• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.287-311
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• 2023

In this paper, we introduce the notion of cyclic structure Jacobi semi-symmetric real hypersurfaces in the complex hyperbolic quadric Q^m* = SO⁰_2,m/SO₂SO_m. We give a classifiction of when real hypersurfaces in the complex hyperbolic quadric Q^m* having 𝔄-principal or 𝔄-isotropic unit normal vector fields have cyclic structure Jacobi semi-symmetric tensor.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.959-1008
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• 1999

This paper considers foundational issues related to connections in the tangent bundle of a manifold. The approach makes use of second order tangent vectors, i.e., vectors tangent to the tangent bundle. The resulting second order tangent bundle has certain properties, above and beyond those of a typical tangent bundle. In particular, it has a natural secondary vector bundle structure and a canonical involution that interchanges the two structures. The involution provides a nice way to understand the torsion of a connection. The latter parts of the paper deal with the Levi-Civita connection of a Riemannian manifold. The idea is to get at the connection by first finding its.spary. This is a second order vector field that encodes the second order differential equation for geodesics. The paper also develops some machinery involving lifts of vector fields form a manifold to its tangent bundle and uses a variational approach to produce the Riemannian spray.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.849-861
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• 2023

In this paper, we introduce the notion of semi-symmetric structure Jacobi operator for Hopf real hypersufaces in the complex quadric Q^m = SO_m+2/SO_mSO₂. Next we prove that there does not exist any Hopf real hypersurface in the complex quadric Q^m = SO_m+2/SO_mSO₂ with semi-symmetric structure Jacobi operator. As a corollary, we also get a non-existence property of Hopf real hypersurfaces in the complex quadric Q^m with either symmetric (parallel), or recurrent structure Jacobi operator.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.319-329
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• 2014

In this paper we study the properties of conformally recurrent pseudo Riemannian manifolds admitting a proper conformal vector field with respect to the scalar field ${\sigma}$, focusing particularly on the 4-dimensional Lorentzian case. Some general properties already proven by one of the present authors for pseudo conformally symmetric manifolds endowed with a conformal vector field are proven also in the case, and some new others are stated. Moreover interesting results are pointed out; for example, it is proven that the Ricci tensor under certain conditions is Weyl compatible: this notion was recently introduced and investigated by one of the present authors. Further we study conformally recurrent 4-dimensional Lorentzian manifolds (space-times) admitting a conformal vector field: it is proven that the covector ${\sigma}_j$ is null and unique up to scaling; moreover it is shown that the same vector is an eigenvector of the Ricci tensor. Finally, it is stated that such space-time is of Petrov type N with respect to ${\sigma}_j$.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.131-140
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• 2014

In this paper we investigate (n+1)($n{\geq}3$)-dimensional contact CR-submanifolds M of (n-1) contact CR-dimension in a complete simply connected Sasakian space form of constant ${\phi}$-holomorphic sectional curvature $c{\neq}-3$ which satisfy the condition h(FX, Y)+h(X, FY) = 0 for any vector fields X, Y tangent to M, where h and F denote the second fundamental form and a skew-symmetric endomorphism (defined by (2.3)) acting on tangent space of M, respectively.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.989-999
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• 2023

The aim of this paper is to study the projective curvature tensor field of the Curvature tensor Rⁱ_jkh on a recurrent non Riemannian space admitting recurrent affine motion, which is also decomposable in the form Rⁱ_jkh=Xⁱ Y_jkh, where Xⁱ and Y_jkh are non-null vector and tensor respectively. In this paper we decompose Special Pseudo Projective Curvature Tensor Field. In the sequal of decomposition we established several properties of such decomposed tensor fields. We have considered the curvature tensor field Rⁱ_jkh in a Finsler space equipped with non symmetric connection and we study the decomposition of such field. In a special Pseudo recurrent Finsler Space, if the arbitrary tensor field 𝜓ⁱ_j is assumed to be a covariant constant then, in view of the decomposition rule, 𝜙_kh behaves as a recurrent tensor field. In the last, we have considered the decomposition of curvature tensor fields in Kaehlerian recurrent spaces and have obtained several related theorems.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.5
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• pp.713-721
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• 2001

Characteristics of the conical vortices on the roof corner of a rectangular prism have been investigated by using a PIV(Particle Image Velocimetry) technique. The Reynolds number based on the free stream velocity and the height of the model was 5.3$\times$10$^3$. The mean, instantaneous velocity vector fields, vorticity fields, and turbulent kinetic energy distribution were measured for two different angles of attack, 30$^{\circ}$and 45$^{\circ}$. The PIV measurements clearly observed not only the conical main vortex and the secondary vortex but also the tertiary vortex which is firstly reported in this paper. Asymmetric formation of the corner vortex for the case of 30$^{\circ}$angle of attack produces relatively the high magnitude of vorticity and turbulent kinetic energy around the bigger vortex which generates the peak suction pressure on the roof. Fairly symmetric features of the roof vortex are observed in the case of 45$^{\circ}$angle of attack, however, the dynamic characteristics are proved to be asymmetric due to the rectangular shape of the roof.

