• Title/Summary/Keyword: $L_{\infty}$-structure

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EXPLICIT SOBOLEV ESTIMATES FOR THE CAUCHY-RIEMANN EQUATION ON PARAMETERS

  • Cho, Sang-Hyun;Choi, Jae-Seo
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.2
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    • pp.321-338
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    • 2008
  • Let $\bar{M}$ be a smoothly bounded pseudoconvex complex manifold with a family of almost complex structures $\{L^{\tau}\}_{{\tau}{\in}I}$, $0{\in}I$, which extend smoothly up to bM, the boundary of M, and assume that there is ${\lambda}{\in}C^{\infty}$(bM) which is strictly subharmonic with respect to the structure $L^0|_{bM}$ in any direction where the Levi-form vanishes on bM. We obtain explicit estimates for the $\bar{\partial}$-Neumann problem in Sobolev spaces both in space and parameter variables. Also we get a similar result when $\bar{M}$ is strongly pseudoconvex.

STRUCTURE OF STABLE MINIMAL HYPERSURFACES IN A RIEMANNIAN MANIFOLD OF NONNEGATIVE RICCI CURVATURE

  • Kim, Jeong-Jin;Yun, Gabjin
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.4
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    • pp.1201-1207
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    • 2013
  • Let N be a complete Riemannian manifold with nonnegative Ricci curvature and let M be a complete noncompact oriented stable minimal hypersurface in N. We prove that if M has at least two ends and ${\int}_M{\mid}A{\mid}^2\;dv={\infty}$, then M admits a nonconstant harmonic function with finite Dirichlet integral, where A is the second fundamental form of M. We also show that the space of $L^2$ harmonic 1-forms on such a stable minimal hypersurface is not trivial. Our result is a generalization of one of main results in [12] because if N has nonnegative sectional curvature, then M admits no nonconstant harmonic functions with finite Dirichlet integral. And our result recovers a main theorem in [3] as a corollary.

Age Determination and Estimation of Growth Parameters Using Otoliths of Small Yellow Croaker, Pseudosciaena polyactis Bleeker in Korean Waters (이석을 이용한 참조기(Pseudosciaena polyactis Bleeker)의 연령사정과 성장식 추정)

  • 이만우;장창익;이장욱
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.36 no.3
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    • pp.222-233
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    • 2000
  • A methodology for determining age by otolith of small yellow croaker, Pseudosoiaena polyactis Bleeker, was developed. A thin section method was chosen to be suitable for age determination because the otolith had a three-dimensional shape and thus it was not possible to read the otolith rings on the surface. The clear rings were identified on the vertical-axis cross-sectioned otoliths. The total length-total weight relationship and the growth parameters were estimated with error structure to endow with accuracy. In the relationship between total length and total weight, a multiplicative error structure was assumed because variability in growth increased as a function of the length, and the estimated equation was $W=0.0049L^{3.2153}$. The variability in growth was constant as a function of the age, revealing an additive error structure. The von Bertalanffy growth parameters were obtained from a nonlinear regression as $L_{\infty}= 37.11cm, K=0.20/yr and t_0=-1.88.$

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Growth and Reproduction of Deep-Water Mud Shrimp (Solenocera melantho) around Geomun Island, Korea (거문도 해역 대롱수염새우(Solencer melantho)의 성자과 성 성숙)

  • OH Taeg Yun;CHOI Jung Hwa;CHA Hyung Kee;KIM Joo Il;KIM Dea Hyun;LEE Ju Hee
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.38 no.4
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    • pp.232-238
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    • 2005
  • This paper describes reproduction, population structure, growth and size at sexual maturity of a deep-water mud shrimp (Solenocera melantho) in the adjacent waters of Geomun Island, Korea. The shrimp was caught by a beam trawl from November 1998 to December 1999. Spawning period was estimated by gonadosomatic index to be from August to early November with a peak in October to early November. Female shrimps were $12\%$ matured at 16 mm in carapace length, $33\%$ matured at 18 mm and $75\%$ matured at 22 mm. The size at $50\%$ maturity for female was estimated to be 20.65 mm in carapace length. Breeding season was estimated to be from August to early November with a peak in October to early November. The size at $50\%$ inseminated was 19.81 mm CL. The fecundity was 87,500-405,200 and related exponentially to carapace length and total weight. This species survived between 25 and 26 months. The maximum carapace length of females and males were 48 mm and 34 mm respectively. Sex ratio was $51.3\%$, and the females were preponderant. Growth was estimated by modified von Bertalanffy growth function incorporating seasonal variation in growth in both years females (K=1.019/yr and $L_{\infty}$=51.731 mm CL) grew faster, reaching a larger size at a given age than males (K=1.848/yr, and $L_{\infty}$=27.499 mm CL). This is indicated by differences in growth performance indices $(\varphi')$ between females (3.291) and males (3.145).

