• 호남수학학술지
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• 제1권1호
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• pp.1-9
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• 1979

Positive Local Coordmate($(x^1,x^2,{\cdots}x^n)$)을 갖는 Oriented Manifold M을 생각한다. M이 Compact Carrier를 갖는 경우, M위의 n차(次) Differential Form ${\phi}^{(n)}$의 적분(積分)을 $${\int}{\phi}^{(n)}=\sum_{\alpha}{\int}_{-{\infty}}^{\infty}{\cdots}{\int}_{-{\infty}}^{\infty}f_{\alpha}{\phi}^{(n)}dx^1{\cdots}dx^n$$로 정의(定義)하며 (정의(定義) 7), M위의 p 차(次)의 Differential form $\beta^{(p)}$와 Differential simplex $S^{(p)}=(S^{(p)},\;{\pi},\;{\varepsilon})$에 대하여 $S^{(p)}$위의 $\beta^{(p)}$의 적분(積分)을 $${\int}_{^{(p)}S}{\beta}^{(p)}={\int}_{S^{(p)}}{\varepsilon}{\pi}^*{\beta}^{(p)}={\int}_{E^p}f{\cdot}{\varepsilon}{\cdot}{\pi}^*{\beta}^{(p)}$$로 정의(定義)한다 (정의(定義) 9). 단(但) $\bar{S}^{(p)}$는 $S^{(p)}=(p_0{\cdot}p_1{\cdots}p_p)$에 의(依)하여 Spanning 되는 $E^p$의 Subspace이고 f는 $\bar{S}^{(p)}$의 특성함수(特性函數)이다. 이때 (n-1)차(次)의 Differential Form ${\beta}^{(n-1)}$이 Compart인 Carrier를 가지면 ${\int}d{\beta}^{(n-1)}=0$이 됨을 고찰(考察)하며(정리(定理 8), (p-1)차(次) Differential Form ${\beta}^{(p-1)$과 p차(次) Differential Chain $C^{(p)}$에 관(關)하여 $${\int}_{C^{(p)}}d{\beta}^{(p-1)}={\int}_{{\partial}C^{(p)}}{\beta}^{(p-1)}$$이 성립(成立)함을 구명(究明)하려 한다(정리(定理) 10).

• 호남수학학술지
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• 제8권1호
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• pp.51-74
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• 1986

The thery of measure is significant in that we extend from it to the theory of integration. AS specific metric outer measures we can take Hausdorff outer measure and Lebesgue-Stieltjes outer measure connecting measure with monotone functions.([12]) The purpose of this paper is to find some properties of Lebesgue-Stieltjes measure by extending it from $R^1$ to $R^n(n{\geq}1)$ $({\S}3)$ and differentiation of the integral defined by Borel measure $({\S}4)$. If in detail, as follows. We proved that if $_n{\lambda}_{f}^{\ast}$ is Lebesgue-Stieltjes outer measure defined on a finite monotone increasing function $f:R{\rightarrow}R$ with the right continuity, then $$_n{\lambda}_{f}^{\ast}(I)=\prod_{j=1}^{n}(f(b_j)-f(a_j))$$, where $I={(x_1,...,x_n){\mid}a_j$<$x_j{\leq}b_j,\;j=1,...,n}$. (Theorem 3.6). We've reached the conclusion of an extension of Lebesgue Differentiation Theorem in the course of proving that the class of continuous function on $R^n$ with compact support is dense in $L^p(d{\mu})$ ($1{\leq$}p<$\infty$) (Proposition 2.4). That is, if f is locally $\mu$-integrable on $R^n$, then $\lim_{h\to\0}\left(\frac{1}{{\mu}(Q_x(h))}\right)\int_{Qx(h)}f\;d{\mu}=f(x)\;a.e.(\mu)$.

• 유통과학연구
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• 제20권2호
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• pp.55-64
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• 2022

Purpose: This research is aimed to study the level of the intellectual potential distribution, as well as the correlation between economic growth and key indicators of intellectual potential in each region of Kazakhstan. A review of the conceptual framework shows that there is a large body of research evaluating the level of intellectual potential in different ways based on different factors. Research design, data, and methodology: The research methodology is divided into two groups the integral index method using the normalization of indicators, weighting, and ranking; the method of correlation analysis. By the proposed methodological approaches, were calculated a set of factors affect the distribution of the intellectual potential. Statistics are taken for indicators of development of the intellectual potential for 2011-2020 from the Bureau of National Statistics. Results: Ranking results showed gaps between regions in Kazakhstan by the level of intellectual potential. Correlation analysis results revealed a statistically significant relationship on expenditures on R&D, computer literacy, innovative products, number of PhD students, and cultural and leisure indicators. Conclusions: Based on the obtained results of the intellectual potential level development there were given recommendations for the reproduction and regulation of the intellectual potential in the future.

