• Journal of architectural history
• /
• v.3 no.2 s.6
• /
• pp.125-141
• /
• 1994

Alois Riegl's aesthetic theory of visual perception provided one of important conceptual backgrounds for Vienna Art Nouveau architecture. Riegls theory of visual perception consists of geometric style and two-dimensional transformation. Riegl's theory of geometric style is based on the modern aesthetic theory of abstraction, which says that the artistic perfection can be obtained not from a direct imitation of natural objects, but from an abstract transformation of them. Riegl's theory of two-dimensional transformation, on the other hand, aims at obtaining artistic perfection by disintegrating volumetric conditions of natural things into planes and combining the planes thus obtained into another new world of art. These two theories of Alois Rigl's provided an important aesthetical background for the design strategy of 'abstract ornamentaion of two-dimension' in Vienna Art Nouveau architecture. This paper is to review the basic concept of Alois Rigl's theory of geometric style and two-dimensional transformation.

• Steel and Composite Structures
• /
• v.47 no.6
• /
• pp.795-811
• /
• 2023

When studying the resonance problem of nanoplates, the existing papers do not consider the influences of geometric nonlinearity and initial geometric imperfection, so this paper is to fill this gap. In this paper, based on the nonlocal strain gradient theory (NSGT), the nonlinear resonances of functionally graded (FG) nanoplates with initial geometric imperfection under different boundary conditions are established. In order to consider the small size effect of plates, nonlocal parameters and strain gradient parameters are introduced to expand the assumptions of the first-order shear deformation theory. Subsequently, the equations of motion are derived using the Euler-Lagrange principle and solved with the help of perturbation method. In addition, the effects of initial geometrical imperfection, functionally graded index, strain gradient parameter, nonlocal parameter and porosity on the nonlinear forced vibration behavior of nanoplates under different boundary conditions are discussed.

• Research in Mathematical Education
• /
• v.11 no.3
• /
• pp.209-218
• /
• 2007

The purpose of this study is to create an interactive tool Geometry Player for geometric explorations. In designing this software, we referred to van Hiele's geometric learning theory of and Duval's cognitive comprehension theory of geometric figures. With Geometry Player, it is easy to construct and manipulate dynamic geometric figures. Teachers can easily present the dynamic process of geometric figures in class, and students can use it as a leaning tool to construct geometric concepts by themselves. It is hoped that Geometry Player can be a useful assistant for teachers and a nice partner for students. A brief introduction to Geometry Player and some application examples are included in this paper.

• Kyungpook Mathematical Journal
• /
• v.47 no.1
• /
• pp.133-150
• /
• 2007

In a development of efficient primal-dual interior-points algorithms for self-scaled convex programming problems, one of the important properties of such cones is the existence and uniqueness of "scaling points". In this paper through the identification of scaling points with the notion of "(metric) geometric means" on symmetric cones, we extend several well-known matrix inequalities (the classical L$\ddot{o}$wner-Heinz inequality, Ando inequality, Jensen inequality, Furuta inequality) to symmetric cones. We also develop a theory of spectral geometric means on symmetric cones which has recently appeared in matrix theory and in the linear monotone complementarity problem for domains associated to symmetric cones. We derive Nesterov-Todd inequality using the spectral property of spectral geometric means on symmetric cones.

• 제어로봇시스템학회:학술대회논문집
• /
• 1993.10b
• /
• pp.491-495
• /
• 1993

In this paper, we present a methodology to model an indoor environment of a mobile robot using fuzzy numbers and to make a global map of the robot environment using graph theory. We describe any geometric primitive of robot environment as a parameter vector in parameter space and represent the ill-known values of the prameterized geometric primitive by means of fuzzy numbers restricted to appropriate membership functions. Also we describe the spatial relations between geometric prinitives using graph theory for local maps. For making the global map of the mobile robot environment, the correspondence problem between local maps is solved using a fuzzy similarity measure and a Bipartite graph matching technique.

• Journal of the Korean Institute of Rural Architecture
• /
• v.2 no.3
• /
• pp.77-84
• /
• 2000

Kurye-gun, which Hwaeomsa temple is located, has huge scale's geographical characteristics, such as mountains, rivers and open fields. This is really blessing area because of Som-jin river at the bottom of Ghiri mountain and open fields, which this situation is very difficult. The location of Hwaeomsa temple is an end of The Baek-Doo Mountains and very important spot(where influences to its geometric converge) of the theory of feng-shui. On exposure logic of the Korean traditional theory of feng-shui, the organization in Ga-Ram of Hwaeomsa temple is inconsistent with representative theory and analyzing system. So, this is one of successful examples with the theory of feng-shui because exhalation from the earth and water was organized well with accuracy.

