• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.621-639
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• 2011

The purpose of this paper is to introduce a general iterative process by viscosity approximation method with parallel method to ap-proximate a common element of the set of solutions of a mixed equilibrium problem and of the set of common fixed points of a finite family of $k_i$-strict pseudo-contractions in a Hilbert space. We obtain a strong convergence theorem of the proposed iterative method for a finite family of $k_i$-strict pseudo-contractions to the unique solution of variational inequality which is the optimality condition for a minimization problem under some mild conditions imposed on parameters. The results obtained in this paper improve and extend the corresponding results announced by Liu (2009), Plubtieng-Panpaeng (2007), Takahashi-Takahashi (2007), Peng et al. (2009) and some well-known results in the literature.

• Structural Engineering and Mechanics
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• 제38권6호
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• pp.733-751
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• 2011

In the present study, a new kind of multivariable Reissner-Mindlin plate elements with two kinds of variables based on B-spline wavelet on the interval (BSWI) is constructed to solve the static and vibration problems of a square Reissner-Mindlin plate, a skew Reissner-Mindlin plate, and a Reissner-Mindlin plate on an elastic foundation. Based on generalized variational principle, finite element formulations are derived from generalized potential energy functional. The two-dimensional tensor product BSWI is employed to form the shape functions and construct multivariable BSWI elements. The multivariable wavelet finite element method proposed here can improve the solving accuracy apparently because generalized stress and strain are interpolated separately. In addition, compared with commonly used Daubechies wavelet finite element method, BSWI has explicit expression and a very good approximation property which guarantee the satisfying results. The efficiency of the proposed multivariable Reissner-Mindlin plate elements are verified through some numerical examples in the end.

• Structural Engineering and Mechanics
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• 제69권6호
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• pp.615-626
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• 2019

The 3-noded metric Timoshenko beam element with an offset of the internal node from the element centre is used here to demonstrate the best-fit paradigm using function space formulation under locking and mesh distortion. The best-fit paradigm follows from the projection theorem describing finite element analysis which shows that the stresses computed by the displacement finite element procedure are the best approximation of the true stresses at an element level as well as global level. In this paper, closed form best-fit solutions are arrived for the 3-noded Timoshenko beam element through function space formulation by combining field consistency requirements and distortion effects for the element modelled in metric Cartesian coordinates. It is demonstrated through projection theorems how lock-free best-fit solutions are arrived even under mesh distortion by using a consistent definition for the shear strain field. It is shown how the field consistency enforced finite element solution differ from the best-fit solution by an extraneous response resulting from an additional spurious force vector. However, it can be observed that when the extraneous forces vanish fortuitously, the field consistent solution coincides with the best-fit strain solution.

• 한국자기학회지
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• 제26권2호
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• pp.39-44
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• 2016

대표적 열전물질인 비스무스 텔루라이드에 자성원자를 도핑한 합금에 대한 구조 및 전자적 그리고 자기적 성질에 관한 연구는 고효율 열전물질의 개발이라는 목적뿐만 아니라 특이한 자기적 상호작용 규명 및 위상절연체 분야에서도 큰 관심을 끌고 있다. 본 연구에서는 희토류 원자로서 매우 국소화된 f 전자를 갖는 Gd이 Bi을 치환하여 도핑된 비스무스 텔루라이드 합금의 자성 안정성을 밀도범함수(Density Functional Theory)에 입각하여 제일원리적으로 연구하기 위하여 모든 전자(all-electron) FLAPW(full-potential linearized augmented plane-wave) 방법을 이용하여 전자구조 계산을 수행하였다. 전자간 교환-상관 상호작용은 일반기울기 근사법(Generalized Gradient Approximation)을 도입하여 계산하였으며, 국소화된 f 전자를 기술하는 데 필요한 Hubbard+U 보정과 스핀-궤도 각운동량 상호작용은 제2 변분법적 방법을 이용하여 고려하였다. 계산 결과, 강자성 안정성을 보이는 Gd 덩치계와 다르게 이 합금은 강자성과 반강자성의 총에너지 차이가 ~1 meV/Gd 정도의 아주 작은 값으로 얻어져서, 그 자성 안정성은 결함이나 strain 등에 의한 구조변화에 민감하게 의존하여 변할 수 있음을 알 수 있었다. 특히 Gd 스핀자기모멘트는 덩치에서의 값에 비해 감소하였고, Gd에 가장 가까운 Te에 유도 자기모멘트가 형성되는 것으로 미루어 Te를 매개로 한 자성상호작용이 자성 안정성을 결정하는 데에 중요한 역할을 하는 것으로 예측할 수 있었다.

