• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.399-415
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• 2024

We looked at nonlocal controllability for Hilfer fractional differential equations with almost sectorial operator in this manuscript. We show certain necessary criteria for nonlocal controllability using the measure of noncompactness and the Mönch fixed point theorem. Finally, we provided theoretical and practical applications are given to demonstrate how the abstract results might be applied.

• Proceedings of the Korean Society of Rheology Conference
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• 2002.11a
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• pp.47-50
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• 2002

No Abstract, See Full Text

• Journal for History of Mathematics
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• v.29 no.3
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• pp.157-172
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• 2016

Sophus Lie's research is regarded as one of the most important mathematical advancements in the $19^{th}$ century. His pioneering research in the field of differential equations resulted in an invaluable consolidation of calculus and group theory. Lie's group theory has been investigated and constantly modified by various mathematicians which resulted in a beautifully abstract yet concrete theory. However Lie's early intentions and ideas are lost in the mists of modern transfiguration. In this paper we explore Lie's early academic years and his object of studies which clarify the ground breaking ideas behind his theory.

• Journal for History of Mathematics
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• v.21 no.3
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• pp.1-30
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• 2008

The success of Newton's Gravitational Theory has influenced the theory of capillarity, beginning in the early nineteenth century, by providing a major model of molecular attraction. He used the equation of the attraction of spheroids, which is expressed by second order partial differential equations, to utilize this analogy as the same kind of a particle's force, between gravitational, refractive force of light, and capillarity. The solution of the differential equation corresponds to the geometrical figure of the vessel and the contact angle which is made by the fluid. Unknown abstract functions $\varphi(f)$ represent interaction forces between molecules, giving their potential functions. By conducting several kinds of experimental conditions, it was found that the height of the ascending fluid in the tube is inversely proportional to the rayon of the tube or the distance of the plate. This model is an essential element in the theory of capillarity. Laplace has brought Newtonian mechanics to completion, which relates to the standard model of gravitational theory. Laplace-Young's equation of capillarity is applicable to minimal surfaces in mathematics, to surface tensional phenomena in physics, and to soap bubble experiments.

• The International Journal of Costume Culture
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• v.2 no.2
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• pp.60-70
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• 1999

The purposes of this study were to investigate preference and images of Korean traditional motifs, and to identify the relationship between them. The subjects consisted of 369 male and 356 female undergraduate students. The experimental materials used in this study were 48 stimuli and a questionnaire composed of 7-point semantic differential scales of 26 adjectives. Twelve motifs selected from 3 groups of Korean motifs were used as pattern design stimuli. Twelve repeated patterns were constructed from them to be applied on a CAD-simulated dress. The data were analyzed by ANOVA, Duncan's multiple range test, and regression. The major findings were as follows : 1. Category, composition type, and application object had a significant effect on the preference. Interpretation type has no significant effects on the preference independently, but it had interaction effects when combined with composition type, and category. Especially the composition type had a greater effect than the other variables on the preference. Cloud motif and its abstract and decorative type were found to be more related to the preference than the other category and interpretation type. On the basis of the analysis results, image charts and preference charts were developed. By combining information from the image chart and preference chart, motifs and images preferred by consumers may be selected and developed into new valuable designs. 2. The preference was affected mainly by 'quality'image followed by 'simplicity', 'interest', and 'modernity'image. The preference on pattern design was affected by 'quality', 'simplicity', 'interest', and 'interest', 'simplicity', and 'modernity'image in the order. The relationship between the preference and sensibility images has been represented by equations.