• 보존과학회지
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• 제37권4호
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• pp.322-339
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• 2021

This paper focuses on the dating and provenance of two paintings, Climbing the hill and View from St. John's Fort by the prominent Singaporean artist Liu Kang (1911-2004). Climbing the hill, from the National Gallery Singapore collection, was believed to have been created in 1937, based on the date painted by the artist. However, a non-invasive examination unveiled evidence of an underlying paint scheme and a mysterious date, 1948 or 1949. These findings prompted a comprehensive technical study of the artwork in conjunction with comparative analyses of View from St. John's Fort (1948), from the Liu family collection. The latter artwork is considered to be depicting the same subject matter. The investigation was carried out with UVF, NIR, IRFC, XRR, digital microscopy, PLM and SEM-EDS to elucidate the materials and technique of both artworks and find characteristic patterns that could indicate a relationship between both paintings and assist in correctly dating Climbing the hill. The technical analyses were supplemented with the historical information derived from the Liu family archives. The results showed that Climbing the hill was created in 1948 or 1949 on top of an earlier composition painted in Shanghai between 1933 and 1937. As for the companion View from St. John's Fort from 1948, the artist reused an earlier painting created in France in 1931. The analytical methods suggested that Liu Kang used almost identical pigment mixtures for creating new artworks. However, their painting technique demonstrates some differences. Overall, this study contributes to the understanding of Liu Kang's painting materials and his working practice.

• 대한수학회지
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• 제43권1호
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• pp.11-28
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• 2006

The existence, uniqueness and iterative approximation of solutions for a few classes of functional equations arising in dynamic programming of multistage decision processes are discussed. The results presented in this paper extend, improve and unify the results due to Bellman [2, 3], Bhakta-Choudhury [6], Bhakta-Mitra [7], and Liu [12].

• 대한수학회논문집
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• 제24권1호
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• pp.67-83
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• 2009

Several common fixed point theorems for a few contractive type mappings in complete metric spaces are established. As applications, the existence and uniqueness of common solutions for certain systems of functional equations arising in dynamic programming are discussed.

• Journal of Microbiology and Biotechnology
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• 제28권10호
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• pp.1769-1769
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• 2018

• East Asian mathematical journal
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• 제17권2호
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• pp.265-273
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• 2001

In this paper, we prove that under certain conditions the Ishikawa iterative method with errors converges strongly to the unique solution of the nonlinear strongly accretive operator equation Tx=f. Related results deal with the solution of the equation x+Tx=f. Our results extend and improve the corresponding results of Liu, Childume, Childume-Osilike, Tan-Xu, Deng, Deng-Ding and others.

• East Asian mathematical journal
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• 제18권1호
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• pp.127-136
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• 2002

In this paper we obtain some fixed points theorems of expansive mappings and several necessary and sufficient conditions for the existence of common fixed points of families of self-mappings in metric spaces. Our results generalize and improve the main results of Fisher [1]-[5], Furi-Vignoli [6], $Is\'{e}ki$ [7], Jungck [8], [9], Kashara-Rhoades [10], Liu [13], [14] and Sharma and Strivastava [16].

• 한국자기학회:학술대회 개요집
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• 한국자기학회 2014년도 자성 및 자성재료 국제학술대회
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• pp.48-48
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• 2014

• Journal of applied mathematics & informatics
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• 제37권5_6호
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• pp.411-427
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• 2019

The existence, uniqueness and iterative approximations of fixed points for some contractive mappings of integral type defined in complete metric spaces with w-distance are proved. Four examples are given to demonstrate that the results in this paper extend and improve some well-known results in the literature.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.171-183
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• 2005

In this paper, we introduce and study a class of general strongly nonlinear quasivariational inequalities in Hilbert spaces. We prove the existence and uniqueness of solution and convergence of the perturbed the three-step iterative sequences with errors for this kind of general strongly nonlinear quasivariational inquality problems involving relaxed Lipschitz, relaxed monotone, and strongly monotone mappings. Our results extend, improve, and unify many known results due to Liu-Ume-Kang, Kim-Kyung, Zeng and others.

• 대한수학회논문집
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• 제19권1호
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• pp.63-74
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• 2004

Suppose that X is a real Banach space, K is a nonempty closed convex subset of X and T : $K\;\rightarrow\;K$ is a uniformly continuous ${\phi}$-hemicontractive operator or a Lipschitz ${\phi}-hemicontractive$ operator. In this paper we prove that under certain conditions the three-step iteration methods with errors converge strongly to the unique fixed point of T. Our results extend the corresponding results of Chang [1], Chang et a1. [2], Chidume [3]-[7], Chidume and Osilike [9], Deng [10], Liu and Kang [13], [14], Osilike [15], [16] and Tan and Xu [17].