• Title/Summary/Keyword: Uniqueness problem

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A FREQUENCY-DOMAIN METE10D FOR FINITE ELEMENT SOLUTIONS OF PARABOLIC PROBLEMS

  • Lee, Chang-Ock;Lee, Jongwoo;Sheen, Dongwoo
    • Bulletin of the Korean Mathematical Society
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    • v.39 no.4
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    • pp.589-606
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    • 2002
  • We introduce and analyze a frequency-domain method for parabolic partial differential equations. The method is naturally parallelizable. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we propose to solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution in the space-time domain. Existence and uniqueness as well as error estimates are given. Fourier invertibility is also examined. Numerical experiments are presented.

SECOND MAIN THEOREM AND UNIQUENESS PROBLEM OF ZERO-ORDER MEROMORPHIC MAPPINGS FOR HYPERPLANES IN SUBGENERAL POSITION

  • Luong, Thi Tuyet;Nguyen, Dang Tuyen;Pham, Duc Thoan
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.205-226
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    • 2018
  • In this paper, we show the Second Main Theorems for zero-order meromorphic mapping of ${\mathbb{C}}^m$ into ${\mathbb{P}}^n({\mathbb{C}})$ intersecting hyperplanes in subgeneral position without truncated multiplicity by considering the p-Casorati determinant with $p{\in}{\mathbb{C}}^m$ instead of its Wronskian determinant. As an application, we give some unicity theorems for meromorphic mapping under the growth condition "order=0". The results obtained include p-shift analogues of the Second Main Theorem of Nevanlinna theory and Picard's theorem.

INFINITE HORIZON OPTIMAL CONTROL PROBLEMS OF BACKWARD STOCHASTIC DELAY DIFFERENTIAL EQUATIONS IN HILBERT SPACES

  • Liang, Hong;Zhou, Jianjun
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.2
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    • pp.311-330
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    • 2020
  • This paper investigates infinite horizon optimal control problems driven by a class of backward stochastic delay differential equations in Hilbert spaces. We first obtain a prior estimate for the solutions of state equations, by which the existence and uniqueness results are proved. Meanwhile, necessary and sufficient conditions for optimal control problems on an infinite horizon are derived by introducing time-advanced stochastic differential equations as adjoint equations. Finally, the theoretical results are applied to a linear-quadratic control problem.

UNIQUE POSITIVE SOLUTION FOR A CLASS OF THE SYSTEM OF THE NONLINEAR SUSPENSION BRIDGE EQUATIONS

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.16 no.3
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    • pp.355-362
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    • 2008
  • We prove the existence of a unique positive solution for a class of systems of the following nonlinear suspension bridge equation with Dirichlet boundary conditions and periodic conditions $$\{{u_{tt}+u_{xxxx}+\frac{1}{4}u_{ttxx}+av^+={\phi}_{00}+{\epsilon}_1h_1(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,\\{v_{tt}+v_{xxxx}+\frac{1}{4}u_{ttxx}+bu^+={\phi}_{00}+{\epsilon}_2h_2(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,$$ where $u^+={\max}\{u,0\},\;{\epsilon}_1,\;{\epsilon}_2$ are small number and $h_1(x,t)$, $h_2(x,t)$ are bounded, ${\pi}$-periodic in t and even in x and t and ${\parallel} h_1{\parallel}={\parallel} h_2{\parallel}=1$. We first show that the system has a positive solution, and then prove the uniqueness by the contraction mapping principle on a Banach space

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SENSITIVITY ANALYSIS OF SOLUTIONS FOR A SYSTEM OF PARAMETRIC GENERAL QUASIVARIATIONAL-LIKE INEQUALITIES

  • Hao, Yan;Kang, Shin-Min
    • East Asian mathematical journal
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    • v.24 no.2
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    • pp.177-186
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    • 2008
  • In this paper, we introduce and study a new class of system of parametric general quasivariational-like inequalities. Using $\eta$-subdifferential and $\eta$-proximal mappings of proper functionals in Hilbert spaces, we prove the equivalence between the system of parametric general quasivariational-like inequalities and a xed point problem and construct two iterative algorithms. A few existence and uniqueness results as well as the sensitivity analysis of solutions are also established for the system of parametric general quasivariational-like inequalities, and some convergence results of iterative sequence generated by the algorithms are proved. Our results extend a few known results in the literature.

