• Title/Summary/Keyword: existence of weak solution

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BIHARMONIC-KIRCHHOFF TYPE EQUATION INVOLVING CRITICAL SOBOLEV EXPONENT WITH SINGULAR TERM

  • Tahri, Kamel;Yazid, Fares
    • Communications of the Korean Mathematical Society
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    • v.36 no.2
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    • pp.247-256
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    • 2021
  • Using variational methods, we show the existence of a unique weak solution of the following singular biharmonic problems of Kirchhoff type involving critical Sobolev exponent: $$(\mathcal{P}_{\lambda})\;\{\begin{array}{lll}{\Delta}^2u-(a{\int}_{\Omega}{\mid}{\nabla}u{\mid}^2dx+b){\Delta}u+cu=f(x){\mid}u{\mid}^{-{\gamma}}-{\lambda}{\mid}u{\mid}^{p-2}u&&\text{ in }{\Omega},\\{\Delta}u=u=0&&\text{ on }{\partial}{\Omega},\end{array}$$ where Ω is a smooth bounded domain of ℝn (n ≥ 5), ∆2 is the biharmonic operator, and ∇u denotes the spatial gradient of u and 0 < γ < 1, λ > 0, 0 < p ≤ 2# and a, b, c are three positive constants with a + b > 0 and f belongs to a given Lebesgue space.

OPTIMAL CONTROL PROBLEMS FOR THE SEMILINEAR SECOND ORDER EVOLUTION EQUATIONS

  • Park, Jong-Yeoul;Park, Sun-Hye
    • Journal of the Korean Mathematical Society
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    • v.40 no.5
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    • pp.769-788
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    • 2003
  • In this paper, we study the optimal control for the damped semilinear hyperbolic systems with unknown parameters (C(t)y')'+ $A_2$(t, q)y'+ $A_1$(t, q)y = f(t, q, y, u). We will prove the existence of weak solution of this system and is to find the optimal control pair (q, u) $\in$ $Q_{t}$ ${\times}$ $U_{ad}$ such that in $f_{u}$$\in$ $Q_{t}$/ J(q, u) = J(q, u).$_{t}$/ J(q, u) = J(q, u).

Prediction of ground-condition ahead of tunnel face using electromagnetic wave - analytical study (전자기파를 이용한 터널전방 예측 -해석기법 중심으로)

  • Choi, Jun-Su;Cho, Gye-Chun;Lee, Geun-Ha;Yoon, Ji-Nam
    • Journal of Korean Tunnelling and Underground Space Association
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    • v.6 no.4
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    • pp.327-343
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    • 2004
  • During tunnel construction, ground failures often occur due to existence of weak zones, such as faults, joints, and cavities, ahead of tunnel face. It is hard to detect effectively weak zones, which can lead underground structure to fail after excavation and before supporting, by using conventional characterization methods. In this study, an enhanced analytical method of predicting weak zones ahead of tunnel face is developed to overcome some problems in the conventional geophysical exploration methods. The analytical method is based on Coulomb's and Gauss' laws with considering the characteristics of electric fields subjected to rock mass. Using the developed method, closed form solutions are obtained to detect a spherical shaped zone and an oriented fault ahead of tunnel face respectively. The analytical results suggest that the presence of weak zones and their sizes, location, and states can be accurately predicted by combining a proper inversion process with resistance measured from several electrodes on the tunnel face. It appears that the skin depth or resistivity in rock mass is affected by the diameter of tunnel face, natural electric potential and noises induced by experimental measurement and spatial distribution of uncertain properties. The developed analytical solution is verified through experimental tests. About 1800 concrete blocks of 5cm by 5cm by 5cm in size are prepared and used to model a joint rock mass around tunnel face. Weak zones are simulated ahead of tunnel face with a material which has relatively higher conductivity than concrete blocks. Experimental results on the model test show a good agreement with analytical results.

