• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.331-346
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• 2016

The primary aim of this paper is to generalize a theorem of Hirzebruch for the complex 2-dimensional Bott manifolds, usually called Hirzebruch surfaces, to more general Bott towers of height n. To do so, we first show that all complex vector bundles of rank 2 over a Bott manifold are classified by their total Chern classes. As a consequence, in this paper we show that two Bott manifolds $B_n({\alpha}_1,{\ldots},{\alpha}_{n-1},{\alpha}_n)$ and $B_n({\alpha}_1,{\ldots},{\alpha}_{n-1},{\alpha}_n^{\prime})$ are isomorphic to each other, as Bott towers if and only if both ${\alpha}_n{\equiv}{\alpha}_n^{\prime}$ mod 2 and ${\alpha}_n^2=({\alpha}_n^{\prime})^2$ hold in the cohomology ring of $B_{n-1}({\alpha}_1,{\ldots},{\alpha}_{n-1})$ over integer coefficients. This result will complete a circle of ideas initiated in [11] by Ishida. We also give some partial affirmative remarks toward the assertion that under certain condition our main result still holds to be true for two Bott manifolds just diffeomorphic, but not necessarily isomorphic, to each other.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.795-834
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• 2016

The main purpose of this paper is to propose a scheme of a proof of the nonsimpleness of the group $Homeo^{\Omega}$ ($D^2$, ${\partial}D^2$) of area preserving homeomorphisms of the 2-disc $D^2$. We first establish the existence of Alexander isotopy in the category of Hamiltonian homeomorphisms. This reduces the question of extendability of the well-known Calabi homomorphism Cal : $Diff^{\Omega}$ ($D^1$, ${\partial}D^2$)${\rightarrow}{\mathbb{R}}$ to a homomorphism ${\bar{Cal}}$ : Hameo($D^2$, ${\partial}D^2$)${\rightarrow}{\mathbb{R}}$ to that of the vanishing of the basic phase function $f_{\underline{F}}$, a Floer theoretic graph selector constructed in [9], that is associated to the graph of the topological Hamiltonian loop and its normalized Hamiltonian ${\underline{F}}$ on $S^2$ that is obtained via the natural embedding $D^2{\hookrightarrow}S^2$. Here Hameo($D^2$, ${\partial}D^2$) is the group of Hamiltonian homeomorphisms introduced by $M{\ddot{u}}ller$ and the author [18]. We then provide an evidence of this vanishing conjecture by proving the conjecture for the special class of weakly graphical topological Hamiltonian loops on $D^2$ via a study of the associated Hamiton-Jacobi equation.

• Journal of The Korean Society of Agricultural Engineers
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• v.50 no.4
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• pp.99-109
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• 2008

As the price of traditional fossil fuels continue to increase, more people attach importance to the pollution of the environment caused by fossil fuel's burning, developing and using renewable energy resources has become a very important project all over the world. Also, the rural energy planning which is another method to improve energy utilization ratio and reduce environment pollution, is also regarded as a very effective way to reduce the energy consumption. There is a quantity of renewable energy resources and natural tribes in rural area, which is both feasible to develop the renewable energy and the regional energy planning. To carry out this, it is needs to know the area's quantity of renewable energy resources and the total energy consumption. This paper is to find out the relationship between rural energy consumption and rural conditions, and to found a energy consumption model which can conjecture the energy consumption in rural family. and the cost of rural family's energy consumption was founded to conjecture how much money dose it cost in rural family's energy consumption. The energy consumption model was concluded using the surveys of 76 families in 14 villages at the area of Chungcheongbuk-Do(province). The main factors to energy consumption was selected out which were number of family members, acreage of house, acreage of farmland and family's annual income.

• The Bulletin of The Korean Astronomical Society
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• v.35 no.1
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• pp.87.1-87.1
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• 2010

Main-belt comets (hereafter MBCs) are one of the hottest topics in the solar system astronomy. They are objects orbiting in the main asteroid belt which show cometary activity. Unlike most comets, which spend most of their orbit beyond 5AU from the Sun, MBCs follow near-circular orbits within the asteroid belt that are indistinguishable from the orbits of major population of the asteroids. P/2010 A2, the fifth MBC, was discovered by on January 6, 2010 by Lincoln Near-Earth Asteroid Research. It passed its perihelion at 2.01AU on December 3, 2009, about a month before it was discovered. With an aphelion of only 2.6 AU, P/2010 A2 spends all of its time inside of the frostline ~2.7 AU. We made observations of P/2010 A2 with Nishi-Harima Astronomical Observatory 2-m telescope only a week after the discovery. From the observed images, we found that the dust cloud was composed of large particles (>1mm) impulsively ejected between March and June, 2009. No coma was detected by our observations, suggesting that this object was no longer active. Consequently, we conjecture that these dust particles could be released by the impact collision among asteroids.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1123-1132
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• 2015

In this paper, we investigate derivations on the noncommutative Banach algebra $L^{\infty}_0({\omega})^*$ equipped with an Arens product. As a main result, we prove the Singer-Wermer conjecture for the noncommutative Banach algebra $L^{\infty}_0({\omega})^*$. We then show that a derivation on $L^{\infty}_0({\omega})^*$ is continuous if and only if its restriction to rad($L^{\infty}_0({\omega})^*$) is continuous. We also prove that there is no nonzero centralizing derivation on $L^{\infty}_0({\omega})^*$. Finally, we prove that the space of all inner derivations of $L^{\infty}_0({\omega})^*$ is continuously homomorphic to the space $L^{\infty}_0({\omega})^*/L^1({\omega})$.

