• 대한수학회논문집
• /
• 제34권2호
• /
• pp.685-699
• /
• 2019

This research is focused on a continuous epidemic model of transmission of Plasmodium vivax malaria with a time delay. The model is represented as a system of ordinary differential equations with delay. There are two equilibria, which are the disease-free state and the endemic equilibrium, depending on the basic reproduction number, $R_0$, which is calculated and decreases with the time delay. Moreover, the disease-free equilibrium is locally asymptotically stable if $R_0<1$. If $R_0>1$, a unique endemic steady state exists and is locally stable. Furthermore, Hopf bifurcation is applied to determine the conditions for periodic solutions.

• 대한기계학회논문집
• /
• 제19권3호
• /
• pp.820-833
• /
• 1995

An analysis is performed to examine the equilibrium state and the stability of modeled Reynolds stress equations for homogeneous turbulent shear flows. The system of the governing equations consists of four coupled ordinary differential equations. The equilibrium states are found by the steady state solution of the governing equations. In order to investigate the stability of the system about its state in equilibrium, and eigenvalue problem is constructed. As a result, constraints for the coeffieients in the model equations are obtained by the stability condition of the equilibrium state as well as by their physically realizable bounds. It is observed that the models with pressure-strain rate correlation that are linear in the anisotropy tensor are stable and produce reasonable equilibrium tensor do not behave properly. Stability considerations about three most commonly used models are given in detail in the final section.

• 한국공간구조학회논문집
• /
• 제13권2호
• /
• pp.75-82
• /
• 2013

For each cable component in a cable dome structure, pre-tension is needed for stability of whole the structure. The summation of these pre-tension at each joint should be zero to achieve the self equilibrium structure. The first step in cable dome structure analysis is to find the ratio of pre-tension in each member which can produce a stable and structure on self-equilibrium. In this paper, a new method based on the basic principle of closed force polygon for equilibrium system is proposed for the determination of self-equilibrium mode of cable dome structure. A single layer cable dome and two multi layer type domes have been analyzed. The ratios of cable members are determined by the presented method, and check the validation of the results by numerical calculation.

• Journal of applied mathematics & informatics
• /
• 제30권3_4호
• /
• pp.365-380
• /
• 2012

Non-negative matrix factorization (NMF) is a very efficient method to explain the relationship between functions for finding basis information of multivariate nonnegative data. The multiplicative update (MU) algorithm is a popular approach to solve the NMF problem, but it fails to approach a stationary point and has inner iteration and zero divisor. So the elementwisely alternating projected gradient (eAPG) algorithm was proposed to overcome the defects. In this paper, we use the fact that the equilibrium point is stable to prove the convergence of the eAPG algorithm. By using a classic model, the equilibrium point is obtained and the invariant sets are constructed to guarantee the integrity of the stability. Finally, the convergence conditions of the eAPG algorithm are obtained, which can accelerate the convergence. In addition, the conditions, which satisfy that the non-zero equilibrium point exists and is stable, can cause that the algorithm converges to different values. Both of them are confirmed in the experiments. And we give the mathematical proof that the eAPG algorithm can reach the appointed precision at the least iterations compared to the MU algorithm. Thus, we theoretically illustrate the advantages of the eAPG algorithm.

• 한국주조공학회지
• /
• 제27권4호
• /
• pp.167-172
• /
• 2007

In the present study, the microstructural evolution and mechanical properties of $Al_{71.6}Ge_{28.4}$ eutectic alloy have been investigated. Stable (fcc ${\alpha}$-Al and diamond cubic ${\beta}$-Ge) and various metastable crystalline (monoclinic, rhombohedral) phases were produced by competitive phase selection during non-equilibrium processing methods i.e. melt spinning and injection casting. The as-injection casted samples containing metastable-equilibrium eutectic (${\alpha}$-Al + monoclinic) structure showed much higher strength than samples with equilibrium eutectic (${\alpha}-Al+{\beta}-Ge$) structure but plasticity disappointingly diminished. In order to endow the enhanced ductility without significant strength drop, the alloys was heat-treated at transition temperature from metastable phase to stable phase. The annealed specimen displayed the phase transformed microstructural evolution and enhanced macroscopic plasticity.

• Computers and Concrete
• /
• 제11권5호
• /
• pp.411-440
• /
• 2013

Large fluctuations in surface strain at the level of steel are expected in reinforced concrete flexural members at a given stage of loading due to the emergent structure (emergence of new crack patterns). This has been identified in developing deterministic constitutive models for finite element applications in Ibrahimbegovic et al. (2010). The aim of this paper is to identify a suitable probability distribution for describing the large deviations at far from equilibrium points due to emergent structures, based on phenomenological, thermodynamic and statistical considerations. Motivated by the investigations reported by Prigogine (1978) and Rubi (2008), distributions with heavy tails (namely, alpha-stable distributions) are proposed for modeling the variations in strain in reinforced concrete flexural members to account for the large fluctuations. The applicability of alpha-stable distributions at or in the neighborhood of far from equilibrium points is examined based on the results obtained from carefully planned experimental investigations, on seven reinforced concrete flexural members. It is found that alpha-stable distribution performs better than normal distribution for modeling the observed surface strains in reinforced concrete flexural members at these points.