• Advances in materials Research
• /
• v.8 no.3
• /
• pp.219-235
• /
• 2019

This research is devoted to analyzing mechanical-thermal post-buckling behavior of a micro-size beam reinforced with graphene platelets (GPLs) based on geometric imperfection effects. Graphene platelets have three types of dispersion within the structure including uniform-type, linear-type and nonlinear-type. The micro-size beam is considered to be perfect (ideal) or imperfect. Buckling mode shape of the micro-size beam has been assumed as geometric imperfection. Modified couple stress theory has been used for describing scale-dependent character of the beam having micro dimension. Via an analytical procedure, post-buckling path of the micro-size beam has been derived. It will be demonstrated that nonlinear buckling characteristics of the micro-size beam are dependent on geometric imperfection amplitude, thermal loading, graphene distribution and couple stress effects.

• Steel and Composite Structures
• /
• v.46 no.1
• /
• pp.93-105
• /
• 2023

This paper examines a high-speed railway CRTS-II ballastless track-bridge system. Using the stationary potential energy theory, the mapping analytical solution between the bridge deformation and the rail vertical geometric irregularity was derived. A theoretical model (TM) considering the nonlinear stiffness of interlayer components was also proposed. By comparing with finite element model results and the measured field data, the accuracy of the TM was verified. Based on the TM, the effect of bridge deformation amplitude, girder end cantilever length, and interlayer nonlinear stiffness (fastener, cement asphalt mortar layer (CA mortar layer), extruded sheet, etc.) on the rail vertical geometric irregularity were analyzed. Results show that the rail vertical deformation extremum increases with increasing bridge deformation amplitude. The girder end cantilever length has a certain influence on the rail vertical geometric irregularity. The fastener and CA mortar layer have basically the same influence on the rail deformation amplitude. The extruded sheet and shear groove influence the rail geometric irregularity significantly, and the influence is basically the same. The influence of the shear rebar and lateral block on the rail vertical geometric irregularity could be negligible.

• Steel and Composite Structures
• /
• v.48 no.6
• /
• pp.693-708
• /
• 2023

Composite beams, two materials joined together, have become more common in structural engineering over the past few decades because they have better mechanical and structural properties. The shear connectors between their layers exhibit some deformability with finite stiffness, resulting in interfacial shear slip, a phenomenon known as partial shear interaction. Such a partial shear interaction contributes significantly to the composite beams. To provide precise predictions of the geometric nonlinear behavior shown by two-layered composite beams with interfacial shear slips, a robust analytical model has been developed that incorporates the influence of significant displacements. The application of a higher-order beam theory to the two material layers results in a third-order adjustment of the longitudinal displacement within each layer along the depth of the beam. Deformable shear connectors are employed at the interface to represent the partial shear interaction by means of a sequence of shear connectors that are evenly distributed throughout the beam's length. The Von-Karman theory of large deflection incorporates geometric nonlinearity into the governing equations, which are then solved analytically using the Navier solution technique. Suggested model exhibits a notable level of agreement with published findings, and numerical outputs derived from finite element (FE) model. Large displacement substantially reduces deflection, interfacial shear slip, and stress values. Geometric nonlinearity has a significant impact on beams with larger span-to-depth ratio and a greater degree of shear connector deformability. Potentially, the analytical model can accurately predict the geometric nonlinear responses of composite beams. The model has a high degree of generality, which might aid in the numerical solution of composite beams with varying configurations and shear criteria.

• Journal of Educational Research in Mathematics
• /
• v.8 no.1
• /
• pp.291-298
• /
• 1998

This study deals with the problem of proof education in the middle school geometry bby examining van Hiele#s geometric thought level theory and Freudenthal#s mathematization teaching theory. The implications that have been revealed by examining the theory of van Hie이 and Freudenthal are as follows. First of all, the proof education at present that follows the order of #definition-theorem-proof#should be reconsidered. This order of proof-teaching may have the danger that fix the proof education poorly and formally by imposing the ready-made mathematics as the mere record of proof on students rather than suggesting the proof as the real thought activity. Hence we should encourage students in reinventing #proving#as the means of organization and mathematization. Second, proof-learning can not start by introducing the term of proof only. We should recognize proof-learning as a gradual process which forms with understanding the meaning of proof on the basic of the various activities, such as observation of geometric figures, analysis of the properties of geometric figures and construction of the relationship among those properties. Moreover students should be given this natural ground of proof.