• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1267-1276
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• 2009

This paper presents a method for approximation of the standard normal distribution by using hyperbolic tangent based functions. The presented approximate formula for the cumulative distribution depends on one numerical coefficient only, and its accuracy is admissible. Furthermore, in some particular cases, closed forms of inverse formulas are derived. Numerical results of the present method are compared with those of an existing method.

• Journal of Korean Society for Quality Management
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• v.25 no.1
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• pp.173-181
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• 1997

A modified periodic inspection policy is examined. It is troublesome to know the life distribution and burdensome to compute an optimum planned inspection time numerically as well. A nonparametric a, pp.oximation is used so that equations for the optimum inspection time are expressed as closed forms. To show that the a, pp.oximation can be used in practice, simulations are conducted in the case of Weibull failure times.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.309-315
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• 2009

We extended the results of Roy and Guria (2008) to multiple deletions in logistic regression models. Since single deletions may not exactly detect outliers or influential observations due to swamping effects and masking effects, it needs multiple deletions. We developed conditional deletion diagnostics which are designed to overcome problems of masking effects. We derived the closed forms for several statistics in logistic regression models. They give useful diagnostics on the statistics.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.577-584
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• 2004

In a 4-valent multi 3-gon graph, every cut-through curve forms a simple closed circuit. Hence it is a weak arrangement of simple curves that is defined by Branko Grunbaum. In this paper, we study the edge properties of the 4-valent multi 3-gon graphs from the point of view of arrangement, and we show that they are 3 colorable.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.445-454
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• 2012

On a closed, connected Riemannian manifold with a K$\ddot{a}$ahler foliation $\mathcal{F}$ of codimension $q$, any transverse Killing $r$-form ($2{\leq}r{\leq}q$) is parallel.

• Proceedings of the Acoustical Society of Korea Conference
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• 1994.06a
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• pp.680-685
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• 1994

The acoustic phenomena in the actual sound systems involve a variety of compound problems. In this paper, the well-known Bayes' theorem is first employed and expanded into orthonormal and non-orthonomal series forms matched to the digital processing of lower and higher order statistical informations and the noisy observations. Proposed on-line algorithms of digital filter type are applied to the actual state estimation for a reverberation characteristics in a room under contamination of background noises.

• Journal of Electrical Engineering and information Science
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• v.1 no.1
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• pp.151-155
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• 1996

This paper derives the two-dimensional probability distribution and density functions of morphological dilation and erosion of a one-dimensional memoryless source and reports numerical results for a uniform source, thus providing methodology for joint distributions for other morphological operations. The joint density functions expressed in closed forms contain the Dirac delta functions due to the joint discontinuity within the dilation and erosion. They also exhibit symmetry between these two morphological density functions of dilated and/or eroded sources, in the computation of other higher moments thereof, and in multidimensional quantization.

• Steel and Composite Structures
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• v.36 no.2
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• pp.143-161
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• 2020

In nanosized structures as the surface area to the bulk volume ratio increases the classical continuum mechanics approaches fails to investigate the mechanical behavior of such structures. In perforated nanobeam structures, more decrease in the bulk volume is obtained due to perforation process thus nonclassical continuum approaches should be employed for reliable investigation of the mechanical behavior these structures. This article introduces an analytical methodology to investigate the size dependent, surface energy, and perforation impacts on the nonclassical bending behavior of regularly squared cutout nanobeam structures for the first time. To do this, geometrical model for both bulk and surface characteristics is developed for regularly squared perforated nanobeams. Based on the proposed geometrical model, the nonclassical Gurtin-Murdoch surface elasticity model is adopted and modified to incorporate the surface energy effects in perforated nanobeams. To investigate the effect of shear deformation associated with cutout process, both Euler-Bernoulli and Timoshenko beams theories are developed. Mathematical model for perforated nanobeam structure including surface energy effects are derived in comprehensive procedure and nonclassical boundary conditions are presented. Closed forms for the nonclassical bending and rotational displacements are derived for both theories considering all classical and nonclassical kinematics and kinetics boundary conditions. Additionally, both uniformly distributed and concentrated loads are considered. The developed methodology is verified and compared with the available results and an excellent agreement is noticed. Both classical and nonclassical bending profiles for both thin and thick perforated nanobeams are investigated. Numerical results are obtained to illustrate effects of beam filling ratio, the number of hole rows through the cross section, surface material characteristics, beam slenderness ratio as well as the boundary and loading conditions on the non-classical bending behavior of perforated nanobeams in the presence of surface effects. It is found that, the surface residual stress has more significant effect on the bending deflection compared with the corresponding effect of the surface elasticity, Es. The obtained results are supportive for the design, analysis and manufacturing of perforated nanobeams.

• Steel and Composite Structures
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• v.49 no.4
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• pp.361-380
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• 2023

A size dependent bending behavior of piezoelectrical flexoelectric layered perforated functionally graded (FG) composite nanobeam rested on an elastic foundation is investigated analytically. The composite beam is composed of regularly cutout FG core and two piezoelectric face sheets. The material characteristics is graded through the core thickness by power law function. Regular squared cutout perforation pattern is considered and closed forms of the equivalent stiffness parameters are derived. The modified nonlocal strain gradient elasticity theory is employed to incorporate the microstructure as well as nonlocality effects into governing equations. The Winkler as well as the Pasternak elastic foundation models are employed to simulate the substrate medium. The Hamiltonian approach is adopted to derive the governing equilibrium equation including piezoelectric and flexoelectric effects. Analytical solution methodology is developed to derive closed forms for the size dependent electromechanical as well as mechanical bending profiles. The model is verified by comparing the obtained results with the available corresponding results in the literature. To demonstrate the applicability of the developed procedure, parametric studies are performed to explore influences of gradation index, elastic medium parameters, flexoelectric and piezoelectric parameters, geometrical and peroration parameters, and material parameters on the size dependent bending behavior of piezoelectrically layered PFG nanobeams. Results obtained revealed the significant effects both the flexoelectric and piezoelectric parameters on the bending behavior of the piezoelectric composite nanobeams. These parameters could be controlled to improve the size dependent electromechanical as well as mechanical behaviors. The obtained results and the developed procedure are helpful for design and manufacturing of MEMS and NEMS.

• Journal of Dental Rehabilitation and Applied Science
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• v.34 no.1
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• pp.56-62
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• 2018

When it comes to treat patient with loss of vestibule, conventional denture impression have limitation which can cause problems of excessive border extension. Suction denture with closed mouth technique which was introduced to solve this problem, forms negative pressure being sealed denture flanges by mobile mucosa when the patient swallows and chews. Also, it can decrease patient's visiting time by taking impression and gothic arch tracing at once. In this case, considering patient's chief complain which is a loose fit of present lower denture, suction dentures with closed mouth technique was planned.