• Journal of the Korean Data and Information Science Society
• /
• v.25 no.5
• /
• pp.1069-1077
• /
• 2014

A clubfoot is a kind of congenital deformity of foot, which is internally rotated at the ankle. In this paper, we are going to cluster the curves of relative differences between regular and operated feet. Since these curves are irregular and sparsely sampled, general clustering models could not be applied. So the clustering model for sparsely sampled functional data by James and Sugar (2003) are applied and parameters are estimated using EM algorithm. The number of clusters is determined by the distortion function (Sugar and James, 2003) and two clusters of the curves are found.

• Bulletin of the Korean Mathematical Society
• /
• v.30 no.1
• /
• pp.99-107
• /
• 1993

A vector space K with scalar product <.,.> is called a Krein space if it can be decomposed as a northogonal sum of a Hilbert space and an anti-space of a Hilbert space. The space K induces a Hilbert space $K_{J}$ in the inner product <.,.> $K_{J}$=<.,.>K, where $J^{2}$=I. the eigenspaces of J are denoted by $K^{+}$$_{J}$, which is a Hilbert space and $K^{-}$$_{J}$, which is an anti-space of a Hilbert space. Then the Krein space K is the orthogonal sum of $K^{+}$$_{J}$ and $K^{-}$$_{J}$. Such a decomposition of K is called a fundamental decomposition. In general, fundamental decompositions are not unique. The norm of the Hilbert space depends on the choice of a fundamental decomposion, but such norms are equivalent. The topology generated by these norms is called the strong or Mackey topology of K. It is used to define all topological notions on the Krein space K with respect to this topology. The Pontryagin index of a Krein space is the dimension of the antispace of a Hilbert space in any such decomposition. the dimension does not depend on the choice of orthogonal decomposition. A Krein space is called a Pontryagin space if it has finite Pontryagin index.dex.yagin index.dex.

• Journal of Korean Society for Quality Management
• /
• v.49 no.4
• /
• pp.569-579
• /
• 2021

Purpose: The purpose of this study is the time series analysis for predicting the yield of crops applicable to each farm using environmental variables measured by smart farms cultivating tomato. In addition, it is intended to confirm the influence of environmental variables using a deep learning model that can be explained to some extent. Methods: A time series analysis was performed to predict production using environmental variables measured at 75 smart farms cultivating tomato in two periods. An LSTM-based encoder-decoder model was used for cases of several farms with similar length. In particular, Dual Attention Mechanism was applied to use environmental variables as exogenous variables and to confirm their influence. Results: As a result of the analysis, Dual Attention LSTM with a window size of 12 weeks showed the best predictive power. It was verified that the environmental variables has a similar effect on prediction through wieghtss extracted from the prediction model, and it was also verified that the previous time point has a greater effect than the time point close to the prediction point. Conclusion: It is expected that it will be possible to attempt various crops as a model that can be explained by supplementing the shortcomings of general deep learning model.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.5
• /
• pp.1279-1300
• /
• 2021

Let P be a finite point set in ℝ² with the set of distance n-chains defined as ∆_n(P) = {(|p₁ - p₂|, |p₂ - p₃|, …, |p_n - p_n+1|) : p_i ∈ P}. We show that for 2 ⩽ n = O_|P|(1) we have ${\mid}{\Delta}_n(P){\mid}{\gtrsim}{\frac{{\mid}P{\mid}^n}{{\log}^{\frac{13}{2}(n-1)}{\mid}P{\mid}}}$. Our argument uses the energy construction of Elekes and a general version of Rudnev's rich-line bound implicit in [28], which allows one to iterate efficiently on intersecting nested subsets of Guth-Katz lines. Let G is a simple connected graph on m = O(1) vertices with m ⩾ 2. Define the graph-distance set ∆_G(P) as ∆_G(P) = {(|p_i - p_j|)_{i,j}∈E(G) : p_i, p_j ∈ P}. Combining with results of Guth and Katz [17] and Rudnev [28] with the above, if G has a Hamiltonian path we have ${\mid}{\Delta}_G(P){\mid}{\gtrsim}{\frac{{\mid}P{\mid}^{m-1}}{\text{polylog}{\mid}P{\mid}}}$.

• International journal of advanced smart convergence
• /
• v.10 no.4
• /
• pp.59-65
• /
• 2021

Electricity contributes to the development of the economy. Therefore, forecasting electricity demand plays an important role in the development of the electricity industry in particular and the economy in general. This study aims to provide a precise model for long-term electricity demand forecast in the residential sector by using three independent variables include: Population, Electricity price, Average annual income per capita; and the dependent variable is yearly electricity consumption. Based on the support of Multiple variable regression, the proposed method established a model with variables that relate to the forecast by ignoring variables that do not affect lead to forecasting errors. The proposed forecasting model was validated using historical data from Vietnam in the period 2013 and 2020. To illustrate the application of the proposed methodology, we presents a five-year demand forecast for the residential sector in Vietnam. When demand forecasts are performed using the predicted variables, the R square value measures model fit is up to 99.6% and overall accuracy (MAPE) of around 0.92% is obtained over the period 2018-2020. The proposed model indicates the population's impact on total national electricity demand.

