• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.2 no.1
• /
• pp.83-88
• /
• 2002

We study some properties of smooth uniform spaces. We investigate the relationship between smooth topological spaces and smooth uniform spaces. In particular, we define a subspace of a smooth uniform space and a product of smooth uniform spaces.

• Journal of applied mathematics & informatics
• /
• v.23 no.1_2
• /
• pp.435-443
• /
• 2007

An important approach towards solving the scattered data problem is by using radial basis functions. However, for a large class of smooth basis functions such as Gaussians, the existing theories guarantee the interpolant to approximate well only for a very small class of very smooth approximate which is the so-called 'native' space. The approximands f need to be extremely smooth. Hence, the purpose of this paper is to study approximation by a scattered shifts of a radial basis functions. We provide error estimates on larger spaces, especially on the homogeneous Sobolev spaces.

• Journal of the Korean Institute of Landscape Architecture
• /
• v.36 no.4
• /
• pp.15-26
• /
• 2008

The purpose of this study is to attempt to interpret golf courses as event-generating spaces with consideration given to the time factor. Through a golf game, a variety of events such as the tee shot, second shot, putt, and hole out are generated. These events have been connected to a series of events after hole out such as birdie, par, bogey and so on. The series of events do not always occur in the same way. They reveal unexpected changes over time. These unexpected changes cause changes in the spatial characteristics and offer unforgettable memories for golfers. Gilles Deleuze mentioned the spatial characteristics as striated space and smooth space. Striated space can be defined as sedentary space. It is distant vision-optical space that has dimensional, metric and centered characteristics, whereas smooth space is defined as nomadic, close vision-haptic space that has directional and acentered characteristics. This study focused on the analysis of spatial characteristics according to striated space and smooth space. Golf courses generally show the characteristics of striated space before beginning the game. As soon as the game begins, however, the golf courses are converted into an event-generating space. The characteristics of striated space are transformed into smooth space, a nomadic space that amplifies the dynamic, changeable, de-scaled and non-metric system. Through the whole game, this transformation is dramatically repeated. On the other hand, the golfer, the subject of the game, senses the phenomenological experience in the process of orientation, center, definition, and domestication.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.14 no.3
• /
• pp.231-239
• /
• 2014

It presents the concepts of ordinary smooth interior and ordinary smooth closure of an ordinary subset and their structural properties. It also introduces the notion of ordinary smooth (open) preserving mapping and addresses some their properties. In addition, it develops the notions of ordinary smooth compactness, ordinary smooth almost compactness, and ordinary near compactness and discusses them in the general framework of ordinary smooth topological spaces.

• Honam Mathematical Journal
• /
• v.34 no.4
• /
• pp.559-570
• /
• 2012

We construct a new definition of a base for ordinary smooth topological spaces and introduce the concept of a neighborhood structure in ordinary smooth topological spaces. Then, we state some of their properties which are generalizations of some results in classical topological spaces.

• Kyungpook Mathematical Journal
• /
• v.52 no.4
• /
• pp.459-472
• /
• 2012

A piecewise smooth system is characterized by non-differentiability on a curve in the phase space. In this paper, we discuss particular bifurcation phenomena in the dynamics of a piecewise smooth system. We consider a two-dimensional piecewise smooth system which is composed of a linear map and a nonlinear map, and analyze the stability of the system to determine the existence of dangerous border-collision bifurcation. We finally present some numerical examples of the bifurcation phenomena in the system.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.20 no.6
• /
• pp.875-883
• /
• 2010

We introduce the concept of intuitionistic smooth topology in Lowen's sense and we prove that the family IST(X) of all intuitionistic smooth topologies on a set is a meet complete lattice with least element and the greatest element [Proposition 3.6]. Also we introduce the notion of level fuzzy topology on a set X with respect to an intuitionistic smooth topology and we obtain the relation between the intuitionistic smooth topology $\tau$ and the intuitionistic smooth topology $\eta$ generated by level fuzzy topologies with respect to $\tau$ [Theorem 3.10].

• Korean Institute of Interior Design Journal
• /
• v.18 no.3
• /
• pp.47-56
• /
• 2009

This research aims to analyze the characteristics of the architectural space of Rem Koolhaas based on the spatial discourse of Gilles Deleuze, a philosopher of post-structuralism which comprehends pluralism accepting even contingency and uncertainty beyond deterministic attitudes of structuralism that has led the western discourses since the 19th century. First of all, this research will reflect on Deleuze's spatial concept through literatures and extract the characteristics related to architectural spaces. Then, on the basis of these characteristics, it will analyze the characteristics which were applied to the interior space of the recent architectural works of Rem Koolhaas to find out how Deleuze's spatial dicourse was embodied. Among Deleuze's speculations, the characteristics which falls under the spatial discourse were classified into three categories; degree between the striated space and the smooth one, the space of events and singularity, and the space of the multiple sense. These analysis words are used to look into the correlations among the specific practicing methods embodied in the architecture of Kookhaas. In conclusion, in the architectural space of Rem Koolhaas, it was found that the characteristics of Gilles Deleuze's spatial discourse of post-structuralism were embodied by the methods such as (1) Space of continuous transition, (2) Space of the $multiplicit{\acute{e}}$ accepting contingent events, (3) Space of the multiple sense, and (4) Space of movement.

• Honam Mathematical Journal
• /
• v.37 no.4
• /
• pp.487-504
• /
• 2015

For a smooth plane curve, the curvature can be characterized by the rate of change of the angle between the tangent vector and a fixed vector. In this article we prove that the curvature of a space curve can also be given by the rate of change of the locally defined angle between the tangent vector at a point and the nearby point. By using height functions, we introduce turning angle of a space curve and characterize the curvature by the rate of change of the turning angle. The main advantage of the turning angle is that it can be used to characterize the curvature of discrete curves. For this purpose, we introduce a discrete turning angle and a discrete curvature called visual curvature for space curves. We can show that the visual curvature is an approximation of curvature for smooth curves.

• Journal of applied mathematics & informatics
• /
• v.4 no.2
• /
• pp.477-485
• /
• 1997

Let E be a smooth Banach space. Suppose T:$E \rightarrow E$ is a strongly accretive map. It is proved that each of the two well known fixed point iteration methods (the Mann and ishikawa iteration methods), under suitable conditions converges strongly to a solution of the equation $T_x=f$.