• Bulletin of the Korean Chemical Society
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• v.33 no.12
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• pp.4103-4108
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• 2012

Efficient double click methods for the synthesis of diblock codendrimers were developed. The synthetic strategy involved the sequential click reactions between an alkyne and an azide. The short core building block, 1,4-diazidobutane, was chosen to serve as the azide functionalities for dendrimer growth via click reactions with the alkyne-functionalized PAMAM dendrons as hydrophilic dendron and alkyne-functionalized Fr$\acute{e}$chet-type dendrons as hydrophobic dendron. The structure of diblock codendrimers was confirmed by $^1H$ and $^{13}C$ NMR spectroscopy, IR spectroscopy, mass spectrometry, and GPC analysis.

• The Pure and Applied Mathematics
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• v.16 no.4
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• pp.405-416
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• 2009

In this study we are concerned with the problem of approximating a locally unique solution of an equation in a Banach space setting using Newton's and modified Newton's methods. We provide weaker convergence conditions for both methods than before [5]-[7]. Then, we combine Newton's with the modified Newton's method to approximate locally unique solutions of operator equations. Finer error estimates, a larger convergence domain, and a more precise information on the location of the solution are obtained under the same or weaker hypotheses than before [5]-[7]. The results obtained here improve our earlier ones reported in [4]. Numerical examples are also provided.

• 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].

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1393-1404
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• 2008

Let K be a nonempty closed convex subset of a Banach space E. Suppose $\{T_{n}\}$ (n = 1,2,...) is a uniformly asymptotically regular sequence of nonexpansive mappings from K to K such that ${\cap}_{n=1}^{\infty}$ F$\(T_n){\neq}{\phi}$. For $x_0{\in}K$, define $x_{n+1}={\lambda}_{n+1}x_{n}+(1-{\lambda}_{n+1})T_{n+1}x_{n},n{\geq}0$. If ${\lambda}_n{\subset}[0,1]$ satisfies $lim_{n{\rightarrow}{\infty}}{\lambda}_n=0$, we proved that $\{x_n\}$ weakly converges to some $z{\in}F\;as\;n{\rightarrow}{\infty}$ in the framework of reflexive Banach space E which satisfies the Opial's condition or has $Fr{\acute{e}}chet$ differentiable norm or its dual $E^*$ has the Kadec-Klee property. We also obtain that $\{x_n\}$ strongly converges to some $z{\in}F$ in Banach space E if K is a compact subset of E or there exists one map $T{\in}\{T_{n};n=1,2,...\}$ satisfy some compact conditions such as T is semi compact or satisfy Condition A or $lim_{n{\rightarrow}{\infty}}d(x_{n},F(T))=0$ and so on.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.31 no.6_1
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• pp.483-491
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• 2013

By a development of car navigation systems and mobile or positioning technology, it increases interest in location based services, especially pedestrian navigation systems. Updating of digital maps is important because digital maps are mass data and required to short updating cycle. In this paper, we proposed change detection for different network data-sets based on areal feature matching. Prior to change detection, we defined type of updating between different network data-sets. Next, we transformed road lines into areal features(block) that are surrounded by them and calculated a shape similarity between blocks in different data-sets. Blocks that a shape similarity is more than 0.6 are selected candidate block pairs. Secondly, we detected changed-block pairs by bipartite graph clustering or properties of a concave polygon according to types of updating, and calculated Fr$\acute{e}$chet distance between segments within the block or forming it. At this time, road segments of KAIS map that Fr$\acute{e}$chet distance is more than 50 are extracted as updating road features. As a result of accuracy evaluation, a value of detection rate appears high at 0.965. We could thus identify that a proposed method is able to apply to change detection between different network data-sets.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.677-693
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• 2018

In this work, we generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study its local convergence to approximate a locally-unique solution of a system of nonlinear equations. The convergence in this study is shown under hypotheses only on the first derivative. Our analysis avoids the usual Taylor expansions requiring higher order derivatives but uses generalized Lipschitz-type conditions only on the first derivative. Moreover, our new approach provides computable radius of convergence as well as error bounds on the distances involved and estimates on the uniqueness of the solution based on some functions appearing in these generalized conditions. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives which may not exist or may be very expensive or impossible to compute. The convergence order is computed using computational order of convergence or approximate computational order of convergence which do not require usage of higher derivatives. This technique can be applied to any iterative method using Taylor expansions involving high order derivatives. The study of the local convergence based on Lipschitz constants is important because it provides the degree of difficulty for choosing initial points. In this sense the applicability of the method is expanded. Finally, numerical examples are provided to verify the theoretical results and to show the convergence behavior.

