Korean curriculum is emphasizing the reasonable problem-solving ability developed on the base of the mathematical knowledge and skill. Meantime, Japanese puts much value on the is focusing on discretion and the capability in life so that they emphasize each person's learning and raising the power of self-learning and thinking. The ratio on mathematics in both company are high, but Japanese ensures much more hours than Korean. Second, the chapter of Korean textbook is composed of 8 units and the title of the chapter is shown as key word, then the next objects are describes as 'Shall we do$\sim$' type. Hence, the chapter composition of Japanese textbook is different among the chapter and the title of the chapter is described as 'Let's do$\sim$'. Moreover, Korean textbook is arranged focusing on present study, however Japanese is composed with each independent segments in the present study subject to the study contents. Third, Japanese makes students understand the decimal as the extension of the decimal system with measuring unit($\ell$, km, kg) then, learn the operation by algorithm. In Korea, students learn fraction earlier than decimal, but, in Japan students learn decimal earlier than fraction. For the diagram, in Korea, making angle with vertex and side comes after the concept of angle, vertex and side is explained. Hence, in Japan, they show side and vertex to present angle.

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A Study on Learning and Teaching Environments for Computers and Mathematics Education ('컴퓨터와 수학교육' 학습-지도 환경에 관한 연구)

  • Kim, Hwa-Kyung
    • Journal of Educational Research in Mathematics
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    • v.16 no.4
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    • pp.367-386
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    • 2006
  • There are two strands for considering tile relationships between education and technology. One is the viewpoint of 'learning from computers' and the other is that of 'learning with computers'. In this paper, we call mathematics education with computers as 'computers and mathematics education' and this computer environments as microworlds. In this paper, we first suggest theoretical backgrounds ai constructionism, mathematization, and computer interaction. These theoretical backgrounds are related to students, school mathematics and computers, relatively As specific strategies to design a microworld, we consider a physical construction, fuctiionization, and internet interaction. Next we survey the different microworlds such as Logo and Dynamic Geometry System(DGS), and reform each microworlds for mathematical level-up of representation. First, we introduce the concept of action letters and its manipulation for representing turtle actions and recursive patterns in turtle microworld. Also we introduce another algebraic representation for representing DGS relation and consider educational moaning in dynamic geometry microworld. We design an integrating microworld between Logo and DGS. First, we design a same command system and we get together in a microworld. Second, these microworlds interact each other and collaborate to construct and manipulate new objects such as tiles and folding nets.

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Teaching and Learning Middle School Mathematics through Cyber Learning System : The Concept of Centroid (가상학습체계를 통한 중학교 수학의 교수 및 학습)

  • In chul Jung;Seung Dong Kim;Young Soon Ro;Dal-Won Park;Du-Won Byun
    • School Mathematics
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    • v.5 no.4
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    • pp.507-520
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    • 2003
  • 본 연구는 실질적인 의미에서 학생들로 하여금 수학을 더 잘 이해할 수 있도록 돕기 위해 테크놀로지를 학교 교실에서 직접 활용하는 방안에 대한 연구이다. 특히 여기서는 수학을 가르치고 배우는 과정에서 가상학습체계가 주요한 도구로서 적용되었다. 내용은 무게중심을 택했고 12명의 중학생을 대상으로 현직교사가 직접 지도하였다. 학생들은 수업초기에 교사에 의해 소개되는 학생중심 학습활동에 강한 관심과 호기심을 보였고 집중력이 아주 강했다. 전통적인 수업방식과는 달리 학생들이 참여하였고 테크놀로지를 이용하여 전통적인 방식의 교실에서 할 수 없었던 수업의 시작은 학생들의 호기심을 자극하는데 충분하였다. 전반적으로 테크놀로지 환경에서의 수업을 선호하였지만 아직 전통적인 방식인 칠판과 분필을 이용한 수업을 선호한 학생들도 있었다. 새로운 변화도 좋지만 새로운 환경에 친화적이지 않거나 테크놀로지를 이용한 수업의 빠른 진행이 학생을 오히려 혼란하게 만들기도 하였다. 마지막으로 교사는 가상학습체계를 교실에서 활용함에 있어서 현 교육과정과 교과서를 크게 개혁하지 않아도 잘 준비되고 계획된 테크놀로지의 활용에 대한 잠재력을 확인할 수 있었다. 우리는 현재 테크놀로지의 보급에 비해 그 활용도가 낮다는 것을 잘 알고 있고 기타 입학시험이라는 현실이 교육과정과 학습방법의 개혁을 현실적으로 추진하는 것이 어려운 일임을 잘 알고 있다. 그래서 현 상황에서 테크놀로지의 사용을 가능하게 할 수 있는 방법을 모색하였다. 이미 보급된 테크놀로지와 교사와 학생의 테크놀로지에 대한 이해가 앞으로 그 잠재력을 갖고 있다고 확인하였다.보다 낮은 일반세균수 값을 보여주었다. 봄철 시료에 있어서 소규모 도계장은 본 냉각 후 도계과정을 제외하곤 모든 도계공정 단계에서 대규모 도계장보다 높은 일반 세균수의 측정값을 보여주었다. 봄철 시료의 냉각말기의 냉각수 일반세균수는 소규모 도계장이 대규모 도계장보다 높은 측정값을 보여주었다.주었다.다.㏖/s/$m^2$에서는 이앙후 각각 18일로 두 품종 모두 늦어, 약광은 유묘기에 분화되었던 분얼아를 휴면으로 유도할 수 있음을 시사하였다. 4. 유효경비율은 1220~220 $\mu$㏖/s/$m^2$에서 다산벼는 47~55%, 화성벼는 100~72%로 다산벼가 화성벼보다 낮았다. 이것은 다산벼는 무효분얼이 많다는 것을 시사하는 것으로 품종 육성시 유효경비율을 높여야 할 것이다.타났고, \circled2 회복상태에서, 10 lu$\chi$인 경우 서간에 1.26 $\mu\textrm{V}$, 야간에 1.59 $\mu\textrm{V}$였고, 100 lu$\chi$인 경우 서간에 2.63 $\mu\textrm{V}$ 야간에 3.65 $\mu\textrm{V}$였으며, 400 lu$\chi$인 경우 서간에 2.52 $\mu\textrm{V}$, 야간에 3.67 $\mu\textrm{V}$로 나타났다.히, 흉선, F냥, 비장 등의 림프구에 초기 세포용해성 감염을 일으키는데, B