• Journal of Mechanical Science and Technology
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• v.15 no.12
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• pp.1853-1859
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• 2001

An experimental study is presented for a flow field in a two dimensional wavy channels by PIV. This flow has two major applications such as a blood flow simulation and the enhancement of heat transfer in a heat exchanger. While the numerical flow visualization results have been limited to the fully developed cases, existing experimental results of this flow were simple qualitative ones by smoke or dye streak test. Therefore, the main purpose of this study is to produce quantitative flow data for fully developed and developing flow regimes by the Correlation Based Correction PIV (CBC PIV) and to conjecture the analogy between flow characteristics and heat transfer enhancement with low pumping power. Another purpose of this paper is to examine the onset position of the transition and the global mixing, which results in transfer enhancement. PIV results on the Fully developed and developing flow in a wavy channel at Re=500, 1000 and 2000 are obtained. for the case Reynolds Number equals 500, the PIV results are compared with the finite difference numerical solution.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.16 no.4
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• pp.368-373
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• 2004

A flow field in a passage with periodically converging-diverging cross-section is investigated experimentally by PIV measurement. A tube with a sinusoidally wavy cross section is one of several devices employed for enhancing the heat and mass transfer efficiency due to turbulence promotion and unsteady vortical motion. While the numerical flow visualization results have been limited to the fully developed cases, existing experimental results of this flow were simple qualitative ones by smoke or dye streak test. Therefore, the main purpose of this study is to produce quantitative flow data for fully developed and transient flow regime by the Correlation Based Correction PIV (CBC PIV) and to conjecture the analogy between flow characteristics and heat transfer enhancement with low pumping power. Another purpose of this paper is to examine the onset position of the transition and the global mixing, which results in transfer enhancement. At Re=2000, evidences of the global mixing are captured at 2.5 wavy module through the variation of RMS values and instantaneous velocity plot.

• Asian Journal of Innovation and Policy
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• v.2 no.1
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• pp.20-36
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• 2013

In this practice article, we present the results of a scenario planning approach that is a hybrid of the three main schools of thought. Our research objective was to study the future of Interactive Digital Media applications such as online music, on-demand television and massively multi-player online role-playing games. Our approach, while essentially qualitative in nature, nevertheless draws from the rigors of the quantitative school in identifying and then tracking the significant dimensions of analysis that emerge over time as strands of events leading to plausible scenarios. Our empirical analysis revealed mapping strands to three themes - ownership, distribution and innovation - which we used in an expert validation exercise to formulate scenarios. We present and discuss the major findings and implications of this empirical investigation. In a nutshell, we conjecture that an open, competitive IDM marketplace with performance safeguards may serve both and lead to a win-win scenario. While there are differences among IDM sectors, a unified approach to regulation and policy would be effective.

• The Mathematical Education
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• v.44 no.3 s.110
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• pp.375-396
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• 2005

This paper reports on the main results of 3 study that compared students' beliefs, skills, and understandings in an innovative approach to differential equations to more conventional approaches. The innovative approach, referred to as the Realistic Mathematics Education Based Differential Equations (IODE) project, capitalizes on advances within the discipline of mathematics and on advances within the discipline of mathematics education, both at the K-12 and tertiary levels. Given the integrated leveraging of developments both within mathematics and mathematics education, the IODE project is paradigmatic of an approach to innovation in undergraduate mathematics, potentially sewing as a model for other undergraduate course reforms. The effect of the IODE projection maintaining desirable mathematical views and in developing students' skills and relational understandings as judged by the three assessment instruments was largely positive. These findings support our conjecture that, when coupled with careful attention to developments within mathematics itself, theoretical advances that initially grew out research in elementary school classrooms can be profitably leveraged and adapted to the university setting. As such, our work in differential equations may serve as a model for others interested in exploring the prospects and possibilities of improving undergraduate mathematics education in ways that connect with innovations at the K-12 level

• Journal of architectural history
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• v.14 no.3 s.43
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• pp.7-21
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• 2005

This paper is an attempt to find/make an entrance to John Hejduk's architecture. Based explicitly on both Karl Popper's model of knowledge production called 'conjecture and refutation' and Harold Bloom's theory of poetry called 'revisionism', this paper, in order to produce a new problem, mainly deals with an existing knowledge as an object to refute, that is, Michael Hays' interpretation of Wall House by Jacques Lacan's notion of the gaze, Hejduk's a pivotal architectural finding. The arguments underlying this paper are two: First, Hejduk, just like this paper, follows Popper's model and Bloom's theory in conducting his own architectural research. Secondly, he takes what might be called artist's attitude when absorbing previous knowledge and producing new one. These two arguments are made in the first part and then served as a basic propositions for further arguments. In the process of criticizing the way in which Hays explicates Hejduk's Wall House, this paper reaches two main arguments. First, Lacan's notion of the gaze is not proper specifically for the explication of it. However, it may be useful and even promising when dealing with other works such as Subject/Object and House of the Inhabitant Who Refused to Participate. Secondly, Freud's notion of 'uncanny', arguably Hejduk's strong architectural orientation, may serve much better as a main gate among possibly many ones in trying to open his architecture. It is considered that this might also serve as an important clue to solving mysticism remaining yet untouched in his architecture.