• Journal for History of Mathematics
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• v.15 no.2
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• pp.49-68
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• 2002

One of the characteristics of modem mathematics is to use algebra in every fields of mathematics. But we don't have the exact definition of algebra, and we can't clearly define algebraic thinking. In order to solve this problem, this paper investigate the history of algebra. First, we describe some of the features of proportional Babylonian thinking by analysing some problems. In chapter 4, we consider Greek's analytical method and proportional theory. And in chapter 5, we deal with Diophantus' algebraic method by giving an overview of Arithmetica. Finally we investigate Viete's thinking of algebra through his ‘the analytical art’. By investigating these history of algebra, we reach the following conclusions. 1. The origin of algebra comes from problem solving(various equations). 2. The origin of algebraic thinking is the proportional thinking and the analytical thinking. 3. The thing that plays an important role in transition from arithmetical thinking to algebraic thinking is Babylonian ‘the false value’ idea and Diophantus’ ‘arithmos’ concept.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.16 no.4
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• pp.225-237
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• 2016

In conventional transportation problem (TP), all the parameters are always certain. But, many of the real life situations in industry or organization, the parameters (supply, demand and cost) of the TP are not precise which are imprecise in nature in different factors like the market condition, variations in rates of diesel, traffic jams, weather in hilly areas, capacity of men and machine, long power cut, labourer's over time work, unexpected failures in machine, seasonal changes and many more. To counter these problems, depending on the nature of the parameters, the TP is classified into two categories namely type-2 and type-4 fuzzy transportation problems (FTPs) under uncertain environment and formulates the problem and utilizes the trapezoidal fuzzy number (TrFN) to solve the TP. The existing ranking procedure of Liou and Wang (1992) is used to transform the type-2 and type-4 FTPs into a crisp one so that the conventional method may be applied to solve the TP. Moreover, the solution procedure differs from TP to type-2 and type-4 FTPs in allocation step only. Therefore a simple and efficient method denoted by PSK (P. Senthil Kumar) method is proposed to obtain an optimal solution in terms of TrFNs. From this fuzzy solution, the decision maker (DM) can decide the level of acceptance for the transportation cost or profit. Thus, the major applications of fuzzy set theory are widely used in areas such as inventory control, communication network, aggregate planning, employment scheduling, and personnel assignment and so on.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1790-1795
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• 1991

The optimal load distribution for two cooperating robots is studied in this paper, and a new solution approach utilizing force ellipsoid is proposed. The load distribution problem is formulated as a nonlinear optimization problem with a quadratic cost function. The limit on instantaneous power is considered in the problem formulation as the joint torque constraints. The optimal solution minimizing energy consumption is obtained using the concept of force ellipsoid and the nonlinear optimization theory. The force ellipsoid provides a useful geometrical insight into the load distribution problem. Despite the presence of the joint torque constraints, the optimal solution is obtained almost as a closed form, in which the joint torques are given in terms of a single scalar parameter that can be obtained numerically by solving a scalar equation.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.4
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• pp.2028-2041
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• 2019

Compressed sensing (CS) is a new theory. With regard to the sparse signal, an exact reconstruction can be obtained with sufficient CS measurements. Nevertheless, in practical applications, the transform coefficients of many signals usually have weak sparsity and suffer from a variety of noise disturbances. What's worse, most existing classical algorithms are not able to effectively solve this issue. So we proposed an efficient algorithm based on smoothed ${\ell}_0$ norm for sparse signal reconstruction. The direct ${\ell}_0$ norm problem is NP hard, but it is unrealistic to directly solve the ${\ell}_0$ norm problem for the reconstruction of the sparse signal. To select a suitable sequence of smoothed function and solve the ${\ell}_0$ norm optimization problem effectively, we come up with a generalized approximate function model as the objective function to calculate the original signal. The proposed model preserves sharper edges, which is better than any other existing norm based algorithm. As a result, following this model, extensive simulations show that the proposed algorithm is superior to the similar algorithms used for solving the same problem.

• Advances in nano research
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• v.13 no.3
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• pp.297-312
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• 2022

Coughing and breath shortness are common symptoms of nano (small) cell lung cancer. Smoking is main factor in causing such cancers. The cancer cells form on the soft tissues of lung. Deformation behavior and wave vibration of lung affected when cancer cells exist. Therefore, in the current work, phase velocity behavior of the small cell lung cancer as a main part of the body via an exact size-dependent theory is presented. Regarding this problem, displacement fields of small cell lung cancer are obtained using first-order shear deformation theory with five parameters. Besides, the size-dependent small cell lung cancer is modeled via nonlocal stress/strain gradient theory (NSGT). An analytical method is applied for solving the governing equations of the small cell lung cancer structure. The novelty of the current study is the consideration of the five-parameter of displacement for curved panel, and porosity as well as NSGT are employed and solved using the analytical method. For more verification, the outcomes of this reports are compared with the predictions of deep neural network (DNN) with adaptive optimization method. A thorough parametric investigation is conducted on the effect of NSGT parameters, porosity and geometry on the phase velocity behavior of the small cell lung cancer structure.