• Geophysics and Geophysical Exploration
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• v.5 no.4
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• pp.280-290
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• 2002

Three-dimensional (3-D) electromagnetic (EM) modeling algorithm has been developed using finite element method (FEM) to acquire more efficient interpretation techniques of EM data. When FEM based on nodal elements is applied to EM problem, spurious solutions, so called 'vector parasite', are occurred due to the discontinuity of normal electric fields and may lead the completely erroneous results. Among the methods curing the spurious problem, this study adopts vector element of which basis function has the amplitude and direction. To reduce computational cost and required core memory, complex bi-conjugate gradient (CBCG) method is applied to solving complex symmetric matrix of FEM and point Jacobi method is used to accelerate convergence rate. To verify the developed 3-D EM modeling algorithm, its electric and magnetic field for a layered-earth model are compared with those of layered-earth solution. As we expected, the vector based FEM developed in this study does not cause ny vector parasite problem, while conventional nodal based FEM causes lots of errors due to the discontinuity of field variables. For testing the applicability to high frequencies 100 MHz is used as an operating frequency for the layer structure. Modeled fields calculated from developed code are also well matched with the layered-earth ones for a model with dielectric anomaly as well as conductive anomaly. In a vertical electric dipole source case, however, the discontinuity of field variables causes the conventional nodal based FEM to include a lot of errors due to the vector parasite. Even for the case, the vector based FEM gave almost the same results as the layered-earth solution. The magnetic fields induced by a dielectric anomaly at high frequencies show unique behaviors different from those by a conductive anomaly. Since our 3-D EM modeling code can reflect the effect from a dielectric anomaly as well as a conductive anomaly, it may be a groundwork not only to apply high frequency EM method to the field survey but also to analyze the fold data obtained by high frequency EM method.

• Proceedings of the Korean Vacuum Society Conference
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• 2013.02a
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• pp.153-153
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• 2013

Turbomolecular pump (TMP) is widely used to obtain and maintain high vacuum by spinning turbine rotors to migrate gas molecules to the exhaust of the pump. However, performance of the TMP has not been well observed when it is influenced by strong magnetic field. Such study may give useful information about magnetic field tolerance of TMP, development of magnetic shielding technique for key components of TMP, etc. For this purpose, magnetic field induced by a circular current source was firstly designed and investigated. Using spherical coordinates and vector potential, magnetic field throughout the space including axis of rotation was calculated. Due to the rotational symmetry of the circular current source, induced magnetic field is azimuthally symmetric and, thus, is analyzed by radial and polar components of the magnetic fields. In order to enhance the numerical accuracy for the calculation, magnetic field was expressed by complete elliptic integrals of first and second kinds. According to the calculation, when 1 A of DC-current passes through a 1 turned circular wire with 50 cm of diameter, overall magnitude of the inducedmagnetic field was about 0.02 Gauss, which was used to the determination of the current and the number of turns of wires to fabricate the coil for the study on the magnetic field tolerance of TMP.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.13 no.7
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• pp.667-678
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• 2002

In this paper, a new radiating structure with a multi-layered two-dimensional metallic disk array was proposed for shaping the flat-topped element pattern. It is an infinite periodic planar array structure with metallic disks finitely stacked above the radiating circular waveguide apertures. The theoretical analysis was in detail performed using rigid full-wave analysis, and was based on modal representations for the fields in the partial regions of the array structure and for the currents on the metallic disks. The final system of linear algebraic equations was derived using the orthogonal property of vector wave functions, mode-matching method, boundary conditions and Galerkin's method, and also their unknown modal coefficients needed for calculation of the array characteristics were determined by Gauss elimination method. The application of the algorithm was demonstrated in an array design for shaping the flat-topped element patterns of $\pm$20$^{\circ}$ beam width in Ka-band. The optimal design parameters normalized by a wavelength for general applications are presented, which are obtained through optimization process on the basis of simulation and design experience. A Ka-band experimental breadboard with symmetric nineteen elements was fabricated to compare simulation results with experimental results. The metallic disks array structure stacked above the radiating circular waveguide apertures was realized using ion-beam deposition method on thin polymer films. It was shown that the calculated and measured element patterns of the breadboard were in very close agreement within the beam scanning range. The result analysis for side lobe and grating lobe was done, and also a blindness phenomenon was discussed, which may cause by multi-layered metallic disk structure at the broadside. Input VSWR of the breadboard was less than 1.14, and its gains measured at 29.0 GHz. 29.5 GHz and 30 GHz were 10.2 dB, 10.0 dB and 10.7 dB, respectively. The experimental and simulation results showed that the proposed multi-layered metallic disk array structure could shape the efficient flat-topped element pattern.