Reproductive Biology and Population Dynamics of Luciogobius guttatus (Pisces: Gobiidae) in the Southwestern of Korea (서해 중부 해역에 출현하는 미끈망둑, Luciogobius guttatus (Gobiidae)의 생식생태와 개체군 동태)

  • Kim, Byung Gi;Kim, Ji Hye;Han, Kyung Nam
    • Korean Journal of Ichthyology
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    • v.27 no.3
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    • pp.217-227
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    • 2015
  • Reproductive biology and population dynamics of Luciogobius guttatus were investigated. Higher gonadosomatic index (GSI) was observed from March~May. The fecundity ranged form 241 eggs at 3.1~4.0 cm (SL) to 716 eggs at 5.1~5.7 cm (SL). The relationship between length (SL) and fecundity (F) was $F=11.242SL^{2.464}$ ($R^2=0.65$) and fecundity increased with length. We estimated the SL at 50% group maturity as 2.6 cm. The spawning period was March~May. The von Bertalanffy growth function (VBGF) estimates were: $L_{\infty}=63.00mm$ TL; $K=0.85yr^{-1}$. The structure of recruitment pattern obtained by the FiSAT II program indicated one normally distributed group. The growth performance index (${\phi}$) was calculated with 3.53. Natural mortality rate (M) was $1.00yr^{-1}$.

A Study on the Optimum Mix Proportion of the Mass Concrete Designed as Massive and Deep Structure

  • Kwon Yeong-Ho;Lee Hwa-Jin
    • Journal of the Korea Concrete Institute
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    • v.17 no.2 s.86
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    • pp.293-302
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    • 2005
  • This study describes data from determination of the optimum mix proportion and site application of the mass concrete placed in bottom slab and side wall having a large depth and section as main structures of LNG in-ground tank. This concrete requires low heat hydration, excellent balance between workability and consistency because concreting work of LNG in-ground tank is usually classified by under-pumping, adaptation of longer vertical and horizontal pumping line than ordinary pumping condition. For this purpose, low heat Portland cement and lime stone powder as cementitious materials are selected and design factors including unit cement and water content, water-binder ratio, fine aggregate ratio and adiabatic temperature rising are tested in the laboratory and batch plant. As experimental results, the optimum unit cement and water content are selected under $270kg/m^3$ and $l55{\~}l60 kg/m^3$ separately to control adiabatic temperature rising below $30^{\circ}C$ and to improve properties of the fresh and hardened concrete. Also, considering test results of the confined water ratio($\beta$p) and deformable coefficient(Ep), $30\%$ of lime stone powder by cement weight is selected as the optimum replacement ratio. After mix proportions of 5cases are tested and compared the adiabatic temperature rising($Q^{\infty}$, r), tensile and compressive strength, modulus of elasticity, teases satisfied with the required performances are chosen as the optimum mix design proportions of the side wall and bottom slab concrete. $Q^{\infty}$ and r are proved smaller than those of another project. Before application in the site, properties of the fresh concrete and actual mixing time by its ampere load are checked in the batch plant. Based on the results of this study, the optimum mix proportions of the massive concrete are applied successfully to the bottom slab and side wall in LNG in-ground tank.