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MOBIGSS: A Group Decision Support System in the Mobile Internet (MOBIGSS: 모바일 인터넷에서의 그룹의사결정지원시스템)

  • Cho Yoon-Ho;Choi Sang-Hyun;Kim Jae-Kyeong
    • Journal of Intelligence and Information Systems
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    • v.12 no.2
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    • pp.125-144
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    • 2006
  • The development of mobile applications is fast in recent years. However, nearly all applications are for messaging, financial, locating services based on simple interactions with mobile users because of the limited screen size, narrow network bandwidth, and low computing power. Processing an algorithm for supporting a group decision process on mobile devices becomes impossible. In this paper, we introduce the mobile-oriented simple interactive procedure for support a group decision making process. The interactive procedure is developed for multiple objective linear programming problems to help the group select a compromising solution in the mobile Internet environment. Our procedure lessens the burden of group decision makers, which is one of necessary conditions of the mobile environment. Only the partial weak order preferences of variables and objectives from group decision makers are enough for searching the best compromising solution. The methodology is designed to avoid any assumption about the shape or existence of the decision makers' utility function. For the purpose of the experimental study of the procedure, we developed a group decision support system in the mobile Internet environment, MOBIGSS and applied to an allocation problem of investor assets.

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Preparation and Characterization of Multiferroic $0.7BiFeO_3-0.3BaTiO_3$ Thin Films by Pulsed Laser Deposition (펄스 레이저 증착법으로 제작된 다강체 $0.7BiFeO_3-0.3BaTiO_3$ 박막의 특성 연구)

  • Kim, Kyung-Man;Yang, Pan;Zhu, Jinsong;Joh, Young-Gull;Lee, Hee-Young
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2009.11a
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    • pp.88-88
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    • 2009
  • $BiFeO_3$(BFO), when forming a solid solution with $BaTiO_3$(BTO), shows structural transformations over the entire compositional range, which not only gives a way to increase structural stability and electrical resistivity but also applies a means to have better ferromagnetic ordering. In this respect, we have prepared and studied 0.7BFO-0.3BTO thin films on $Pt(111)/TiO_2/SiO_2/Si$ substrates by pulsed laser deposition. Various deposition parameters, such as deposition temperature and oxygen pressure, have been optimized to get better quality films. Based on the X-ray diffraction results, thin films were successfully deposited at the temperature of $600^{\circ}C$ and an oxygen partial pressure of 10mTorr. The dielectric, ferroelectric, and magnetic properties have then been characterized. It was found that the films deposited under lower oxygen pressure corresponded to lower leakage current. Magnetism measurement showed an induced ferromagnetism. The microstructures associated with. the magnetic and dielectric properties of this mixed-perovskite solid solutions were observed by transmission electron. microscopy, which revealed the existence of complicated ferroelectric domains, suggested that the weak spontaneous magnetization was closely associated with the decrease in the extent of rhombohedral distortion by a partial substitution of $BaTiO_3$ for $BiFeO_3$.

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PREPARATION AND CHARACTERIZATION OF MULTIFERROIC 0.8 $BiFeO_3$-0.2 $BaTiO_3$ THIN FIMLS BY PULSED LASER DEPOSITION

  • Kim, K.M.;Yang, P.;Zhu, J.S.;Lee, H.Y.
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2010.06a
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    • pp.313-313
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    • 2010
  • $BiFeO_3$ (BFO), when forming a solid solution with $BaTiO_3$ (BTO), shows structural transformations over the entire compositional range, which not only gives a way to increase structural stability and electrical resistivity but also applies a means to have better ferromagnetic ordering. In this respect, we have prepared and studied 0.8 BFO-0.2 BTO thin films on Pt(111)/$TiO_2/SiO_2$/Si substrates by pulsed laser deposition. Various deposition parameters, such as deposition temperature and oxygen pressure, have been optimized to get better quality films. Based on the X-ray diffraction results, thin films were successfully deposited at the temperature of $700^{\circ}C$ and an oxygen partial pressure of 10mTorr and 330mTorr. The dielectric, ferroelectric, and magnetic properties have then been characterized. It was found that the films deposited under lower and higher oxygen pressure corresponded to lower leakage current. Magnetism measurement showed an induced ferromagnetism. The microstructures associated with the magnetic and dielectric properties of this mixed-perovskite solid solutions were observed by transmission electron microscopy, which revealed the existence of complicated ferroelectric domains, suggested that the weak spontaneous magnetization was closely associated with the decrease in the extent of rhombohedral distortion by a partial substitution of $BaTiO_3$ for $BiFeO_3$.

