• Korean Journal of Mathematics
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• v.20 no.3
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• pp.333-341
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• 2012

We investigate the number of solutions for the superlinear elliptic bifurcation problem with Dirichlet boundary condition. We get a theorem which shows the existence of at least $k$ weak solutions for the superlinear elliptic bifurcation problem with boundary value condition. We obtain this result by using the critical point theory induced from invariant linear subspace and the invariant functional.

• Journal for History of Mathematics
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• v.25 no.1
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• pp.29-43
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• 2012

In this paper, we survey the history of search for axiomatic set theory and show that ${\exists}U(0{\in}U{\wedge}{\forall}x(x{\in}U{\leftrightarrow}{\exists}z(z{\in}U{\wedge}{\forall}y(y{\in}x{\rightarrow}y{\subseteq}z))){\rightarrow}$ ZR.

• Proceedings of the KIEE Conference
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• 2000.07c
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• pp.1617-1619
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• 2000

In this study the nonlinear dielectric properties of amorphous copolymers were analyzed by the related nonlinear dielectric theory. The theory is related to the cooperated dipoles and the number of the dipoles. The relation between the polarization coefficient $R_p$ and the nonlinear coefficient $R_s$ was deduced under the assumption of isotropic media.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.173-184
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• 2016

Mock theta functions are the most interesting topic mentioned in Ramanujan's Lost Notebook, due to its emerging application in the field of Number theory, Quantum invariants theory and etc. In the present research articles we have made an attempt to develop continued fractions representation of all the existing Mock theta functions.

• Journal for History of Mathematics
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• v.1 no.1
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• pp.71-75
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• 1984

Whether the complete Hilbert program could be carried out was rendered very doubtful by results due to Godel. These results may be roughly characterized as a demonstration that, in any system broad enough to contain all the formulas of a formalized elementary number theory, there exist formulas that neither can be proved nor disproved within the system. In this paper, Godel's incompleteness theorem is explained roughly moreover formul system and machines being refered, related to his theory.

• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.913-927
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• 2024

In this paper, we represent regular functions on ternary theory in the view of quaternion. By expressing quaternions using ternary number theory, a new form of regular function, called E-regular, is defined. From the defined regular function, we investigate the properties of the appropriate hyper-conjugate harmonic functions and corresponding Cauchy-Riemann equations by pseudo-complex forms.

• Structural Engineering and Mechanics
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• v.65 no.5
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• pp.621-631
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• 2018

In this paper, an exact analytical solution is developed for the analysis of the post-buckling non-linear response of simply supported deformable symmetric composite beams. For this, a new theory of higher order shear deformation is used for the analysis of composite beams in post-buckling. Unlike any other shear deformation beam theories, the number of functions unknown in the present theory is only two as the Euler-Bernoulli beam theory, while three unknowns are needed in the case of the other beam theories. The theory presents a parabolic distribution of transverse shear stresses, which satisfies the nullity conditions on both sides of the beam without a shear correction factor. The shear effect has a significant contribution to buckling and post-buckling behaviour. The results of this analysis show that classical and first-order theories underestimate the amplitude of the buckling whereas all the theories considered in this study give results very close to the static response of post-buckling. The numerical results obtained with the novel theory are not only much more accurate than those obtained using the Euler-Bernoulli theory but are almost comparable to those obtained using higher order theories, Accuracy and effectiveness of the current theory.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.7
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• pp.3207-3215
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• 2012

In this paper, we study the bending and free vibration analysis of nano plate, using a nonlocal elasticity theory of Eringen with a third-order shear deformation theory. This theory has ability to capture the both small scale effects and quadratic variation of shear strain and consequently shear stress through the plate thickness. Analytical solutions of bending and vibration of a laminated composite nano plate are presented using this theory to illustrate the effect of nonlocal theory on deflection of the nano plates. The relations between nonlocal third-order and local theories are discussed by numerical results. Further, effects of (i) nonlocal parameters, (ii) laminate schemes, (iii) directions of the fiber angle and (iv) number of layers on nondimensional deflections are investigated. In order to validate the present solutions, the reference solutions are used and discussed. The results of anisotropic nano plates using the nonlocal theory may be the benchmark test for the bending analysis.

• Journal of the Korean Society of Costume
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• v.50 no.7
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• pp.113-127
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• 2000

The purpose of this study was to examine the symbolic meaning of oriental numbers based on Yin-Yang(陰陽) theory. Based on the thought of Yin-Yang Wu-Hsing(陰陽五行), the number was divided the number of the heaven (positive number) 1, 3. 5, 7, 9 from the number cf the earth(negative number) 2. 4, 6, 8, 10. It was descrived very well in the dress and its ornaments and the folk customs. In the costume of the Court, there were 9, 7, 5, 3 patterns costume for the king and queen. Even though an even number, 12 patterns costume for the emperor symbolized 12 months and made it of the principal of the universe. Korean traditional costume Han-bock(韓服) was formed with the three dimentional principal of circle (圓.$\bigcirc$), square(方.$\square$) and triangularity(角.$\Delta$). In the middle of odd numbers, number 3 was regarded as a holy number of the heaven (天), the earth(地) and a man(人). Taken for a highest number. number 3 had the symbolism of wishes for good fortune. Number 10 and number 100, which meant the fullness and the long life, were used regularly. With Ten longevity patterns(十長生紋), the feast of a hundred-day-old baby, our race prayed for the healthy long life. As mentioned above. the symbolism of the number though the costume prefered the positive number to the negative one. Accommodating to the universal principal and the cycle. The deep meaning and the symbolism of the number has been implied the mental wishes.

• Asian Journal of Innovation and Policy
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• v.4 no.3
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• pp.397-409
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• 2015

Nowadays, crowdfunding presents a promising development. This research focuses on the influence of platform strategy and market response on the success of crowdfunding from the perspective of the elaboration likelihood model (ELM) theory. Detailed product specifications, crowdfunding difficulty coefficient, vivid advertising video such as introduction and music, and recommendations from relevant figures are all used to depict platform strategy. Meanwhile, we use the number of lovers, followers, comments and 1 RMB backers to measure the level of market response. And thus, we model the impact of platform strategy and market response on crowdfunding success with empirical studies based on 400 samples of observed value. We found firstly that there exist significant positive relations between the total amount of funds pledged and detailed product specification, vivid advertising video, recommendations from relevant figures and the number of 1 RMB backers. Secondly, the crowdfunding difficulty of projects affects negatively, and significantly, the total amount of funds pledged. Thirdly, the influence of the number of lovers and followers on funds pledged is not significant.