• 천문학논총
• /
• 제30권2호
• /
• pp.297-299
• /
• 2015

In this paper we have examined the linear stability of triangular equilibrium points in the photogravitational restricted three body problem when both primaries are triaxial rigid bodies, the bigger one an oblate spheroid and source of radiation. The orbits about the Lagrangian equilibrium points are important for scientific investigation. A number of space missions have been completed and some are being proposed by various space agencies. We analyze the periodic motion in the neighbourhood of the Lagrangian equilibrium points as a function of the value of the mass parameter. Periodic orbits of an infinitesimal mass in the vicinity of the equilibrium points are studied analytically and numerically. The linear stability of triangular equilibrium points in the photogravitational restricted three body problem with Poynting-Robertson drag when both primaries are oblate spheroids has been examined by A. Kumar (2007). We have found the equations of motion and triangular equilibrium points for our problem. With the help of the characteristic equation we have discussed stability conditions. Finally, triangular equilibrium points are stable in the linear sense. It is further seen that the triangular points have long or short periodic elliptical orbits in the same range of ${\mu}$.

• 대한교통학회지
• /
• 제25권4호
• /
• pp.99-108
• /
• 2007

본 연구에서는 가변수요를 고려한 확률적 사용자균형 통행배정모형을 제시한다. 교통망에서 수요와 공급간의 균형을 가정할 경우, 통행비용의 함수인 가변수요는 통행저항함수(공급함수)와 함께 균형상태로 수렴하며, 이때 확률적 통행배정모형은 통행자들간의 경로인지 통행비용이 동일해지는 확률적 사용자균형상태에 도달하게 된다. 본 연구에서 제시하는 확률적 사용자균형모형은 기존 연구들과는 달리 동적체계(dynamic system)를 기초로 개발된다. 동적체계는 시간의 흐름에 따라 하나의 상태가 다음 상태로 변화하는 과정을 표현하는 수리적인 방법으로 시간의 변화에 따라 그 상태가 변하는 여러 분야에 적용이 가능한데, 주로 제어공학(control engineering)분야에서 활용되어 왔다. 동적 체계의 개념을 도입하면, 기존 모형들과는 달리 쉽게 모형화(formulation)할 수 있으며 풀이과정(solution algorithm)도 간단하다는 장점이 있다. 본 연구에서도 동적체계를 이용하여 확률적 사용자균형 통행배정(user equilibrium traffic assignment)모형을 제시하고 제시된 모형이 안정적인 해(stable solution)로 수렴한다는 것을 Lyapunov함수를 통하여 증명한다. 또한, 예제 교통망을 통하여 여러가지 의미있는 결과를 도출한다.

• 한국환경과학회지
• /
• 제4권1호
• /
• pp.91-103
• /
• 1995

The reaction rate, equilibrium, and flow injection analysis methods were fundamentally evaluated for the determination of aqueous ammonia. The selected indophenol blue method was based on the formation of indophenol blue in which ammonium ion reacted with hypochlorite and phenol in alkaline solution. In the optimized reaction condition, the reaction followed 1st order reaction kinetics and the final product was stable. The absorbance measurements before and after the equilibrium were utilized for the reaction rate and equilibrium methods. The reaction rate methods, based on the relative analytical signals for the possibility of eliminating interferents, were shown to have good linear calibration curves but the detection limit and the calibration sensitivity were poorer than those in the equilibrium method. The detection limits were 32-49 pub and 24 pub for the reaction rate and equilibrium methods, respectively In the flow injection analysis, the absorbance was measured before the equilibrium reached and thus resulted in 30% reduction of calibration sensitivity. However, the detection limit was 11 ppb, indicating that the peak-to-peak noise for the blank was remarkably improved. Compared to the manual methods, the optimized experimental condition in a closed reaction system reduced the blank absorbance and the inclusion of ammonia from the atmosphere was prevented. In addition, highly reproducible mixing of sample and reagents and analytical data extracted from continuous recording showed excellent reproducibility.

• 문화기술의 융합
• /
• 제9권6호
• /
• pp.779-787
• /
• 2023

예산 분석에 관한 기존 연구는 이론적 배경 없이 전체 예산 대비 국방예산의 연간 변화만을 기술하는 데 대부분 국한되어 왔다. 본 연구에서는 단절균형이론(Punctuated Equilibrium Theory, PET)을 이용하여 국방비 지출에 대한 실증분석을 실시하였다. 본 연구의 목적은 한국의 국방예산(총예산, 전력운용예산, 방위력개선예산)의 추이를 살펴보고, 단절균형이론을 사용하여 국방예산의 급진적 변화 지점을 파악하고 분석하는 것이다. 본 연구에서는 또한 1998년부터 2017년까지 매년 대한민국 국방예산 자료를 활용하여 국방예산의 추세와 급격한 변화 지점을 탐색하였다. 그 결과, 1998년부터 2017년까지 한국의 국방비 지출 패턴은 다음과 같은 특징을 갖는 것으로 나타났다. 국방예산 총액 기준 19년간 안정적인 성장을 보였고 일회성 단절지점(5.0%)을 보였으며, 전력운영비는 18년 동안은 균형을 이루며 안정적으로 성장하였고 두 번의 단절지점(10%)을 보였다. 방위력개선비는 총 5번의 급격하게 변화는 단절지점을 확인할 수 있었다.