• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.1-27
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• 2010

Wu and Zhao [17] provided a semilocal convergence analysis for a Newton-type method on a Banach space setting following the ideas of Frontini and Sormani [9]-[11]. In this study first: we point out inconsistencies between the hypotheses of Theorem 1 and the two examples given in [17], and then, we provide the proof in affine invariant form for this result. Then, we also establish new convergence results with the following advantages over the ones in [17]: weaker hypotheses, and finer error estimates on the distances involved. A numerical example is also provided to show that our results apply in cases other fail [17].

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.439-447
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• 2003

Let (equation omitted) be a symmetrizable Kac-Moody algebra with the indecomposable generalized Cartan matrix A and W be its Weyl group. Let $\theta$ be the highest root of the corresponding finite dimensional simple Lie algebra ${\gg}$ of g. For the type ${A_N}^{(r)}$, we give an element $\omega_{o}\;\in\;W$ such that ${{\omega}_o}^{-1}({\{\Delta\Delta}_{+}})\;=\;{\{\Delta\Delta}_{-}}$. And then we prove that the degree of nilpotency of the subalgebra (equation omitted) is greater than or equal to $ht{\theta}+1$.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.139-165
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• 2020

Mirror symmetry for del Pezzo surfaces was studied in [3] where they suggested that the mirror should take the form of a Landau-Ginzburg model with a particular type of elliptic fibration. This argument came from symplectic considerations of the derived categories involved. This problem was then considered again but from an algebro-geometric perspective by Gross, Hacking and Keel in [8]. Their construction allows one to construct a formal mirror family to a pair (S, D) where S is a smooth rational projective surface and D a certain type of Weil divisor supporting an ample or anti-ample class. In the case where the self intersection matrix for D is not negative semi-definite it was shown in [8] that this family may be lifted to an algebraic family over an affine base. In this paper we perform this construction for all smooth del Pezzo surfaces of degree at least two and obtain explicit equations for the mirror families and present the mirror to dP₂ as a double cover of ℙ².

• Journal of Biomedical Engineering Research
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• v.24 no.2
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• pp.61-68
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• 2003

This paper presents a quantitative analysis method for fall in sick times of the cerebral infarction patients using three types of magnetic resonance image, which play an important role in deciding method of medical treatment. For this object, image characteristics obtained by three radiographic methods of MRI and their relation were analyzed by means of object centered hierarchical Planning method. This methode presents an approach to the knowledge based processes for image interpretation and analysis. To compare three type of MRI. a multiple warping algorithm and affine transform method performed for image matching. Then each fall in sick times level of cerebral infarction was quantified and pseudo-color mapping performed by comparing gray level value one another according to Previously obtained hand maid data. The result of this study was compared to a medical doctors decision.

• Journal of the korean society of oceanography
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• v.39 no.3
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• pp.172-185
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• 2004

LSU rDNA D1-D2 and SSU rDNA genes of 23 strains in seven Alexandrium (Halim) species, A. tamarense (Lebour) Balech, A. catenella (Whedon et Kofoid), A. fraterculus (Balech) Balech, A. affine (Inoue et Fukuyo) Balech, A. insuetum Balech, A. pseudogonyaulax (Biecheler) Horiguchi ex Yuki et Fukuyo and A. tamiyavanichii Balech, were sequenced and the data were used for molecular phylogenetic analysis. The sequence data revealed 11 and 7 ribotypes in the LSU rDNA D1-D2 region and 4 and 17 ribotypes in the SSU rDNA region of A. catenella and A. tamarense, respectively. Other Alexandrium species had also 1 to 5 ribotypes in the two regions. With the exception of CMC2 and CMC3 of A. catenella, all A. tamarense and A. catenella strains had a common ribotype, a functionally expressed rRNA gene (here termed type A), in both gene regions. In addition to the functionally expressed gene, several pseudogenes were obtained that were found to be good tools to analyze the population designation of regional isolates by grouping them according to shared ribotypes. From the phylogenetic analysis of the sequence data determined in this study and retrieved from GenBank, the genus Alexandrium was divided into 14 groups: 1) A. tamarense, 2) A. excavatum, 3) A. catenella, 4) Tasmanian A. tamarense, 5) A. affine (and/or A. concavum), 6) Thai A. tamarense, 7) A. tamiyavanichii, 8) A. fraterculus, 9) A. margalefii, 10) A. andersonii, 11) A. ostenfeldii, 12) A. minutum (or A. lusitanicum), 13) A. insuetum, and 14) A. pseudogonyaulax. The SSU rDNA gene sequence of A. fundyense was so similar to those of A. tamarense used in this study that the two species were difficult to discriminate each other. A. tamiyavanichii was closest to the A. tamarense strain isolated in Thailand and close to the long chain-forming species of A. affine and A. fraterculus. The phylogenetic tree showed that A. margalefii, A. andersonii, A. ostenfeldii, A. minutum and A. insuetum constituted the basal relative complex, and that A. pseudogonyaulax is an ancestral taxon in the genus Alexandrium.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.5
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• pp.574-578
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• 1998

This paper considers the robust positive real problem for linear systems with linear fractional-type norm-bounded repeated scalar block parameter uncertainty. It is shown that the robust positive real problem can be converted into the standard positive real problem without uncertainty that can be used for the analysis of the given uncertain linear system and the synthesis of a controller that robustly stabilizes and achieves the extended strict positive realness property of the closed-loop transfer function. These results can be also applied to the linear system with general structured uncertainty containing repeated scalar block parameters and are extensions of the previous works that consider only norm-boundedness of the affine unstructured uncertainty.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.1
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• pp.153-158
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• 2017

This paper investigates a robust low-complexity design problem for tracking control of uncertain switched pure-feedback systems in the presence of unknown control direction. The completely unknown non-affine nonlinearities are assumed to be arbitrarily switched. By combining the nonlinear error transformation technique and Nussbaum-type functions, a robust tracking controller is designed without using any adaptive function approximators. Thus, compared with existing results, the proposed control scheme has the low-complexity property. From Lyapunov stability theory, it is shown that the tracking error remains within the preassigned transient and steady-state error bounds.

• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.1949-1951
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• 2001

This paper deals with the control of a nonlinear experimental helicopter system by using the fuzzy-model-based control approach. The fuzzy model of the experimental helicopter system is constructed from the original nonlinear dynamic equations in the form of an affine Takagi-Sugeno (TS) fuzzy system. In order to design a feasible switching-type fuzzy-model-based controller, the TS fuzzy system is converted to a set of uncertain linear systems, which is used as a basic framework to synthesize the fuzzy-model-based controller.

• Proceedings of the Korea Information Processing Society Conference
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• 2011.11a
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• pp.1166-1169
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• 2011

In this paper, we design a Circle dot Code, In our scheme, we design a dot patterns for increasing maximum capacity and also for increasing robustness to Affine Transformation. Our code Can be extended according number of data circle. We use three data circle vision code. In this type code, after acquiring camera images for the Circle dot Codes, and perform error correction decoding using four position symbols and six CRC symbols. We perform graph based dot code analysis which determines the topological distance between dot pixels. Our code can be bridged the real world and ubiquitous computing environment.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.1017-1034
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• 2023

In this paper, we work two different problems. First, we investigate a new class of fractional differential equations involving Caputo sequential derivative with some (e₁, e₂, θ)-periodic conditions. The existence and uniqueness of solutions are proven. The stability of solutions is also discussed. The second part includes studying traveling wave solutions of a conformable fractional Korteweg-de Vries-Burger (KdV Burger) equation through the Tanh method. Graphs of some of the waves are plotted and discussed, and a conclusion follows.