• The Pure and Applied Mathematics
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• v.30 no.2
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• pp.109-129
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• 2023

In this paper, we introduce a second order linear differential operator ^T□: C^∞ (M) → C^∞ (M) as a natural generalization of Cheng-Yau operator, [8], where T is a (1, 1)-tensor on Riemannian manifold (M, h), and then we show on compact Riemannian manifolds, divT = divT^t, and if divT = 0, and f be a smooth function on M, the condition ^T□ f = 0 implies that f is constant. Hereafter, we introduce T-energy functionals and by deriving variations of these functionals, we define T-harmonic maps between Riemannian manifolds, which is a generalization of L_k-harmonic maps introduced in [3]. Also we have studied fT-harmonic maps for conformal immersions and as application of it, we consider fL_k-harmonic hypersurfaces in space forms, and after that we classify complete fL₁-harmonic surfaces, some fL_k-harmonic isoparametric hypersurfaces, fL_k-harmonic weakly convex hypersurfaces, and we show that there exists no compact fL_k-harmonic hypersurface either in the Euclidean space or in the hyperbolic space or in the Euclidean hemisphere. As well, some properties and examples of these definitions are given.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.195-203
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• 2005

We show that the exact Bergman kernel function associated to a $C^{\infty}$ bounded domain in the plane relates the derivatives of the Ahlfors map in an explicit way. And we find several formulas relating the exact Bergman kernel to classical kernel functions in potential theory.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.599-627
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• 2020

In this paper, we characterize a class of biharmonic maps from and between doubly product manifolds in terms of theie warping function. Examples are constructed when all of the factors are Euclidean spaces.

• Communications of the Korean Mathematical Society
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• v.9 no.1
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• pp.175-181
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• 1994

• Bulletin of the Korean Chemical Society
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• v.13 no.3
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• pp.268-274
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• 1992

An attempt to improve the second harmonic generation (SHG) efficiency of MAP (methyl (2,4-dinitrophenyl)aminopropanoate) by modifying the substituents on the amino group of MAP is described. Several MAP analogues have been prepared using optically active amino acids alanine, phenylalanine and serine, and their SHG efficiencies measured. None of the MAP analogues exhibited SHG efficiencies as high as that of MAP. X-ray crystal structures of three MAP analogues have been determined. In the crystal structures of two of them, which were the derivatives of phenylalanine, two crystallographically-independent molecules existing in the asymmetric unit are aligned almost antiparallel. These structures are consistent with the very low SHG efficiencies of these compounds. On the other hand, the crystal structure of a serine derivative reveals substantial alignment of the dinitroaniline chromophore along the polar axis. However, the angle of 86.2° between the molecular charge tranfer axis and the polar axis of the crystal is still far away from the optimum value of 54.74° for the phase-matchable SHG. The structure is consistent with the SHG efficiency of this compound which is much higher than those of the phenylalanine derivatives but still lower than that of MAP. This study demonstrates the importance of the orientation of molecules in the crystal lattice in determining secod-order nonlinear optical properties of crystalline materials.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.343-356
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• 2019

In this paper, we introduce metallic maps between metallic Riemannian manifolds, provide an example and obtain certain conditions for such maps to be totally geodesic. We also give a sufficient condition for a map between metallic Riemannian manifolds to be harmonic map. Then we investigate the constancy of certain maps between metallic Riemannian manifolds and various manifolds by imposing the holomorphic-like condition. Moreover, we check the reverse case and show that some such maps are constant if there is a condition for this.

• Korean Journal of Remote Sensing
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• v.27 no.1
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• pp.17-24
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• 2011

Global warming and climatic changes due to human activities impact on marine and terrestrial ecosystems, which feedbacks to climate system. These negative feedbacks amplify or accelerate again global climate change. In particular, it is important to analyze vegetation change. This study attempts to analyze quantitatively vegetation change in Korea peninsula by using harmonic analysis. Harmonic-Analysis based on Fourier Transform is the method to effectively demonstrate for time series data. Especially, Harmonic-Analysis is very suitable method to analyze vegetation change because the vegetation repeats the cycle growth and extinction every year. The result of harmonic-analysis shows vegetation change as time passes. In this study, SPOTNEGETATION S10 MVC NDVI data was used during last 10 years (1999-2008) in Korea Peninsula. Also, land type classification used MODIS Land Cover Map data. The study estimated that phase values moved up approximately 0.5 day per year in cropland and 0.8 day per year in forest.

• Korean Journal of Remote Sensing
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• v.24 no.1
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• pp.79-89
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• 2008

Irregular temporal sampling is a common feature of geophysical and biological time series in remote sensing. This study proposes an on-line system for reconstructing observation image series contaminated by noises resulted from mechanical problems or sensing environmental condition. There is also a high likelihood that during the data acquisition periods the target site corresponding to any given pixel may be covered by fog or cloud, thereby resulting in bad or missing observation. The surface parameters associated with the land are usually dependent on the climate, and many physical processes that are displayed in the image sensed from the land then exhibit temporal variation with seasonal periodicity. A feedback system proposed in this study reconstructs a sequence of images remotely sensed from the land surface having the physical processes with seasonal periodicity. The harmonic model is used to track seasonal variation through time, and a Gibbs random field (GRF) is used to represent the spatial dependency of digital image processes. The experimental results of this simulation study show the potentiality of the proposed system to reconstruct the image series observed by imperfect sensing technology from the environment which are frequently influenced by bad weather. This study provides fundamental information on the elements of the proposed system for right usage in application.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.941-947
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• 2007

Let M be a complete Riemannian manifold and let N be a Riemannian manifold of nonpositive scalar curvature. Let ${\mu}0$ be the least eigenvalue of the Laplacian acting on $L^2-functions$ on M. We show that if $Ric^M{\ge}-{\mu}0$ at all $x{\in}M$ and either $Ric^M>-{\mu}0$ at some point x0 or Vol(M) is infinite, then every harmonic morphism ${\phi}:M{\to}N$ of finite energy is constant.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.911-922
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• 2014

In the present article we study a special class of surfaces in the four-dimensional Euclidean space, which are one-parameter systems of meridians of the standard rotational hypersurface. They are called meridian surfaces. We show that a meridian surface has a harmonic Gauss map if and only if it is part of a plane. Further, we give necessary and sufficient conditions for a meridian surface to have pointwise 1-type Gauss map and find all meridian surfaces with pointwise 1-type Gauss map.