• Honam Mathematical Journal
• /
• v.44 no.4
• /
• pp.636-645
• /
• 2022

We find a 1-parameter family of homogeneous structure tensors on contact hypersurfaces in Hermitian symmetric spaces. Among their associated Ambrose-Singer connections, we prove that the TanakaWebster connection is the unique pseudo-homothetically invariant connection.

• Bulletin of the Korean Mathematical Society
• /
• v.32 no.2
• /
• pp.281-285
• /
• 1995

The complete classification of the simply connected four dimensional naturally reductive homogeneous spaces is given in [3].

• Journal of Plant Biology
• /
• v.37 no.3
• /
• pp.317-323
• /
• 1994

The calluses formed on the surface of a quarter-girdled Robinia pseudoacacia stems have been shown to originate from immature xylem cells and preexisting cambial cells. The cellus is not only formed by periclinal and anticlinal divisions of radial cells, but also axial cells. In tangential view, the callus at initial stage showed heterogeneous structure composed of long and short cells and then homogeneous one with short cells. Some cells of homogeneous structure in middle region of callus at early stage is later elongated and others mainly divided in trasverse plane. In the result the homogeneous structure becomes into a heterogeneous one. Subsequently, the long cells in heterogeneous structures elongated further and became fusifrom initials, and the short cells divided transversely became ray initials. The appearence of homogeneous and heterogeneous structure in the callus on debarked stem without organ elongation is almost similar to that of the structure in the procambium of young stem which is elongating extensively. Eventually, the ontogeny of vascular cambium in wound callus resembles that of a young stem grown normally, although the debarked stem does not grow in length but in girth and the young stem elongates activity. These findings mean that the active intrusive growth of short procambial cells occurs during the differentiation of fusiform cambial cells.

• Journal of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.859-869
• /
• 1997

It is shown that for $A_{k, m}$ a k-homogeneous $C^*$-algebra over $S^{2n - 1} \times S^1$ such that no non-trivial matrix algebra can be factored out of $A_{k, m}$ and $A_{k, m} \otimes M_l(C)$ has a non-trivial bundle structure for any positive integer l, we construct an $A_{k, m^-} C(S^{2n - 1} \times S^1) \otimes M_k(C)$-equivalence bimodule to show that every k-homogeneous $C^*$-algebra over $S^{2n - 1} \times S^1)$. Moreover, we prove that the tensor product of the k-homogeneous $C^*$-algebra $A_{k, m}$ with a UHF-algebra of type $p^\infty$ has the tribial bundle structure if and only if the set of prime factors of k is a subset of the set of prime factors of pp.

• The Transactions of the Korean Institute of Electrical Engineers D
• /
• v.54 no.12
• /
• pp.723-731
• /
• 2005

The $4{\times}4$ homogeneous transformation matrix is a compact representation of orientation and position of an object in robotics and computer graphics. A coordinate transformation is accomplished through the successive multiplications of homogeneous matrices, each of which represents the orientation and position of each corresponding link. Thus, for real time control applications in robotics or animation in computer graphics, the fast multiplication of homogeneous matrices is quite demanding. In this paper, a parallel-architecture vector processor is designed for this purpose. The processor has several key features. For the accuracy of computation for real application, the operands of the processors are floating point numbers based on the IEEE Standard 754. For the parallelism and reduction of hardware redundancy, the processor takes column vectors of homogeneous matrices as multiplication unit. To further improve the throughput, the processor structure and its control is based on a pipe-lined structure. Since the designed processor can be used as a special purpose coprocessor in robotics and computer graphics, additionally to special matrix/matrix or matrix/vector multiplication, several other useful instructions for various transformation algorithms are included for wide application of the new design. The suggested instruction set will serve as standard in future processor design for Robotics and Computer Graphics. The design is verified using FPGA implementation. Also a comparative performance improvement of the proposed design is studied compared to a uni-processor approach for possibilities of its real time application.

• Journal of the Korean Mathematical Society
• /
• v.43 no.6
• /
• pp.1301-1324
• /
• 2006

The affine homogeneous hypersurface in ${\mathbb{R}}^{n+1}$, which is a graph of a function $F:{\mathbb{R}}^n{\rightarrow}{\mathbb{R}}$ with |det DdF|=1, corresponds to a complete unimodular left symmetric algebra with a nondegenerate Hessian type inner product. We will investigate the condition for the domain over the homogeneous hypersurface to be homogeneous through an extension of the complete unimodular left symmetric algebra, which is called the graph extension.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.58 no.11
• /
• pp.2242-2246
• /
• 2009

In this paper, a homogeneous dual composite right/left-handed (D-CRLH) transmission line (TL) is proposed by using a defected ground structure (DGS) on the ground plane. In order to satisfy a homogeneity condition of metamaterial, a subwavelength unit cell is designed by way of a spiral DGS and a meander stub. From a dispersion diagram, it is expected that the frequency bands for the left-handed (LH) property is 3.5 - 4.4 GHz. At 3.8 GHz in the LH band, backward propagating phenomenon is observed from full-wave analysis. The experimental results show that the proposed TL has a stop-band in 1.75 - 3.6 GHz.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.26 no.4
• /
• pp.263-279
• /
• 2022

This paper presents an automatic inspection of defects in semiconductor images. We devise a statistical method to find defects on homogeneous background from the observation that it has a log-normal distribution. If computer aided design (CAD) data is available, we use it to construct a signed distance function (SDF) and change the pixel values so that the average of pixel values along the level curve of the SDF is zero, so that the image has a homogeneous background. In the absence of CAD data, we devise a hybrid method consisting of a model-based algorithm and two neural networks. The model-based algorithm uses the first right singular vector to determine whether the image has a linear or complex structure. For an image with a linear structure, we remove the structure using the rank 1 approximation so that it has a homogeneous background. An image with a complex structure is inspected by two neural networks. We provide results of numerical experiments for the proposed methods.

• Honam Mathematical Journal
• /
• v.41 no.3
• /
• pp.609-617
• /
• 2019

We characterize two-point homogeneous spaces M by means of the structural operator $h={\frac{1}{2}}{\mathcal{L}}_{\xi}{\phi}$ or the characteristic Jacobi operator ${\ell}=R({\cdot},{\xi}){\xi}$ on the unit tangent sphere bundles $T_1M$.

• Honam Mathematical Journal
• /
• v.33 no.4
• /
• pp.557-573
• /
• 2011

Let G be a compact and connected semisimple Lie group, H a closed subgroup, g (resp. h) the Lie algebra of G (resp. H), B the Killing form of g, g the normal metric on the homogeneous space G/H which is induced by -B. Let D be an invarint connection with Weyl structure (D, g, ${\omega}$) in the tangent bundle over the normal homogeneous Riemannian manifold (G/H, g) which is projectively flat. Then, the affine connection D on (G/H, g) is a Yang-Mills connection if and only if D is the Levi-Civita connection on (G/H, g).