A new approach to deal with sensor errors in structural controls with MR damper

  • Wang, Han;Li, Luyu;Song, Gangbing;Dabney, James B.;Harman, Thomas L.
    • Smart Structures and Systems
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    • v.16 no.2
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    • pp.329-345
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    • 2015
  • As commonly known, sensor errors and faulty signals may potentially lead structures in vibration to catastrophic failures. This paper presents a new approach to deal with sensor errors/faults in vibration control of structures by using the Fault detection and isolation (FDI) technique. To demonstrate the effectiveness of the approach, a space truss structure with semi-active devices such as Magneto-Rheological (MR) damper is used as an example. To address the problem, a Linear Matrix Inequality (LMI) based fixed-order $H_{\infty}$ FDI filter is introduced and designed. Modeling errors are treated as uncertainties in the FDI filter design to verify the robustness of the proposed FDI filter. Furthermore, an innovative Fuzzy Fault Tolerant Controller (FFTC) has been developed for this space truss structure model to preserve the pre-specified performance in the presence of sensor errors or faults. Simulation results have demonstrated that the proposed FDI filter is capable of detecting and isolating sensor errors/faults and actuator faults e.g., accelerometers and MR dampers, and the proposed FFTC can maintain the structural vibration suppression in faulty conditions.

FIXED POINTS OF A CERTAIN CLASS OF ASYMPTOTICALLY REGULAR MAPPINGS

  • Jung, Jong-Soo;Thakur, Balwant-Singh;Sahu, Daya-Ram
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.4
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    • pp.729-741
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    • 2000
  • In this paper, we study in Banach spaces the existence of fixed points of asymptotically regular mapping T satisfying: for each x, y in the domain and for n=1, 2,…, $$\parallelT^nx-T^ny\parallel\leq$\leq$a_n\parallelx-y\parallel+b_n (\parallelx-T^nx\parallel+\parallely-T^ny\parallely)$$ where $a_n,\; b_n,\; C_n$ are nonnegative constants satisfying certain conditions. We also establish some fixed point theorems for these mappings in a Hibert space, in L(sup)p spaces, in Hardy space H(sup)p, and in Soboleve space $H^{k,p} for 1<\rho<\infty \; and \; k\geq0$. We extend results from papers [10], [11], and others.

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Sparse Second-Order Cone Programming for 3D Reconstruction

  • Lee, Hyun-Jung;Lee, Sang-Wook;Seo, Yong-Duek
    • Proceedings of the Korean Society of Broadcast Engineers Conference
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    • 2009.01a
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    • pp.103-107
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    • 2009
  • This paper presents how to minimize the second-order cone programming problem occurring in the 3D reconstruction of multiple views. The $L_{\infty}$-norm minimization is done by a series of the minimization of the maximum infeasibility. Since the problem has many inequality constraints, we have to adopt methods of the interior point algorithm, in which the inequalities are sequentially approximated by log-barrier functions. An initial feasible solution is found easily by the construction of the problem. Actual computing is done by an iterative Newton-style update. When we apply the interior point method to the problem of reconstructing the structure and motion, every Newton update requires to solve a very large system of linear equations. We show that the sparse bundle-adjustment technique can be utilized in the same way during the Newton update, and therefore we obtain a very efficient computation.

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Population Biology of Korean Pomfret Pampus echinogaster (Basilewsky, 1855) (Perciformes: Stromateidae) on the Western Coast of Korea, Yellow Sea

  • Oh, Chul-Woong;Na, Jong-Hun;Kim, Jin-Koo
    • Animal cells and systems
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    • v.13 no.1
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    • pp.83-89
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    • 2009
  • Investigations were made on population biology of Pampus echinogaster (Basilewsky, 1855) in the coastal areas of Korea, Yellow Sea, between August 2005 and July 2006. Population structure was not significantly different between male and females. Monthly variation of gonadosomatic index (GSI) of both sexes defined spawning period extending from March through July. A similar pattern was also observed in change at maturity stages. For males and females GSI was positively correlated with hepatosomatic index (HSI). Fecundity, ranging from 41,250 to 103,610 eggs, was related to body size, indicating that body size is the useful determinant of fecundity. The sexual maturity ($L_{50}$) was estimated as 14.98 cm TL for males and 19.32 cm TL for females. Parameters of growth estimated by the modified von Bertalanffy growth function model showed that the values of $L_{\infty}$ and K for combined data were 39.12 cm TL and 0.65 $yr^{-1}$. The growth performance index of this study (2.75) was higher than that of the previous study (2.45). This difference could be attributed to sampling method. The recruitment patterns indicated one normally distributed group. Percentage of the recruitment was 51.04% in the spawning season and the highest in August (19.78%).