• Korean Journal of Logic
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• v.8 no.1
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• pp.23-46
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• 2005

The purpose of the paper Is to discuss and estimate early Popper's theory of probability, which is presented in his book, The Logic of of Scientific Discovery. For this, Von Mises' frequency theory shall be discussed in detail, which is regarded as the most systematic and sophisticated frequency theory among others. Von Mises developed his theory to response to various critical questions such as how finite and empirical collectives can be represented in terms of infinite and mathematical collectives, and how the axiom of randomness can be mathematically formulated. But his theory still has another difficulty, which is concerned with the inconsistency between the axiom of convergence and the axiom of randomness. Defending the objective theory of probability, Popper tries to present his own frequency theory, solving the difficulty. He suggests that the axiom of convergence be given up and that the axiom of randomness be modified to solve Von Mises' problem. That is, Popper introduces the notion of ordinal selection and neighborhood selection to modify the axiom of randomness. He then shows that Bernoulli's theorem is derived from the modified axiom. Consequently, it can be said that Popper solves the problem of inconsistency which is regarded as crucial to Von Mises' theory. However, Popper's suggestion has not drawn much attention. I think it is because his theory seems anti-intuitive in the sense that it gives up the axiom of convergence which is the basis of the frequency theory So for more persuasive frequency theory, it is necessary to formulate the axiom of randomness to be consistent with the axiom of convergence.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.53-56
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• 2000

The problem ( Ρ ) of optimizing a linear function d$\^$T/x over the set of efficient set for a multiple objective linear program ( Μ ) is difficult because the efficient set is nonconvex. There some interesting properties between the objective linear vector ｄ and the matrix of multiple objectives C and those properties lead us to establish criteria to solve ( Ρ ) with a linear program. In this paper we investigate a system of the linear equations C$\^$T/${\alpha}$=d and construct two linearly independent positive vectors ${\mu}$, ν such that ${\alpha}$=${\mu}$-ν. From those vectors ${\mu}$, ν, solving an weighted sum linear program for finding an efficient extreme point for the ( Μ ) is a way to get an optimal solution ( Ρ ). Therefore our theory gives an easy way of solving nonconvex program ( Ρ ) with a weighted sum linear program.

• Hwankyungkyoyuk
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• v.22 no.3
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• pp.15-30
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• 2009

This study focuses on the comparison of PBL and GBS. PBL is a famous model that emphasizes diversity of students and self directed learning within the theory of constructivism. GBS has not been studied that extensively. GBS is most similar to PBL but this model has not been actively applied to school education. This study focuses on how to enhance students' interest in an educational environment that is encompassing a new and changing teach-learn paradigm and the development of new technology. Furthermore, PBL and GBS methods were compare actively applied to "Environmental Education" to make the students learn self-directed education through the transformation of one's environmental awareness. Specifically, the models were applied to the "Ecology and Environment" subject taught in general high schools and the degree of 'environmental literacy' were measured, From March to May of 2007, the PBL and GBS models were applied to 3rd grade students at D high school and the subject was 'Ecology and Environment'. The students were divided according to age into groups of $5{\sim}7$. The PBL group attempted to solve the given problems and the GBS group carried out their missions. In conclusion, after analyzing the 'environmental literacy' survey results by SPSS 12.0, just 'Knowledge of Ecology (KEOC)' and 'Locus of Control (LOC)' were slightly significant in PBL. This shows that PBL enhances the students' problem solving ability and thinking power. This is a result of the enhancement of students' problem-solving and thinking abilities through PBL. Students can learn many things because they completed their projects based on their experience and knowledge, both individually and interpersonally. We have to study how to apply PBL and GBS to the education field in spite of the many limited conditions. Therefore, this study looks at the application of PBL and GBS in environmental education and suggests specific strategies for educators who want to apply GBS and PBL and adapt them into their education curricula.

• Journal of the Korea Society of Computer and Information
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• v.26 no.12
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• pp.29-43
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• 2021

In this paper, a new approach to solve the constrained dynamic programming is proposed by using the constraint programming. While the conventional dynamic programming scheme has the state space augmented with states on constraints, this approach, without state augmentation, represents states of constraints as domains in a contraining programming solver. It has a hybrid computational mechanism in its computation by combining solving the Bellman equation in the dynamic programming framework and exploiting the propagation and inference methods of the constraint programming. In order to portray the differences of the two approaches, this paper solves a simple version of the long-term car rental financing problem. In the conventional scheme, data structures for state on constraints are designed, and a simple inference borrowed from the constraint programming is used to the reduction of violation of constraints because no inference risks failure of a solution. In the hybrid approach, the architecture of interface of the dynamic programming solution method and the constraint programming solution method is shown. It finally discusses the advantages of the proposed method with the conventional method.

• Journal of Korean Association for Spatial Structures
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• v.5 no.3 s.17
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• pp.65-74
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• 2005

An analytical model was developed to investigate the flexural behavior of a pultruded fiber-reinforced plastic deck of rectangular unit module. The model is based on first-order shea. deformable plate theory (FSDT), and capable of predicting deflection of the deck of arbitrary laminate stacking sequences. To formulate tile problem, two-dimensional plate finite element method is employed. Numerical results are obtained for FRP decks under uniformly-distributed loading, addressing the effects of fiber angle and span-to-height ratio. It is found that the present analytical model is accurate and efficient for solving flexural behavior of FRP decks. Also, as the height of FRP deck plate is higher, the necessity of higher order Shear deformable plate theory(HSDT) is announced, not the FSDT in the plate analysis theory.