• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1049-1070
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• 2004

We classify all partial differential equations with polynomial coefficients in $\chi$ and y of the form A($\chi$) $u_{{\chi}{\chi}}$ ＋ 2B($\chi$, y) $u_{{\chi}y}$ ＋ C(y) $u_{yy}$ ＋ D($\chi$) $u_{{\chi}}$ ＋ E(y) $u_{y}$ = λu, which has weak orthogonal polynomials as solutions and show that partial derivatives of all orders are orthogonal. Also, we construct orthogonal polynomials in d-variables satisfying second order partial differential equations in d-variables.s.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.165-177
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• 2013

In this paper, we apply Homotopy perturbation transform method (HPTM) for solving singular fourth order parabolic partial differential equations with variable coefficients. This method is the combination of the Laplace transform method and Homotopy perturbation method. The nonlinear terms can be easily handled by the use of He's polynomials. The aim of using the Laplace transform is to overcome the deficiency that is mainly caused by unsatisfied conditions in other semi-analytical methods such as Homotopy perturbation method (HPM), Variational iteration method (VIM) and Adomain Decomposition method (ADM). The proposed scheme finds the solutions without any discretization or restrictive assumptions and avoids the round-off errors. The comparison shows a precise agreement between the results and introduces this method as an applicable one which it needs fewer computations and is much easier and more convenient than others, so it can be widely used in engineering too.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.1
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• pp.130-140
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• 1998

This paper presents a method to estimate subpixel accuracy motion vectors using a mathermatical model withoug interpolation. the proposed method decides the coefficients of mathematical model, which represents the motion vector which is achieved by full search. And then the proposed method estimates subpixel accuracy motion vector from achieved mathematical model. Step by step mathematical models such as type 1, type 2, type 3, modified bype 2, modified type 3, and Partial Interpolation type 3 are presented. In type 1, quadratic polynomial, which has 9 unknown coefficients and models the 3by 3 pixel plane, is used to get the subpixel accuracy motion vectors by inverse matrix solution. In type 2 and 3, each quadratic polynomial which is simplified from type 1 has 5 and 6 unknown coefficients and is used by least square solution. Modified type 2 and modified type 3 are enhanced models by weighting only 5 pixels out of 9. P.I. type 3 is more accurate method by partial interpolation around subpixel which isachieved by type 3. LThese simulation results show that the more delicate model has the better performance and modified models which are simplified have excellent performance with reduced computational complexity.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.875-883
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• 2012

Let $\mathbb{F}_q$ be a finite field with q elements and $\mathbb{F}_q((X^{-1}))$ be the field of all formal Laurent series with coefficients lying in $\mathbb{F}_q$. This paper concerns with the size of the set of points $x{\in}\mathbb{F}_q((X^{-1}))$ with their partial quotients $A_n(x)$ both lying in a given subset $\mathbb{B}$ of polynomials in $\mathbb{F}_q[X]$ ($\mathbb{F}_q[X]$ denotes the ring of polynomials with coefficients in $\mathbb{F}_q$) and deg $A_n(x)$ tends to infinity at least with some given speed. Write $E_{\mathbb{B}}=\{x:A_n(x){\in}\mathbb{B},\;deg\;A_n(x){\rightarrow}{\infty}\;as\;n{\rightarrow}{\infty}\}$. It was shown in [8] that the Hausdorff dimension of $E_{\mathbb{B}}$ is inf{$s:{\sum}_{b{\in}\mathbb{B}}(q^{-2\;deg\;b})^s$ < ${\infty}$}. In this note, we will show that the above result is sharp. Moreover, we also attempt to give conditions under which the above dimensional formula still valid if we require the given speed of deg $A_n(x)$ tends to infinity.