• 한국측량학회지
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• 제22권3호
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• pp.245-251
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• 2004

최근 지형공간정보 분야의 눈부신 발전과 함께 지적 분야에서도 지적도면 전산화 사업이 진행되고 있으며 다양한 토지관련 정보의 통합관리 및 활용을 위하여 토지정보 및 건물정보의 통합에 관한 요구가 증가하고 있지만 3차원지적제도 구축에 있어 기본이 되는 건물의 지적도 등록 시 전국에 산재되어 있는 수많은 건물을 일일이 지상측량방법을 통하여 지적도에 등록하는 것은 많은 어려움이 뒤따르는 실정이다. 이 연구에서는 유럽을 중심으로 활발히 연구되고 있는 3차원지적제도의 이론을 고찰하고 실험대상지역을 선정하여 지적기준점에서 토탈스테이션을 이용하여 건물위치를 직접 측량하였고, 수치지형도와 수치정사영상을 제작하여 건물위치를 측량한 후 건물좌표들을 비교 분석하여 지적도에 건물등록 시 가장 효율적인 측량 방법을 제시하고 지적도에 건물을 등록한 후 등록된 건물에 기존 토지지번과는 별도로 새로운 건물번호를 식별자로 부여하여 지적도를 제작하였고, 건축물관리대장과 건물등기부 및 관련 속성정보와 건물사진 등을 연계하여 토지와 건물관리를 통합 관리할 수 있는 새로운 3차원정보지적도 모델을 구축 하였다.

• Nuclear Engineering and Technology
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• 제52권3호
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• pp.461-468
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• 2020

The improvements of the DeCART/MUSAD code system for uncertainty analysis of HTGR neutronic parameters are presented in this paper. The function for quantifying an uncertainty of critical-spectrumweighted few group cross section was implemented using the generalized adjoint B₁ equation solver. Though the changes between the infinite and critical spectra cause a considerable difference in the contribution by the graphite scattering cross section, it does not significantly affect the total uncertainty. To reduce the number of iterations of the generalized adjoint transport equation solver, the generalized adjoint B₁ solution was used as the initial value for it and the number of iterations decreased to 50%. To reflect the implicit uncertainty, the correction factor was derived with the resonance integral. Moreover, an additional correction factor for the double heterogeneity was derived with the effective cross section of the DH region and it reduces the difference from the complete uncertainty. The code system was examined with the MHTGR-350 Ex.II-2 3D core benchmark. The k_eff uncertainty for Ex.II-2a with only the fresh fuel block was similar to that of the block and the uncertainty for Ex.II-2b with the fresh fuel and the burnt fuel blocks was smaller than that of the fresh fuel block.

• 한국지능시스템학회논문지
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• 제7권2호
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• pp.70-78
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• 1997

여러 가지 고급 제어 이론들에 관한 연구가 심도있게 진행되고 있음에도 불구하고 아직까지 산업현장에는 여러가지 변형된 형태의 PID 제어기가 널리 사용되고있다. 이는 PID 제어기 자체가 가진 제어 구조의 단순성, 효율성, 강건성, 그리고 제어 기술자들에 대한 친밀감 등에 기인한다. 또한 요즘 제어 분야에서는 퍼지 이론을 도입하는 연구가 활발히 진행되고 있다. 특히, 퍼지 이론을 사용해서 거의 모든 함수들을 근사화시킬 수 있다는 연구 결과들이 발표되면서 수학적으로 안정성 및 강건성을 명확히 증명하기에 다소 미흡하였던 퍼지 논리 제어에 관한 연구가 활기를 띠고 있다. 본 논문에서는 먼저 간단한 퍼지 제어기로부터 선형 PID 제어기를 유도한다. 그리고 나서 다소 일반적인 경우의 퍼지 제어기를 사용하여 산업 현장에서 가장 널리 사용되고있는 선형PID 제어기를 유도하여 결굴 PID 제어기는 퍼지 제어기의 일종에 불과함을 입증할 것이다.