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Characteristics of Consumers and Their Perceptions of Natural-Dyed Clothes (천연염색 의류에 대한 소비자 반응 및 소비자 특성)

  • 홍나영;유혜경;이주현;석혜정;신혜성;김찬주
    • The Research Journal of the Costume Culture
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    • v.11 no.3
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    • pp.404-415
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    • 2003
  • The main purpose of this exploratory research was to examine the characteristics of consumers who patronize natural-dyed clothes and their perceptions regarding natural-dyed clothes. Thirty three participants who have worn natural-dyed clothes were interviewed for the study. They were asked about the styles and price of natural-dyed clothes they owned, their evaluation on them, and the lifestyles of themselves. Existence of subculture among the interviewes and its characteristics were also probed. The results indicated that natural-dyed clothes are relatively high-priced, mostly of modified hanbok style, and became popular in recent years. Interviewees frequently mentioned uniqueness and comfort as the main benefits of natural-dyed clothes, and expressed dissatisfaction regarding color fastness, easy care and problem of coordination. The consumers of natural-dyed clothes appeared to have strong preferences for environment conservation and Korean traditional culture. They also seemed to form a subcultural group who have commonality in their involvement in Korean cultural activities, mainly tea ceremony.

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A Field Study of Supportive Housing 'The Christopher' in New York, USA (미국 뉴욕시 서포티브주택 '더 크리스토퍼' 현장분석 연구)

  • Lee, Yeunsook;Park, Jae-Hyun
    • Journal of the Korean housing association
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    • v.26 no.1
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    • pp.19-30
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    • 2015
  • As the number of homeless is increasing, there have been worries for social burden and social insecurity, along with crisis in human dignity. The purpose of this research is to identify characteristics of a Supportive Housing (SH) project which is considered best practice in dealing with homeless problem. A field visit walk through observation and in-depth interview was utilized as the main research method. As results, overall management, spatial and service characteristics were delineated, and its meaning and uniqueness were discussed, as well as, comparison with Korean conditions. In conclusion, the characteristics of the Supportive Housing were more realistically revealed through a current field case to inspire to explore housing for Korea. Besides current concerns were linked and implication to Korean adaptation was suggested. This study is unique in that SH of USA is firstly introduced in such details.

Fingerprint Identification System Using Ridge Direction Extraction by Index Table (Index table에 의한 융선의 방향성 추출을 이용한 지문 인식 시스템)

  • Lee, Jee-Won;Ahn, Do-Rang;Lee, Dong-Wook
    • Proceedings of the KIEE Conference
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    • 2005.10b
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    • pp.180-182
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    • 2005
  • Fingerprint-based identification is known to be used for a very long time. Owing to their uniqueness and immutability, fingerprints are today the most widely used biometric features. Therefore, recognition using fingerprints is one of the safest methods as a way of personal identification. But fingerprint identification system has a critical weakness. Since the fingerprint identification time dramatically increase when we compare the unknown fingerprint's minutiae with fingerprint database's minutiae. In this paper, a ridge orientation extraction method using Index table is proposed to solve the problem. The goal of fast direction image extraction is to reduce the identification time and to improve the clarity of ridge and valley structures of input fingerprint image.

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Particle Dispersion and Effect of Spin in the Turbulent Boundary Layer Flow (난류 경계층 유동에서 입자의 확산과 스핀의 영향)

  • Kim, Byung-Gu;Lee, Chang-Hoon
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.28 no.1
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    • pp.89-98
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    • 2004
  • In this paper, we develope a dispersion model based on the Generalized Langevin Model. Thomson's well-mixed condition is the well known criterion to determine particle dispersion. But, it has 'non-uniqueness problem'. To resolve this, we adopt a turbulent model which is a new approach in this field of study. Our model was greatly simplified under the self-similarity condition, leaving model only two model constants $C_{0}$ and ${\gamma}$$_{5}$ that control the dispersion and spin which measures rotational property of the Lagrangian particle trajectory. We investigated the sign of spin as well as magnitude by using the Direct Numerical Simulation. Model calculations were performed on the neutrally stable boundary layer flow. We found that spin has weak effect on the particle dispersion but it shows the significant effect on the horizontal flux compared to the zero-spin model.

Need for Reinforcement of Safety Assessment on Genetically Modified Organisms (GMO 안전성평가제도의 고찰)

  • Kim Eun-Jin;Choi Dong-Keun
    • Korean Journal of Organic Agriculture
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    • v.14 no.2
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    • pp.139-157
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    • 2006
  • Biotechnology has reached the level of giving birth to new forms of life and with this is a growing controversy in the conflict between science and ethics. Especially, GMOs are closely linked to the food products we consume and thus, the majority of the public shows a very sensitive reaction to the safety of GMO food products. Many perspectives arose surrounding the issues of safety on the human body and the ecology. This outlines diverse structural mechanisms to be set up to ensure safety such as risk assessment, risk management etc. Despite the precautionary principle guaranteed in many ways, the problem arises whether and how this principle can be taken in the safety assessment. GMOs due to its uniqueness do not end with just the possession of the technology involved but must also be considered with the prerequisite that they could be cultured again. Therefore the reinforcement of safety assessment system is necessary. That is, the reinforcement of risk assessment including field tests, the consideration of socio-economic effects, the coordinated system of relevant authorities, the development of technology for safety assessment.

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