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Relationship between Music Cognitive Skills and Academic Skills (음악의 인지기술과 학습 기술과의 관계)

  • Chong, Hyun Ju
    • Journal of Music and Human Behavior
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    • v.3 no.1
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    • pp.63-76
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    • 2006
  • Melody is defined as adding spatial dimension to the rhythm which is temporal concept. Being able to understand melodic pattern and to reproduce the pattern also requires cognitive skills. Since 1980, there has been much research on the relationship between academic skills and music cognitive skills, and how to transfer the skills learned in music work to the academic learning. The study purported to examine various research outcomes dealing with the correlational and causal relationships between musical and academic skills. The two dominating theories explaining the connection between two skills ares are "neural theory" and "near transfer theory." The theories focus mainly on the transference of spatial and temporal reasoning which are reinforced in the musical learning. The study reviewed the existing meta-analysis studies, which provided evidence for positive correlation between academic and musical skills, and significance of musical learning in academic skills. The study further examined specific skills area that musical learning is correlated, such as mathematics and reading. The research stated that among many mathematical concepts, proportional topics have the strongest correlation with musical skills. Also with reading, temporal processing also has strong relationship with auditory skills and motor skills, and further affect language and literacy ability. The study suggest that skills learned in the musical work can be transferred to other areas of learning and structured music activities may be every efficient for children for facilitating academic concepts.

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Optimization for Concurrent Spare Part with Simulation and Multiple Regression (시뮬레이션과 다중 회귀모형을 이용한 동시조달수리부속 최적화)

  • Kim, Kyung-Rok;Yong, Hwa-Young;Kwon, Ki-Sang
    • Journal of the Korea Society for Simulation
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    • v.21 no.3
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    • pp.79-88
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    • 2012
  • Recently, the study in efficient operation, maintenance, and equipment-design have been growing rapidly in military industry to meet the required missions. Through out these studies, the importance of Concurrent Spare Parts(CSP) are emphasized. The CSP, which is critical to the operation and maintenance to enhance the availability, is offered together when a equipment is delivered. Despite its significance, th responsibility for determining the range and depth of CSP are done from administrative decision rather than engineering analysis. The purpose of the paper is to optimize the number of CSP per item using simulation and multiple regression. First, the result, as the change of operational availability, was gained from changing the number of change in simulation model. Second, mathematical regression was computed from the input and output data, and the number of CSP was optimized by multiple regression and linear programming; the constraint condition is the cost for optimization. The advantage of this study is to respond with the transition of constraint condition quickly. The cost per item is consistently altered in the development state of equipment. The speed of analysis, that simulation method is continuously performed whenever constraint condition is repeatedly altered, would be down. Therefore, this study is suitable for real development environment. In the future, the study based on the above concept improves the accuracy of optimization by the technical progress of multiple regression.