• Journal of Advanced Research in Ocean Engineering
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• 제1권3호
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• pp.157-167
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• 2015

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

• 한국표면공학회지
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• 제53권3호
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• pp.95-103
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• 2020

In this study, the material used in the hot dip galvanizing equipment was poorly corrosion-resistant, so it was performed to solve the cost and time problems caused by equipment replacement. The theoretical calculation was performed using the DV-Xα method(Discrete Variational Local-density approximation method). The alloy (STS4XX series) of the equipment currently used has a martensite phase. Therefore, the theoretical calculation was performed by applying P4 / mmm, which is a tetragonal structure. The new alloy was chosen by designing theoretical values close to existing materials. Considering elements that contribute to corrosion, most have high prices. Therefore, the design was completed by adjusting the content using only the components of the reference material in the theoretical design. The final design alloys were chosen as D6 and D9. Designed D6 and D9 were dissolved and prepared using an induction furnace. After the heat treatment process was completed, the corrosion rate of the alloys was confirmed by using the potentiodynamic polarization test. The surface of the prepared alloys were processed horizontally and then polished to # 1200 using sand paper to perform potentiodynamic polarization test. Domestic products: 4.735 mpy (mils / year), D6: 0.9166 mpy, D9: 0.3372 mpy, alloys designed than domestic products had a lower corrosion rate. Therefore, the designed alloy was expected to have better erosion resistance.

• 한국전기전자재료학회논문지
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• 제17권7호
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• pp.691-696
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• 2004

The electronic state and chemical bonding of $\beta$-MnO$_2$ with transition metal dopants were theoretically investigated by DV-X$_{\alpha}$ (the discrete variational X$_{\alpha}$) method, which is a sort of the first principles molecular orbital method using the Hartree-Fock-Slater approximation. The calculations were performed with a $_Mn_{14}$ MO$_{56}$ )$^{-52}$ (M = transition metals) cluster model. The electron energy level, the density of states (DOS), the overlap population, the charge density distribution, and the net charges, were calculated. The energy level diagram of MnO$_2$ shows the different band structure and electron occupancy between the up spin states and down spin states. The dopant levels decrease between the conduction band and the valence band with the increase of the atomic number of dopants. The covalency of chemical bonding was shown to increase and ionicity decreased in increasing the atomic number of dopants. Calculated results were discussed on the basis of the interaction between transition metal 3d and oxygen 2p orbital. In conclusion it is expected that when the transition metals are added to MnO$_2$ the band gap decreases and the electronic conductivity increases with the increase of the atomic number of dopants. the atomic number of dopants.

• 대한핵의학회지
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• 제38권6호
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• pp.486-491
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• 2004

목적: 요소분석법. 독립성분분석법 등이 PET을 이용하여 심근혈류를 비침습적으로 측정하기 위하여 사용되어 왔다. 이론적으로 뛰어나고 새로운 방법인 앙상블 독려성분분석법을 이용하여 $H_2^{15}O$ 동적 심근 PET데이터의 정량분석방법을 개발하였다. 이 연구에서 사용한 앙상블 독려성분분석법을 이용하여 환자의 혈류를 정량화 하였다. 대상 및 방법: 관동맥질환이 의심되어 관류 SPECT를 시행한 환자 20명을 대상으로 $H_2^{15}O$ 동적 심근 PET을 시행한 후 앙상블 독립성분분석법을 이용하여 심근 독립성분영상을 추출하였으며, 좌심실영역과 심근영역에 대한 영상대조도를 조사하였다. 앙상블 학습은 독립성분과 가중치 행렬에 대한 확률분포를 가정하고 베이지안 이론에 의해서 혼합자료에 대한 확률분포를 추정한다. 이렇게 추정한 혼합자료의 확률분포와 실제 분포간의 차이인 Kullback-Leibler 발산치가 최소가 되도록 독립성분과 가중치 행렬을 순차적으로 변화시켜가며 최종 해를 찾는 방식이다. 이 연구에서 사후확률분포는 동적 핵의학 영상에 적합한 비음성제약조건과 함께 수정된 가우시안 분포를 이용하여 최적화 하였다. 혈류량은 심첨부, 중벽 네 부분, 하벽 네 부분의 9개 영역으로 나누어 측정하였으며, 측정결과에 대해 관류 SPECT 소견과 관동맥조영술의 소견과 비교하였다. 결과: 전체 20명의 휴식기 및 부하기 영상에서 5명을 제외한 15명의 데이터에 대해 심근혈류를 측정할 수 있었다. $H_2^{15}O$ 동적 심근 PET에서 앙상블 독립성분분석법을 이용하여 정량화한 휴식기 혈류량은 $1.2{\pm}0.40$ ml/min/g, 부하기 혈류량은 $1.85{\pm}1.12$ml/min/g이었다. 같은 영역에 대해 두 번 측정했을 때 측정된 심근혈류값의 상관계수는 0.99로 재현성이 높았다. 분리된 독립성분영상에서 영상대조도는 좌심실에 대한 심근영역의 비는 평균 1:2.7이었다. 관동맥 조영술을 시행한 9명에서 협착이 없는 분절과 협착이 있는 분절의 혈류예비능에 유의한 차이가 있었다(P<0.01). 또한, 관동맥조영술에서 협착이 확인된 66분절의 심근관류 SPECT 소견에서 가역적 혈류감소를 보인 분절의 혈류예비능이 더 많이 감소되는 경향을 보였으나 통계적 유의성을 보이지는 않았다. 결론: 앙상블 학습을 이용한 독립성분분석방법을 이용하여 심근혈류가 측정이 되었다. 앙상블 독립성분분석법을 이용한 $H_2^{15}O$ 동적 심근 PET 분석방법이 관상동맥 질환의 분석 및 동적 핵의학 영상 데이터의 연구에 도움이 될 것으로 기대된다.