• Journal of the Korean Data and Information Science Society
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• v.9 no.1
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• pp.77-88
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• 1998

Smoothing spline estimators are modified to remove boundary bias effects using the technique proposed in Eubank and Speckman (1991). An O(n) algorithm is developed for the computation of the resulting estimator as well as associated generalized cross-validation criteria, etc. The asymptotic properties of the estimator are studied for the case of a linear smoothing spline and the upper bound for the average mean squared error of the estimator given in Eubank and Speckman (1991) is shown to be asymptotically sharp in this case.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.139-153
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• 2021

In this paper, we study the existence of positive solutions for a class of conformable fractional differential equations with integral boundary conditions. By using the properties of Green's function with the fixed point theorem in a cone, we prove the existence of a positive solution. We also provide some examples to illustrate our results.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.871-884
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• 2000

Polyharmonic operator with Dirichlet boundary condition is considered in a n-dimensional cone. The regularity properties of weak solutions are studied. In particular, it is proved the Holder contionuity of solutions near the vertex of the cone for dimensions n=2m+3,2m+4, where 2m is the order of the polyharmonic operator.

• East Asian mathematical journal
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• v.22 no.1
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• pp.53-59
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• 2006

We introduce the resistant length and examine its properties. And consider the applications of resistant length to the boundary behavior of conformal mappings. We obtain the theorems in the connection with the resistant length zero and the fundamental sequences. The method of resistant length leads a simple proofs of theorems.

• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.163-172
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• 1998

In this paper, we will study properties of the Green's potential for the Green's function of B which is defined in [8]. In particular, we will investigate boundary behavior of some functions related with Green's function within tangential approach regions that were used in [4].

• Journal of the Chungcheong Mathematical Society
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• v.18 no.2
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• pp.205-213
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• 2005

We introduce the conductance and examine its properties. We study the local behavior of quasiconformal mappings on the boundary of a domain $D{\subset}\overline{R}^n$ n and present some geometric applications of conductance.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.2
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• pp.23-30
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• 2003

In this note, we introduce the concept of the modulus of a curve family in $R^n$ and examine some basic properties. And we study the boundary behavior of quasiconformal mappings on a domain $D{\subset}\bar{R}^n$ and present some geometric applications.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11b
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• pp.204-207
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• 2005

A reliable and practical finite element modeling technique to predict the lifetime of automotive electronics is important for engineers in reliability. In reliability evaluation on the automotive electronics, most studies rarely used FE model verification process. The material properties and boundary conditions are very important factors in this process to assure the reliability of the automotive electronics. This study aims to develop a better and more accurate FE model in order to predict fatigue life of the automotive electronics using Virtual Qualification lifetime assessment techniques. After conducting the modal analysis by the experiments to grasp a system characteristic, this paper presents material properties and boundary conditions that is obtained by the comparisons of FEA simulation results using DOE technique and the experiment results.

• Structural Engineering and Mechanics
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• v.59 no.2
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• pp.343-371
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• 2016

In this paper thermo-mechanical vibration analysis of a porous functionally graded (FG) Timoshenko beam in thermal environment with various boundary conditions are performed by employing a semi analytical differential transform method (DTM) and presenting a Navier type solution method for the first time. The temperature-dependent material properties of FG beam are supposed to vary through thickness direction of the constituents according to the power-law distribution which is modified to approximate the material properties with the porosity phases. Also the porous material properties vary through the thickness of the beam with even and uneven distribution. Two types of thermal loadings, namely, uniform and linear temperature rises through thickness direction are considered. Derivation of equations is based on the Timoshenko beam theory in order to consider the effect of both shear deformation and rotary inertia. Hamilton's principle is applied to obtain the governing differential equation of motion and boundary conditions. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of several parameters such as porosity distributions, porosity volume fraction, thermal effect, boundary conditions and power-low exponent on the natural frequencies of the FG beams in detail. It is explicitly shown that the vibration behavior of porous FG beams is significantly influenced by these effects. Numerical results are presented to serve benchmarks for future analyses of FG beams with porosity phases.

• Journal of the Korean Ceramic Society
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• v.49 no.4
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• pp.301-307
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• 2012

SiAlON glasses are silicates or alumino-silicates, containing Mg, Ca, Y or rare earth (RE) ions as modifiers, in which nitrogen atoms substitute for oxygen atoms in the glass network. These glasses are found as intergranular films and at triple point junctions in silicon nitride ceramics and these grain boundary phases affect their fracture behaviour. This paper provides an overview of the preparation of M-SiAlON glasses and outlines the effects of composition on properties. As nitrogen substitutes for oxygen in SiAlON glasses, increases are observed in glass transition temperatures, viscosities, elastic moduli and microhardness. These property changes are compared with known effects of grain boundary glass chemistry in silicon nitride ceramics. Oxide sintering additives provide conditions for liquid phase sintering, reacting with surface silica on the $Si_3N_4$ particles and some of the nitride to form SiAlON liquid phases which on cooling remain as intergranular glasses. Thermal expansion mismatch between the grain boundary glass and the silicon nitride causes residual stresses in the material which can be determined from bulk SiAlON glass properties. The tensile residual stresses in the glass phase increase with increasing Y:Al ratio and this correlates with increasing fracture toughness as a result of easier debonding at the glass/${\beta}-Si_3N_4$ interface.