• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1483-1503
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• 2008

Let f : M ${\rightarrow}$ M be a self-map on the Klein bottle M. We compute the Lefschetz number and the Nielsen number of f by using the infra-nilmanifold structure of the Klein bottle and the averaging formulas for the Lefschetz numbers and the Nielsen numbers of maps on infra-nilmanifolds. For each positive integer n, we provide an explicit algorithm for a complete computation of the Nielsen type numbers $NP_n(f)$ and $N{\Phi}_{n}(f)\;of\;f^{n}$.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.63-70
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• 1996

Let K be a field of characteristic 0 and G a Klein's four group. We find the idempotent elements and units of the group ring KG by using the basic group table matrix of G.

• Journal of Fashion Business
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• v.14 no.3
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• pp.154-171
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• 2010

This study is to examine and compare the brand power such as image, satisfaction and loyalty, of the main brands(Donna Karan, Anne Kelin, Michaa, Obzee) with successful second brands(DKNY, AK Anne Klein, it michaa, O'2nd) to launch the brand Extension. The results are the following. First, in the many demographical characteristics, the main brand most favored by women in their 20s were only affected by age. Second, All 4 brands had a strong urbane and luxurious image, while 'exotic' or 'sporty' scored the bottom. Third, the results of the brand satisfaction were given out different values for the 4 brands. The overall satisfaction level was highest in Donna Karan and Obzee equally. Fourth, if we look at the brand loyalty level of the brands, Donna Karan scored highest followed by Obzee, Michaa, and Anne Klein. All 4 brands have shown that customers had high confidence to the brand and a high willingness to repurchase them. Fifth, about how the images of the main brand influence the satisfaction level of the brands. For Donna Karan, Michaa, and Obzee, the brand images did have effects on the brand satisfaction, but Anne Klein's brand image didn't affect its satisfaction level. Sixth, all 4 brands have shown that satisfaction levels had effects in brand loyalty.

• Journal of the Korean Society of Clothing and Textiles
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• v.30 no.6 s.154
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• pp.880-891
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• 2006

This study is to be focused on the sportswear combining common wear with the design elements of activewear. The objectives of this study are four designers in compliance with the book of Ann Marie Fiore and Patricia Anne Kimle; Calvin Klein, Donna Karan, Ralph Lauren and Anna Sui and the times to be studied are limited to the early 21st Century from 2001 to 2005. Main results are as follow. This research divides sportswear into four groups; 'Function oriented style', 'Sensible style', 'Retro American sports style', and 'Street sports style'. Comparison of four designers' sportswear shows that Calvin Klein is function oriented, Donna Karan is function oriented and sensitivity driven, whereas Ralph Lauren focuses on retro American sports style along with function oriented characteristics. Anna Sui places emphasis on youth oriented street sports style. In terms of color, Calvin Klein and Donna Karan use White & Black and natural tone while Ralph Lauren uses pastel tone, and Anna Sui uses mostly vivid colors. In terms of material, Calvin Klein and Donna Karan use mostly elastic and synthetic materials whereas Ralph Lauren and Anna Sui use natural materials.

• The International Journal of Costume Culture
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• v.5 no.3
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• pp.173-183
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• 2002

The main focus of this study is to understand realities of postmodern consumer culture by deconstructing fashion advertisements, Calvin Klein's ck One and cK be. The metaphysics of critical theory, visual and textual analysis are used to deconstructing the ads applying one of the postmodern cultural critics, Baudrillard' s notion of hyperreality. Through deconstructing the ads five postmodern characteristics representing hyperreality were found. First, there is no message regarding functional characteristics of the product offered in the ad, which is far from the modernist's utilitarian Point of view. Hyperreality in Postmodern consumer culture is consumption centered and focuses on the product's symbolic meanings. Second, especially for cK be, the ad uses atypicai, irrelevant models and images, which are introduced as a concept of ‘real people’ rather than the ideal person or body type. Third, there are transformations of the meanings from cK one to cK be such as the notions of globalization and gender which clearly represent ongoing reality in the Postmodern culture. Fourth, there are hidden meaning of hedonism and relativism, which are prevalent in postmodern ideology. Finally, models' bodies are used to convey messages as well as form the ground and figure in the ad that is a significant characteristic of postmodern consumer culture. In conclusion, the study of Calvin Klein's fashion ads supports the notion that advertising mirrors reality in postmodern consumer culture, which is hyperreality.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.1015-1030
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• 2017

This paper is concerned with the following Klein-Gordon-Maxwell system: $$\{-{\Delta}u+{\lambda}V(x)u-(2{\omega}+{\phi}){\phi}u=f(x,u),\;x{\in}\mathbb{R}^3,\\{\Delta}{\phi}=({\omega}+{\phi})u^2,\;x{\in}\mathbb{R}^3$$ where ${\omega}$ > 0 is a constant and ${\lambda}$ is the parameter. Under some suitable assumptions on V (x) and f(x, u), we establish the existence and multiplicity of nontrivial solutions of the above system via variational methods. Our conditions weaken the Ambrosetti Rabinowitz type condition.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.591-598
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• 2018

This paper is concerned with global existence of weak solutions to the relativistic Vlasov-Klein-Gordon system. The energy of this system is conserved, but the interaction term ${\int}_{{\mathbb{R}}^n}\;{\rho}{\varphi}dx$ in it need not be positive. So far existence of global weak solutions has been established only for small initial data [9, 14]. In two dimensions, this paper shows that the interaction term can be estimated by the kinetic energy to the power of ${\frac{4q-4}{3q-2}}$ for 1 < q < 2. As a consequence, global existence of weak solutions for general initial data is obtained.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.1
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• pp.39-78
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• 2020

In this paper, we propose a decoupled local discontinuous Galerkin method for solving the Klein-Gordon-Schrödinger (KGS) equations. The KGS equations is a model of the Yukawa interaction of complex scalar nucleons and real scalar mesons. The advantage of our scheme is that the computation of the nucleon and meson field is fully decoupled, so that it is especially suitable for parallel computing. We present the conservation property of our fully discrete scheme, including the energy and Hamiltonian conservation, and establish the optimal error estimate.

• Journal for History of Mathematics
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• v.15 no.2
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• pp.15-32
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• 2002

The first part of this thesis gives some brief explanation of the theory and history of imaginary elements in analytic geometry in the 19th century. The second part of this thesis discusses the theory of imaginary elements of synthetic geometry in the first half of the 19th century. Then the next part mentions the theory of imaginary elements of geometry in the second half of that same century. Particularly Christian von Staudt's and Felix Klein's theories are handled in this part. Von Staudt, who has completed the system of the synthetic projective geometry, used ‘involution’ in order to introduce a new concept ‘imaginary elements’- imaginary points, imaginary lines and imaginary plane-in synthetic geometry. Klein applied von Staudt's theory as he convey the result of the research in algebraic geometry in a picture. Von Staudt's and Klein's research may be regarded as the top of the effort to investigate possible relationship between real and imaginary structures.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.541-551
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• 1995

The nonlinear Klein Gordon equation $$ (1) \frac{\partial t^2}{\partial^2 u} - \Delta u + V_u(u) = f $$ where $\Delta$ is the Laplacian operator in $R^d (d = 1, 2, 3), V_u(u)$ is the derivative of the "potential function" V, and f is a source term independent of the solution u, in various areas of mathematical physics.l physics.