• Honam Mathematical Journal
• /
• v.40 no.4
• /
• pp.809-816
• /
• 2018

The aim of this research paper is to evaluate fifty double integrals invoving generalized hypergeometric function (25 each) in the form of $${{\int}^1_0}{{\int}^1_0}\;x^{{\gamma}-1}y^{{\gamma}+c-1}(1-x)^{c-1}(1-y)^{c+{\ell}}(1-xy)^{{\delta}-2c-{\ell}-1}{\times}_3F_2\[{^{a,\;b,\;2c+{\ell}+1}_{\frac{1}{2}(a+b+i+1),\;2c+j}}\;;{\frac{(1-x)y}{1-xy}}\]dxdy$$ and $${{\int}^1_0}{{\int}^1_0}\;x^{{\gamma}-1}y^{{\gamma}+c+{\ell}}(1-x)^{c+{\ell}}(1-y)^{c-1}(1-xy)^{{\delta}-2c-{\ell}-1}{\times}_3F_2\[{^{a,\;b,\;2c+{\ell}+1}_{\frac{1}{2}(a+b+i+1),\;2c+j}}\;;{\frac{1-y}{1-xy}}\]dxdy$$ in the most general form for any ${\ell}{\in}{\mathbb{Z}}$ and i, j = 0, ${\pm}1$, ${\pm}2$. The results are derived with the help of generalization of Edwards's well known double integral due to Kim, et al. and generalized classical Watson's summation theorem obtained earlier by Lavoie, et al. More than one hundred ineteresting special cases have also been obtained.

• Communications of the Korean Mathematical Society
• /
• v.34 no.1
• /
• pp.279-286
• /
• 2019

Complex Grassmann manifolds $G_{n,k}$ are a generalization of complex projective spaces and have many important features some of which are captured by the $Pl{\ddot{u}}cker$ embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$ where $N=\(^n_k\)$. The problem of existence of cross sections of fibrations can be studied using the Gottlieb group. In a more generalized context one can use the relative evaluation subgroup of a map to describe the cohomology of smooth fiber bundles with fiber the (complex) Grassmann manifold $G_{n,k}$. Our interest lies in making use of techniques of rational homotopy theory to address problems and questions involving applications of Gottlieb groups in general. In this paper, we construct the Sullivan minimal model of the (complex) Grassmann manifold $G_{n,k}$ for $2{\leq}k<n$, and we compute the rational evaluation subgroup of the embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$. We show that, for the Sullivan model ${\phi}:A{\rightarrow}B$, where A and B are the Sullivan minimal models of ${\mathbb{C}}P^{N-1}$ and $G_{n,k}$ respectively, the evaluation subgroup $G_n(A,B;{\phi})$ of ${\phi}$ is generated by a single element and the relative evaluation subgroup $G^{rel}_n(A,B;{\phi})$ is zero. The triviality of the relative evaluation subgroup has its application in studying fibrations with fibre the (complex) Grassmann manifold.

• Journal of Radiation Protection and Research
• /
• v.44 no.3
• /
• pp.90-96
• /
• 2019

The contributions of nuclear science and technology in enhancing prosperity and quality of life all over the world and its potential to achieve many important Sustainable Developments Goals (SDGs) of the United Nations are well recognized. It also is now recognized that with fewer students getting attracted to Science, Technology, Engineering and Mathematics (STEM) in general and nuclear science and technology (NST) in particular; hence, there is a vital need to reach out to young students to provide the crucial human resources needed for these endeavours to continue in this highly specialized area. The success of a recently completed IAEA project related to introducing NST during 2012-2016 in secondary schools in the Asia-Pacific region countries encouraged the formulation of a new IAEA TC project RAS0079 entitled "Educating Secondary Students and Science Teachers on Nuclear Science and Technology" for 2018-2021, focusing on enhancing existing educational approaches through training and development opportunities both for teachers and students. The project aims at reaching a million students during the project duration while keeping the depth of learning between teacher and student. The strategy of executing the project, implementation status and its impact so far is presented in this paper.

• Geosystem Engineering
• /
• v.21 no.6
• /
• pp.335-343
• /
• 2018

Alkali-surfactant polymer flooding has become an important technique to improve oil recovery following the development of oil fields while the function of emulsification in enhanced oil recovery is rarely considered in the existing mathematical model for numerical simulation. In this paper, the mechanism of improving the recovery of the emulsification was analyzed in ASP flooding, and a relatively perfect mathematical model with deep filtration-theory was established, in which oil-water volume equation, saturation equation, viscosity equation, and permeability reduction equation are included. The new model is used to simulate the actual block of an oil field; the simulated results of the new model and an old model without considering the emulsification are compared with the actual well history. It is found that new model which is easy to be realized in numerical simulation has a high precision fitting, and the effect of adding oil and decreasing water is obvious. The sensitivity of emulsification was analyzed, and the results show that the water reducing funnel becomes wider and the rate of water cut decreases rapidly with the increase of emulsifying capacity, and then the rate of recovery slows down. The effect of increasing oil and decreasing water is better, and the degree of recovery increases. The emulsification of the ASP flooding is maintained at a moderate level, which corresponds to ${\Phi}=0.2$ in the new model, and the emulsification is applied to realize the general mathematical quantitative description, so as to better guide the oilfield development.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.13 no.9
• /
• pp.4788-4813
• /
• 2019

In this paper, we introduce concepts of optimal and near optimal secret data hiding schemes. We present a new digital image steganography approach based on the Galois field $GF(p^m)$ using graph and automata to design the data hiding scheme of the general form ($k,N,{\lfloor}{\log}_2p^{mn}{\rfloor}$) for binary, gray and palette images with the given assumptions, where k, m, n, N are positive integers and p is prime, show the sufficient conditions for the existence and prove the existence of some optimal and near optimal secret data hiding schemes. These results are derived from the concept of the maximal secret data ratio of embedded bits, the module approach and the fastest optimal parity assignment method proposed by Huy et al. in 2011 and 2013. An application of the schemes to the process of hiding a finite sequence of secret data in an image is also considered. Security analyses and experimental results confirm that our approach can create steganographic schemes which achieve high efficiency in embedding capacity, visual quality, speed as well as security, which are key properties of steganography.