• Journal of the Korean Society for Nondestructive Testing
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• v.36 no.5
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• pp.353-362
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• 2016

Thermal barrier coating (TBC) is an essential element consisting of a super-alloy base and ceramic coating designed to achieve long operational time under a high temperature and pressure environment. However, the top coat of TBC can be delaminated at certain temperatures with long operation time. As the delamination of TBC is directly related to the blade damage, the coupling status of the TBC should be assured for reliable operation. Conventional studies of nondestructive evaluation have been made for detecting generation of thermally grown oxide (TGO) or qualitatively evaluating delamination in TBC. In this study, the ultrasonic C-scan method was developed to obtain the damage map inside TBC by estimating the delamination in a quantitative way. All specimens were isothermally degraded at $1,100^{\circ}C$ with different time, having different partial delamination area. To detect partial delamination in TBC, the C-scan was performed by a single transducer using pulse-echo method with normal incidence. Partial delamination coefficients of 1 mm to 6 mm were derived by the proportion of the surface reflection signal and flaw signal which were theoretical signals using Rogers-Van Buren and Kim's equations. Using the partial delamination coefficients, the partial delamination maps were obtained. Regardless of the partial delamination coefficient, partial delamination area was increased when degradation time was increased in TBC. In addition, a decrease in partial delamination area in each TBC specimen was observed when the partial delamination coefficient was increased. From the portion of the partial delamination maps, the criterion for delamination was derived.

• Wind and Structures
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• v.19 no.1
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• pp.15-33
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• 2014

This paper describes partial turbulence simulation and validation of the aerodynamic pressures on building models for an open-jet small-scale 12-Fan Wall of Wind (WOW) facility against their counterparts in a boundary-layer wind tunnel. The wind characteristics pertained to the Atmospheric Boundary Layer (ABL) mean wind speed profile and turbulent fluctuations simulated in the facility. Both in the wind tunnel and the small-scale 12-Fan WOW these wind characteristics were produced by using spires and roughness elements. It is emphasized in the paper that proper spectral density parameterization is required to simulate turbulent fluctuations correctly. Partial turbulence considering only high frequency part of the turbulent fluctuations spectrum was simulated in the small-scale 12-Fan WOW. For the validation of aerodynamic pressures a series of tests were conducted in both wind tunnel and the small-scale 12-fan WOW facilities on low-rise buildings including two gable roof and two hip roof buildings with two different slopes. Testing was performed to investigate the mean and peak pressure coefficients at various locations on the roofs including near the corners, edges, ridge and hip lines. The pressure coefficients comparisons showed that open-jet testing facility flows with partial simulations of ABL spectrum are capable of inducing pressures on low-rise buildings that reasonably agree with their boundary-layer wind tunnel counterparts.

• Food Engineering Progress
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• v.14 no.1
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• pp.75-79
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• 2010

Partial least square regression (PLSR) was executed on curve data of force-deformation from back extrusion test and sensory data for commercial instant noodles. Sensory attributes considered were hardness (A), springiness (B), roughness (C), adhesiveness to teeth (D), and thickness (E). Eight and two kinds of fried and non-fried instant noodles respectively were used in the tests. Changes in weighted regression coefficients were characterized as three stages: compaction, yielding, and extrusion. Correlation coefficients appeared in the order of E>D>A>B>C, root mean square error of prediction D>C>E>B>A, and relative ability of prediction D>C>E>B>A. Overall, 'D' was the best in the correlation and prediction. 'A' with poor prediction ability but high correlation was considered good when determining the order of magnitude.

• Communications for Statistical Applications and Methods
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• v.29 no.3
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• pp.393-396
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• 2022

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.407-420
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• 2024

In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, Briot-Bouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.

• The Korean Journal of Ceramics
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• v.4 no.2
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• pp.90-94
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• 1998

Self diffusion coefficients of $^{67}$Co and impurity diffusion coefficients of $^{51}$Mn and $^{65}$Zn in single crystalline CoO have been measured by applying different radioactive isotopes simultaneously. To compare the residual activity method and the tracer sectioning method we analyzed our tracer diffusion experiments by using both methods simultaneously. According to our experimental results, the diffusion coefficients obtained from both methods are identical within experimental error, demonstrating the relibility of our experimental procedures. The diffusion coefficients of all the isotopes obtained during these test experiments for the methodology are similar in magnitude and show similar dependences on oxygen partial pressure. These first observations indicate that impurity diffusion of Mn and Zn occur via a vacancy mechanism as known for self diffusion of cobalt.