• The Pure and Applied Mathematics
• /
• v.18 no.3
• /
• pp.201-217
• /
• 2011

The aim of this paper is to define a new commutativity condition for a pair of self mappings i.e., (DS)-weak commutativity condition, which is weaker that compatibility of mappings in the settings of intuitionistic Menger spaces. We show that a common fixed point theorem can be proved for nonlinear contractive condition in intuitionistic Menger spaces without assuming continuity of any mapping. To prove the result we use (DS)-weak commutativity condition for mappings. We also give examples to validate our results.

• The Pure and Applied Mathematics
• /
• v.12 no.4 s.30
• /
• pp.289-306
• /
• 2005

The aim of this paper is to prove some common fixed point theorems for six discontinuous mappings in non complete fussy metric spaces with condition of weak compatibility.

• Proceedings of the KSME Conference
• /
• 2001.06e
• /
• pp.410-415
• /
• 2001

An analytical and numerical examination of second-order fractional-step methods and boundary condition for the incompressible Navier-Stokes equations is presented. In this study, the compatibility condition for pressure Poisson equation and its boundary conditions, stability, and numerical accuracy of canonical fractional-step methods has been investigated. It has been found that satisfaction of compatibility condition depends on tentative velocity and pressure boundary condition, and that the compatible boundary conditions for type D method and approximately compatible boundary conditions for type P method are proper for divergence-free velocity for type D and approximately divergence-free for type P method. Instability of canonical fractional-step methods is induced by approximation of implicit viscous term with explicit terms, and the stability criteria have been founded with simple model problems and numerical experiments of cavity flow and Taylor vortex flow. The numerical accuracy of canonical fractional-step methods with its consistent boundary conditions shows second-order accuracy except $D_{MM}$ condition, which make approximately first-order accuracy due to weak coupling of boundary conditions.

• The Pure and Applied Mathematics
• /
• v.20 no.3
• /
• pp.181-198
• /
• 2013

C. Vetro [4] gave the concept of weak non-Archimedean in fuzzy metric space. Using the same concept for Menger PM spaces, Mishra et al. [22] proved the common fixed point theorem for six maps, Also they introduced semi-compatibility. In this paper, we generalized the theorem [22] for family of maps and proved the common fixed point theorems using the pair of semi-compatible and reciprocally continuous maps for one pair and R-weakly commuting maps for another pair in Menger WNAPM-spaces. Our results extends and generalizes several known results in metric spaces, probabilistic metric spaces and the similar spaces.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2006.05a
• /
• pp.1235-1239
• /
• 2006

Fractal manufacturing system (FrMS) distinguishes itself from other manufacturing systems by the fact that there is a fractal repeated at every scale. A fractal is a volatile organization which consists of goal-oriented agents referred to as AIR-units (autonomous and intelligent resource units). AIR-units unrestrictedly reconfigure fractals in accordance with their own goals. Their goals can be dynamically changed along with the environmental status. Since goals of AIR-units are represented as fuzzy models, an AIR-unit itself is a fuzzy logic controller. This paper presents a goal regulation mechanism in the FrMS. In particular, a reinforcement learning method is adopted as a regulating mechanism of the fuzzy goal model, which uses only weak reinforcement signal. Goal regulation is achieved by building a feedforward neural network to estimate compatibility level of current goals, which can then adaptively improve compatibility by using the gradient descent method. Goal-oriented features of AIR-units are also presented.

• Proceedings of the KSME Conference
• /
• 2007.05a
• /
• pp.1673-1678
• /
• 2007

The use of flip-chip type electronic package offers numerous advantages such as reduced thickness, improved environmental compatibility, and downed cost. Despite numerous benefits, flip-chip type packages bare several reliability problems. The most critical issue among them is their electrical performance deterioration upon consecutive thermal cycles attributed to gradual delamination growth through chip and adhesive film interface induced by CTE mismatch driven shear and peel stresses. The electronic package in use is heated continuously by itself. When the crack at a weak site of the electronic package occurs, thermal deformationon the chip side is changed. Therefore, we can measure these micro deformations by using Moire interferometry and find out the crack length.

• East Asian mathematical journal
• /
• v.23 no.2
• /
• pp.175-195
• /
• 2007

The object of this paper is to introduce the notion of semi-compatible maps in fuzzy metric spaces, fuzzy 2-metric spaces and fuzzy 3-metric spaces and to establish three common fixed point theorems for these spaces for four self-maps. These results improve, extend and generalize the results of [16]. As an application, these results have been used to obtain translation and generalization of Grabeic's contraction principle in the new settings. All the result presented in this paper are new.

• Communications of the Korean Mathematical Society
• /
• v.27 no.2
• /
• pp.385-397
• /
• 2012

The purpose of this paper is to improve certain results proved in a recent paper of Soliman et al. [20]. These results are the outcome of utilizing the idea of absorbing pairs due to Gopal et al. [6] as opposed to two conditions namely: weak compatibility and the peculiar condition initiated by Pant [15] to ascertain the common fixed points of Lipschitzian mappings. Some illustrative examples are also furnished to highlight the realized improvements.

• KOREAN JOURNAL OF PACKAGING SCIENCE & TECHNOLOGY
• /
• v.19 no.2
• /
• pp.95-102
• /
• 2013

Exfoliated graphite (EFG) with high aspect ratio was incorporated with high density polyethylene (HDPE) for use as high barrier packaging material such as water-sensitivity electric product and pharmaceutical packaging. Also HDPE/EFG nanocomposite films were prepared by adding the compatibilizer for effective dispersion and compatibility. Their chemical properties, crystal structure properties, thermal properties and water barrier properties of as-prepared HDPE/EFG nanocomposite films were investigated as a function of EFG contents. It showed that there is a weak interfacial interaction between HDPE and EFG, however, the water vapor permeations were decreased from 127 to 78 (70 ${\mu}m{\cdot}g/m^2$, $day{\cdot}atm$) by addition of EFG. Especially, the physical properties of HDPE/EFG nanocomposite films were effectively increased up to 0.5 wt%, however, there were no significant improvement of properties in nanocomposite films at the additional EFG loading. To maximize their performance of the nanocomposite films, further research is required to enhance the dispersion of EFG and compatibility of EFG in HDPE matrix.

• Proceedings of the Korean Society For Composite Materials Conference
• /
• 2000.04a
• /
• pp.93-96
• /
• 2000

The theory of non-prismatic folded plate structures was reported by the senior author in 1965 and 1966. Fiber reinforced composite materials are strong in tension. The structural element for such tension force is very thin and weak against bending because of small bending stiffnesses. Naturally, the box type section is considered as the optimum structural configuration because of its high bending stiffnesses. Such structures can be effectively analyzed by the folded plate theory with relative ease. The "hollow" bending member with uniform cross-section can be treated as prismatic folded plates which is a special case of the non-prismatic folded plates. Tn this paper, the result of analysis of a folded plates with one box type uniform cross-section is presented. Each plate is made of composite laminates with fiber orientation of [ABBCAAB]$_r$, with A=-B=$45^{\circ}$, and C=$90^{\circ}$. The influence of the span to depth ratio is also studied. When this ratio is 5, the difference between the results of folded plate theory and beam theory is 1.66%. is 1.66%.