• Journal of KIISE
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• v.43 no.1
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• pp.40-46
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• 2016

Digital road map generation is primarily based on artificial satellite photographing or in-site manual survey work. Therefore, these map generation procedures require a lot of time and a large budget to create and update road maps. Consequently, people have tried to develop automated map generation systems using GPS trajectory data sets obtained by public vehicles. A fundamental problem in this road generation procedure involves the extraction of representative trajectory such as main roads. Extracting a representative trajectory requires the base data set of piecewise line segments(GPS-trajectories), which have close starting and ending points. So, geometrically similar trajectories are selected for clustering before extracting one representative trajectory from among them. This paper proposes a new divide- and-conquer approach by partitioning the whole map region into regular grid sub-spaces. We then try to find similar trajectories by sweeping. Also, we applied the $Fr{\acute{e}}chet$ distance measure to compute the similarity between a pair of trajectories. We conducted experiments using a set of real GPS data with more than 500 vehicle trajectories obtained from Gangnam-gu, Seoul. The experiment shows that our grid partitioning approach is fast and stable and can be used in real applications for vehicle trajectory clustering.

• KIPS Transactions on Software and Data Engineering
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• v.10 no.1
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• pp.9-18
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• 2021

Although Generative Adversarial Networks (GANs) have gained great popularity in computer vision and related fields, generating audio signals independently has yet to be presented. Unlike images, an audio signal is a sampled signal consisting of discrete samples, so it is not easy to learn the signals using CNN architectures, which is widely used in image generation tasks. In order to overcome this difficulty, GAN researchers proposed a strategy of applying time-frequency representations of audio to existing image-generating GANs. Following this strategy, we propose an improved method for increasing the fidelity of synthesized audio signals generated by using GANs. Our method is demonstrated on a public speech dataset, and evaluated by Fréchet Inception Distance (FID). When employing our method, the FID showed 10.504, but 11.973 as for the existing state of the art method (lower FID indicates better fidelity).

• Rapid Communication in Photoscience
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• v.1 no.1
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• pp.1-9
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• 2012

Luminescent lanthanide complexes have been overviewed for advanced photonics applications. Lanthanide(III) ions ($Ln^{3+}$) were encapsulated by the luminescent ligands such as metalloporphyrins, naphthalenes, anthracene, push-pull diketone derivatives and boron dipyrromethene(bodipy). The energy levels of the luminescent ligands were tailored to maintain the effective energy transfer process from luminescent ligands to $Ln^{3+}$ ions for getting a higher optical amplification gain. Also, key parameters for emission enhancement and efficient energy transfer pathways for the sensitization of $Ln^{3+}$ ions by luminescent ligands were investigated. Furthermore, to enhance the optophysical properties of novel luminescent $Ln^{3+}$ complexes, aryl ether-functionalized dendrons as photon antennas have been incorporated into luminescent $Ln^{3+}$ complexes, yielding novel $Ln^{3+}$-cored dendrimer complex such as metalloporphyrins, naphthalenes, and anthracenes bearing the Fr$\acute{e}$chet aryl-ether dendrons, namely, ($Er^{3+}-[Gn-Pt-Por]_3$ (terpy), $Er^{3+}-[Gn-Naph]_3$(terpy) and $Er^{3+}-[Gn-An]_3$(terpy)). These complexs showed much stronger near-IR emission bands at 1530 nm, originated from the 4f-4f electronic transition of the first excited state ($^4I_{13/2}$) to the ground state ($^4I_{15/2}$) of the partially filled 4f shell. A significant decrease in the fluorescence of metalloporphyrins, naphthalenes and anthracene ligand were accompanied by a strong increase in the near IR emission of the $Ln^{3+}$ ions. The near IR emission intensities of $Ln^{3+}$ ions in the lanthanide(III)-encapsulated dendrimer complexes were dramatically enhanced with increasing the generation number (n) of dendrons, due to the site-isolation and the light-harvesting(LH) effects. Furthermore, it was first attempted to distinguish between the site-isolation and the light-harvesting effects in the present complexes. In this review, synthesis and photophysical studies of inert and stable luminescent $Ln^{3+}$ complexes will be dealt for the advanced photonics applications. Also, the review will include the exploratory investigation of the key parameters for emission enhancement and the effective energy transfer pathways from luminescent ligands to $Ln^{3+}$ ions with $Ln^{3+}$-chelated prototype complexes.