• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.1-57
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• 2003

Vector fields in three-space admit bundles of internal variables such as a Heisenberg algebra bundle. Information transmission along field lines of vector fields is described by a wave linked to the Schrodinger representation in the realm of time-frequency analysis. The preservation of local information causes geometric optics and a quantization scheme. A natural circle bundle models quantum information visualized by holographic methods. Features of this setting are applied to magnetic resonance imaging.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.127-134
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• 1998

It is proved [6] that there exists a basis of $L^\Gamma$ (the space of meromorphic vector fields on a Riemann surface, holomorphic away from two fixed points) represented by the vector fields which have the expected zero or pole order at the two points. In this paper, we carry out the same task for the quadratic differentials. More precisely, we compute a basis of $Q^\Gamma$ (the sapce of meromorphic quadratic differentials on a Riemann surface, holomorphic away from two fixed points). This basis consists of the quadratic differentials which have the expected zero or pole order at the two points. Furthermore, we show that $Q^\Gamma$ has a Lie algebra structure which is induced from the Krichever-Novikov algebra $L^\Gamma$.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1299-1320
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• 2023

In the present paper, firstly we obtain the general expression of the canal hypersurfaces that are formed as the envelope of a family of pseudo hyperspheres, pseudo hyperbolic hyperspheres and null hyper-cones whose centers lie on a non-null curve with non-null Frenet vector fields in E⁴₁ and give their some geometric invariants such as unit normal vector fields, Gaussian curvatures, mean curvatures and principal curvatures. Also, we give some results about their flatness and minimality conditions and Weingarten canal hypersurfaces. Also, we obtain these characterizations for tubular hypersurfaces in E⁴₁ by taking constant radius function and finally, we construct some examples and visualize them with the aid of Mathematica.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.316-324
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• 2023

The P-curvature tensor has been studied in the space-time of general relativity and it is found that the contracted part of this tensor vanishes in the Einstein space. It is shown that Rainich conditions for the existence of non-null electro variance can be obtained by P_𝛼𝛽. It is established that the divergence of tensor G_𝛼𝛽 defined with the help of P_𝛼𝛽 and scalar P is zero, so that it can be used to represent Einstein field equations. It is shown that for V₄ satisfying Einstein like field equations, the tensor P_𝛼𝛽 is conserved, if the energy momentum tensor is Codazzi type. The space-time satisfying Einstein's field equations with vanishing of P-curvature tensor have been considered and existence of Killing, conformal Killing vector fields and perfect fluid space-time has been established.

• Journal of Mechanical Science and Technology
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• v.15 no.7
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• pp.895-905
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• 2001

This paper presents vector fields, three dimensional mean velocities, turbulent intensities, turbulent kinetic energy and Reynolds shear stresses measured in the X-Y plane of the gas swirl burner with a cone type baffle plate by using an X-type hot-wire probe. This experiment is carried out at the flow rates of 350 and 450ℓ/min which are equivalent to the combustion air flow rate necessary to release 15,000 kcal/hr in a gas furnace. The results show that the maximum axial mean velocity component exists around the narrow slits situated radially on the edge of a burner. Therefore, there is some entrainment of ambient air in the outer region of a burner. The maximum values of turbulent intensities occur around the narrow slits and in front of a burner up to X/R=1.5. Moreover, the turbulent intensity components show a relatively large value in the inner region due to the flow diffusion and mixing processes between the inclined baffle plate and the swirl vane. Consequently, the combustion reaction is expected to occur actively near these regions.

• Journal of the Korean Mathematical Society
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• v.27 no.1
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• pp.95-109
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• 1990

• Proceedings of the IEEK Conference
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• 2000.09a
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• pp.327-330
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• 2000

In this paper, we describe an intelligent method to detect types of vehicles using Support Vector Machines focused to the Intelligent Transportation System (ITS) applications such as in the CCD based Electronic Toll Collection System (ETCS). This algorithm can be used the various fields of ITS applications. Support Vector Machines employed in this paper has been recently proposed as a very effective method for 3D image recognition. And our proposed feature extraction method using the singluar values that directly come from pixels at input images. Consequently, The low calculation load and the high recognition rate in spite of image rotation and various noises are one of merits of proposed method.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.141-146
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• 2009

Support vector machine is a classification algorithm based on statistical learning theory. It has shown many results with good performances in the data mining fields. But there are some problems in the algorithm. One of the problems is its heavy computing cost. So we have been difficult to use the support vector machine in the dynamic and online systems. To overcome this problem we propose to use stratified sampling of statistical sampling theory. The usage of stratified sampling supports to reduce the size of training data. In our paper, though the size of data is small, the performance accuracy is maintained. We verify our improved performance by experimental results using data sets from UCI machine learning repository.

• International Journal of Contents
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• v.1 no.2
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• pp.26-30
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• 2005

According to the fast growth of information on the Internet, it is becoming increasingly difficult to find and organize useful information. To reduce information overload, it needs to exploit automatic text classification for handling enormous documents. Support Vector Machine (SVM) is a model that is calculated as a weighted sum of kernel function outputs. This paper describes a document classifier for web documents in the fields of Information Technology and uses SVM to learn a model, which is constructed from the training sets and its representative terms. The basic idea is to exploit the representative terms meaning distribution in coherent thematic texts of each category by simple statistics methods. Vector-space model is applied to represent documents in the categories by using feature selection scheme based on TFiDF. We apply a category factor which represents effects in category of any term to the feature selection. Experiments show the results of categorization and the correlation of vector length.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.229-257
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• 2022

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (𝜙, 𝜉, 𝜂, g) in a complex space form M_n+1(c), c ≠ 0. We denote by A and R_𝜉 the shape operator in the direction of distinguished normal vector field and the structure Jacobi operator with respect to the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a scalar 𝜃(< 2c) and any vector fields X and Y on M. In this paper, we prove that if it satisfies R_𝜉A = AR_𝜉 and at the same time ∇_𝜉R_𝜉 = 0 on M, then M is a Hopf hypersurface of type (A) provided that the scalar curvature s of M holds s - 2(n - 1)c ≤ 0.