• Honam Mathematical Journal
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• v.40 no.2
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• pp.347-354
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• 2018

Let ${\mathcal{C}}$, ${\mathcal{M}}$, ${\mathcal{L}}$ be concircular curvature tensor, M-projective curvature tensor and conharmonic curvature tensor, respectively. We obtain that if a non-Kenmotsu ($k,{\mu}$)'-almost Kenmotsu manifold satisfies ${\mathcal{C}}{\cdot}{\mathcal{S}}=0$, ${\mathcal{R}}{\cdot}{\mathcal{M}}=0$ or ${\mathcal{R}}{\cdot}{\mathcal{L}}=0$, then it is locally isometric to the Riemannian product ${\mathds{H}}^{n+1}(-4){\times}{\mathds{R}}^n$.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.795-809
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• 2020

In the present paper, we introduce the notion of quasi hemi-slant submanifolds of almost Hermitian manifolds and give some of its examples. We obtain the necessary and sufficient conditions for the distributions to be integrable. We also investigate the necessary and sufficient conditions for these submanifolds to be totally geodesic and study the geometry of foliations determined by the distributions. Finally, we obtain the necessary and sufficient condition for a quasi hemi-slant submanifold to be local product of Riemannian manifold.

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.41-63
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• 2024

In this paper, we study complete Riemannian immersions into a semi-Riemannian warped product obeying suitable curvature constraints. Under appropriate differential inequalities involving higher order mean curvatures, we establish rigidity and nonexistence results concerning these immersions. Applications to the cases that the ambient space is either an Einstein manifold, a steady state type spacetime or a pseudo-hyperbolic space are given, and a particular investigation of entire graphs constructed over the fiber of the ambient space is also made. Our approach is based on a parabolicity criterion related to a linearized differential operator which is a divergence-type operator and can be regarded as a natural extension of the standard Laplacian.

• Journal of KIISE:Software and Applications
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• v.36 no.5
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• pp.347-352
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• 2009

Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data, the goal of which is decompose a data matrix into a product of two factor matrices with all entries in factor matrices restricted to be nonnegative. NMF was shown to be useful in a task of clustering (especially document clustering). In this paper we present an algorithm for orthogonal nonnegative matrix factorization, where an orthogonality constraint is imposed on the nonnegative decomposition of a term-document matrix. We develop multiplicative updates directly from true gradient on Stiefel manifold, whereas existing algorithms consider additive orthogonality constraints. Experiments on several different document data sets show our orthogonal NMF algorithms perform better in a task of clustering, compared to the standard NMF and an existing orthogonal NMF.

• Journal of KIISE
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• v.42 no.2
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• pp.235-241
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• 2015

Locally linear embedding (LLE) [1] is a type of manifold algorithms, which preserves inner product value between high-dimensional data when embedding the high-dimensional data to low-dimensional space. LLE closely embeds data points on the same subspace in low-dimensional space, because the data points have significant inner product values. On the other hand, if the data points are located orthogonal to each other, these are separately embedded in low-dimensional space, even though they are in close proximity to each other in high-dimensional space. Meanwhile, it is well known that the facial images of the same person under varying illumination lie in a low-dimensional linear subspace [2]. In this study, we suggest an improved LLE method for face recognition problem. The method maximizes the characteristic of LLE, which embeds the data points totally separately when they are located orthogonal to each other. To accomplish this, all of the subspaces made by each class are forced to locate orthogonally. To make all of the subspaces orthogonal, the simultaneous Diagonalization (SD) technique was applied. From experimental results, the suggested method is shown to dramatically improve the embedding results and classification performance.

• Proceedings of the Korean Vacuum Society Conference
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• 2013.08a
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• pp.273-273
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• 2013

Recently, Point-of-care (POC) testing microdevices enable to do the patient monitoring, drug screening, pathogen detection in the outside of hospital. Immunochromatographic strip (ICS) is one of the diagnostic technologies which are widely applied to POC detection. Relatively low cost, simplicity to use, easy interpretations of the diagnostic results and high stability under any circumstances are representative advantages of POC diagnosis. It would provide colorimetric results more conveniently, if the genetic analysis microsystem incorporates the ICS as a detector part. In this work, we develop a reverse transcriptase-polymerase chain reaction (RT-PCR) microfluidic device integrated with a ROSGENE strip for colorimetric influenza H1N1 virus detection. The integrated RT-PCR- ROSGENE device is consist of four functional units which are a pneumatic micropump for sample loading, 2 ${\mu}L$ volume RT-PCR chamber for target gene amplification, a resistance temperature detector (RTD) electrode for temperature control, and a ROSGENE strip for target gene detection. The device was fabricated by combining four layers: First wafer is for RTD microfabrication, the second wafer is for PCR chamber at the bottom and micropump channel on the top, the third is the monolithic PDMS, and the fourth is the manifold for micropump operation. The RT-PCR was performed with subtype specific forward and reverse primers which were labeled with Texas-red, serving as a fluorescent hapten. A biotin-dUTP was used to insert biotin moieties in the PCR amplicons, during the RT-PCR. The RT-PCR amplicons were loaded in the sample application area, and they were conjugated with Au NP-labeled hapten-antibody. The test band embedded with streptavidins captures the biotin labeled amplicons and we can see violet colorimetric signals if the target gene was amplified with the control line. The off-chip RT-PCR amplicons of the influenza H1N1 virus were analyzed with a ROSGENE strip in comparison with an agarose gel electrophoresis. The intensities of test line was proportional to the template quantity and the detection sensitivity of the strip was better than that of the agarose gel. The test band of the ROSGENE strip could be observed with only 10 copies of a RNA template by the naked eyes. For the on-chip RT-PCR-ROSGENE experiments, a RT-PCR cocktail was injected into the chamber from the inlet reservoir to the waste outlet by the micro-pump actuation. After filling without bubbles inside the chamber, a RT-PCR thermal cycling was executed for 2 hours with all the microvalves closed to isolate the PCR chamber. After thermal cycling, the RT-PCR product was delivered to the attached ROSGENE strip through the outlet reservoir. After dropping 40 ${\mu}L$ of an eluant buffer at the end of the strip, the violet test line was detected as a H1N1 virus indicator, while the negative experiment only revealed a control line and while the positive experiment a control and a test line was appeared.