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The Records and Archives Administrative Reform in China in 1930s (1930년대 중국 문서당안 행정개혁론의 이해)

  • Lee, Won-Kyu
    • The Korean Journal of Archival Studies
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    • no.10
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    • pp.276-322
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    • 2004
  • Historical interest in China in 1930s has been mostly focused on political characteristic of the National Government(國民政府) which was established by the KMT(中國國民黨) as a result of national unification. It is certain that China had a chance to construct a modern country by the establishment of the very unified revolutionary government. But, it was the time of expanding national crises that threatened the existence of the country such as the Manchurian Incident and the Chinese-Japanese War as well as the chaos of the domestic situation, too. So it has a good reason to examine the characteristic and pattern of the response of the political powers of those days. But, as shown in the recent studies, the manifestation method of political power by the revolutionary regime catches our attention through the understanding of internal operating system. Though this writing started from the fact that the Nationalist Government executed the administrative reform which aimed at "administrative efficiency" in the middle of 1930s, but it put stress on the seriousness of the problem and its solution rather than political background or results. "Committee on Administrative Efficiency(行政效率委員會)", the center of administrative reform movement which was established in 1934, examined the plan to execute the reform through legislation by the Executive Council(行政院) on the basis of the results of relevant studies. They claimed that the construction of a modern country should be performed by not political revolution anymore but by gradual improvement and daily reform, and that the operation of the government should become modern, scientific and efficient. There were many fields of administrative reform subjects, but especially, the field of records and archives adminstration(文書檔案行政) was studied intensively from the initial stage because that subject had already been discussed intensively. They recognized that records and archives were the basic tool of work performance and general activity but an inefficient field in spite of many input staff members, and most of all, archival reform bring about less conflicts than the fields of finance, organization and personnel. When it comes to the field of records adminstration, the key subjects that records should be written simply, the process of record treatment should be clear and the delay of that should be prevented were already presented in a records administrative meeting in 1922. That is, the unified law about record management was not established, so each government organization followed a conventional custom or performed independent improvement. It was through the other records administrative workshop of the Nationalist Government in 1933 when the new trend was appeared as the unified system improvement. They decided to unify the format of official records, to use marker and section, to unify the registration of receipt records and dispatch records and to strengthen the examination of records treatment. But, the method of records treatment was not unified yet, so the key point of records administrative reform was to establish a unified and standard record management system for preventing repetition by simplifying the treatment procedure and for intensive treatment by exclusive organizations. From the foundation of the Republic of China to 1930s, there was not big change in the field of archives administration, and archives management methods were prescribed differently even in the same section as well as same department. Therefore, the point at issue was to centralize scattered management systems that were performed in each section, to establish unified standard about filing and retention period allowance and to improve searching system through classification and proper number allowance. Especially, the problem was that each number system and classification system bring about different result due to dual operation of record registration and archives registration, and that strict management through mutual contrast, searching and application are impossible. Besides, various problems such as filing tools, arrangement method, preservation facilities & equipment, lending service and use method were raised also. In the process this study for the system improvement of records and archives management, they recognized that records and archives are the identical thing and reached to create a successive management method of records and archives called "Records and Archives Chain Management Method(文書檔案連鎖法)" as a potential alternative. Several principles that records and archives management should be performed unitedly in each organization by the general record recipient section and the general archives section under the principle of task centralization, a consistent classification system should be used by classification method decided in advance according to organizational constitution and work functions and an identical number system should be used in the process of record management stage and archive management stage by using a card-type register were established. Though, this "Records and Archives Chain Management Method" was developed to the stage of test application in several organizations, but it was not adopted as a regular system and discontinued. That was because the administrative reform of the Nationalist Government was discontinued by the outbreak of the Chinese-Japanese War. Even though the administrative reform in the middle of 1930s didn't produce practical results but merely an experimentation, it was verified that the reform against tradition and custom conducted by the Nationalist Government that aimed for the construction of a modern country was not only a field of politics, but on the other hand, the weak basis of the government operation became the obstacle to the realization of the political power of the revolutionary regime. Though the subject of records and archives administrative reform was postponed to the future, it should be understood that the consciousness of modern records and archives administration and overall studies began through this examination of administrative reform.