• Steel and Composite Structures
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• 제42권2호
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• pp.243-256
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• 2022

A coupled finite element method (FEM)-boundary element method (BEM) for analyzing the hydroelastic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) floating plates under moving loads is firstly introduced in this article. For that aim, the plate displacement field is described utilizing a generalized shear deformation theory (GSDT)-based FEM, meanwhile the linear water-wave theory (LWWT)-relied BEM is employed for the fluid hydrodynamic modeling. Both computational domains of the plate and fluid are coincidentally discretized into 4-node Hermite elements. Accordingly, the C1-continuous plate element model can be simply captured owing to the inherent feature of third-order Hermite polynomials. In addition, this model is also completely free from shear correction factors, although the shear deformation effects are still taken into account. While the fluid BEM can easily handle the free surface with a lower computational effort due to its boundary integral performance. Material properties through the plate thickness follow four specific CNT distributions. Outcomes gained by the present FEM-BEM are compared with those of previously released papers including analytical solutions and experimental data to validate its reliability. In addition, the influences of CNT volume fraction, different CNT configurations, water depth, and load speed on the hydroelastic behavior of FG-CNTRC plates are also examined.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권2호
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• pp.123-132
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• 1998

Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of $F_{\alpha}$, he NPBE of F with respect to the Dirichlet process prior D($\alpha$), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, $\alpha$, Hjort(1990) obtained the Bayes estimator $A_{c,\alpha}$ of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator $F_{c,\alpha}$ is recovered from $A_{c,\alpha}$. Continuity assumption on F and G is removed in our proof of the consistency of $A_{c,\alpha}$ and $F_{c,\alpha}$. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.

• Nuclear Engineering and Technology
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• 제54권7호
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• pp.2367-2375
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• 2022

In this work, we propose a new mechanistic model for the treatment of helium behaviour at the grain boundaries in oxide nuclear fuel. The model provides a rate-theory description of helium inter-granular behaviour, considering diffusion towards grain edges, trapping in lenticular bubbles, and thermal resolution. It is paired with a rate-theory description of helium intra-granular behaviour that includes diffusion towards grain boundaries, trapping in spherical bubbles, and thermal re-solution. The proposed model has been implemented in the meso-scale software designed for coupling with fuel performance codes SCIANTIX. It is validated against thermal desorption experiments performed on doped UO₂ samples annealed at different temperatures. The overall agreement of the new model with the experimental data is improved, both in terms of integral helium release and of the helium release rate. By considering the contribution of helium at the grain boundaries in the new model, it is possible to represent the kinetics of helium release rate at high temperature. Given the uncertainties involved in the initial conditions for the inter-granular part of the model and the uncertainties associated to some model parameters for which limited lower-length scale information is available, such as the helium diffusivity at the grain boundaries, the results are complemented by a dedicated uncertainty analysis. This assessment demonstrates that the initial conditions, chosen in a reasonable range, have limited impact on the results, and confirms that it is possible to achieve satisfying results using sound values for the uncertain physical parameters.

• Advances in aircraft and spacecraft science
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• 제8권4호
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• pp.345-372
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• 2021

The analysis of nonlinear vibrations, buckling, post-buckling, flutter boundary determination and post-flutter behavior of a homogeneous curved plate assuming cylindrical bending is conducted in this article. Other assumptions include simply-supported boundary conditions, supersonic aerodynamic flow at the top of the plate, constant pressure conditions below the plate, non-viscous flow model (using first- and third-order piston theory), nonlinear structural model with large deformations, and application of mechanical and thermal loads on the curved plate. The analysis is performed with constant environmental indicators (flow density, heat, Reynolds number and Mach number). The material properties (i.e., coefficient of thermal expansion and modulus of elasticity) are temperature-dependent. The equations are derived using the principle of virtual displacement. Furthermore, based on the definitions of virtual work, the potential and kinetic energy of the final relations in the integral form, and the governing nonlinear differential equations are obtained after fractional integration. This problem is solved using two approaches. The frequency analysis and flutter are studied in the first approach by transferring the handle of ordinary differential equations to the state space, calculating the system Jacobin matrix and analyzing the eigenvalue to determine the instability conditions. The second approach discusses the nonlinear frequency analysis and nonlinear flutter using the semi-analytical solution of governing differential equations based on the weighted residual method. The partial differential equations are converted to ordinary differential equations, after which they are solved based on the Runge-Kutta fourth- and fifth-order methods. The comparison between the results of frequency and flutter analysis of curved plate is linearly and nonlinearly performed for the first time. The results show that the plate curvature has a profound impact on the instability boundary of the plate under supersonic aerodynamic loading. The flutter boundary decreases with growing thermal load and increases with growing curvature.