• 대한수학회논문집
• /
• 제18권3호
• /
• pp.569-580
• /
• 2003

The Lotka-McKendrick equation which describes the evolution of a single population under the phenomenological conditions is developed from the well-known Malthus’model. In this paper, we introduce the Lotka-McKendrick equation for the description of the dynamics of a population. We apply a discontinuous Galerkin finite element method in age-time domain to approximate the solution of the system. We provide some numerical results. It is experimentally shown that, when the mortality function is bounded, the scheme converges at the rate of $h^2$ in the case of piecewise linear polynomial space. It is also shown that the scheme converges at the rate of $h^{3/2}$ when the mortality function is unbounded.

• 한국수학사학회지
• /
• 제30권3호
• /
• pp.137-162
• /
• 2017

The Chinese algebraic method, the tian yuan shu, was developed during Song period (960-1279), of which Li Ye's works contain the earliest testimony. Two 18th century editors commentated on his works: the editor of the Siku quanshu and Li Rui, the latter responding to the former. Korean scholar Nam Byeong-gil added another response in 1855. Differences can be found in the way these commentators considered mathematical objects and procedures. The conflicting nature of these commentaries shows that the same object, the quadratic equation, can beget different interpretations, either a procedure or an assertion of equality. Textual elements in this paper help modern readers reconstruct different authors' understandings and reconsider the evolution of the definition of the object we now call 'equation'.

• 대한수학회보
• /
• 제56권1호
• /
• pp.265-276
• /
• 2019

For a simple implementation, a linear convex splitting scheme was coupled with the Fourier spectral method for the Cahn-Hilliard equation with a logarithmic free energy. However, an inappropriate value of the splitting parameter of the linear scheme may lead to incorrect morphologies in the phase separation process. In order to overcome this problem, we present a nonlinear convex splitting Fourier spectral scheme for the Cahn-Hilliard equation with a logarithmic free energy, which is an appropriate extension of Eyre's idea of convex-concave decomposition of the energy functional. Using the nonlinear scheme, we derive a useful formula for the relation between the gradient energy coefficient and the thickness of the interfacial layer. And we present numerical simulations showing the different evolution of the solution using the linear and nonlinear schemes. The numerical results demonstrate that the nonlinear scheme is more accurate than the linear one.

• Kyungpook Mathematical Journal
• /
• 제62권4호
• /
• pp.729-736
• /
• 2022

To help solving intractable nonlinear evolution equations (NLEEs) of waves in the field of fluid dynamics we develop an algorithm to find new high order solutions of the class of Abel, Bernoulli, Chini and Riccati equations of the form y' = ayⁿ + by + c, n > 1, with constant coefficients a, b, c. The role of this class of equations in NLEEs is explained in the introduction below. The basic algorithm to compute the coefficients of the power series solutions of the class, emerged long ago and is further developed in this paper. Practical application for hitherto unknown solutions is exemplified.

• The Journal of Asian Finance, Economics and Business
• /
• 제9권5호
• /
• pp.119-133
• /
• 2022

The purpose of this study is to examine how change recipients react to change (affective commitment to change) and how change leads to positive consequences (job satisfaction) in Revolution and Evolution, taking into account the change content (perceived change impact), change context (change climate), and change process (participation in the change process). The present study uses a deductive approach with an exploratory research design. Data was collected from 254 employees of the head offices of three major banks, who have gone through Revolution, and 354 employees of the head offices, three banks who have gone through Evolution in the last five years. The hypothesized model is tested and analyzed through structural equation modeling using SmartPLS. The findings revealed that, in the case of Revolution, the presence of the favorable context and process might revert the negative perception of the change and lead towards explicit positive reactions (affective commitment to change) and change consequences (job satisfaction). In the case of Evolution, the change can be more effectively implemented using favorable context and process by achieving explicit positive reactions (affective commitment to change) and change consequences (job satisfaction).

• 대한수학회지
• /
• 제34권4호
• /
• pp.895-909
• /
• 1997

We state the necessary conditions on optimizing the parameters which the damping differential operators contain in abstract linear damped second order evolution equation on the Gelfand five fold.

• 대한수학회지
• /
• 제32권2호
• /
• pp.237-250
• /
• 1995

A hopf bifurcation of a free boundary (or an internal layer) occurs in solidification, chemical reactions and combustion. It is a well-known fact that a free boundary usually appear as sharp transitions with narrow width between two materials ([2]).

• 한국식품과학회지
• /
• 제36권4호
• /
• pp.580-585
• /
• 2004

단감의 호흡에 미치는 산소, 이산화탄소 가스조성과 저장온도의 영향을 조사하기 위하여 비경쟁억제 효소반응속도식$(R=V_m[O_2]/(K_m+(1+[CO_2]/K_i)[O_2]))$과, Arrhenius 식(R=A exp(-E/$(R^*T)$)을 각각 모델로 하였다. 호흡 data는 0, 5, $20^{\circ}C$에서 폐쇄계방법으로 수집하였다. 0, $5^{\circ}C$에서 $K_m$은 0.1%이하, $K_i$는 100%이상이었고, $20^{\circ}C$에서 산소소비와 이산화탄소 발생의 $K_m$은 각각 10.72%와 3.25%로 크게 증가하였고, $K_i$는 각각 59.6%와 44.6%로 크게 감소하였다. 활성화에너지는 산소농도가 낮아지고 이산화탄소 농도가 높아질수록 감소하였고, 산소소비의 활성화에너지가 이산화탄소 발생의 활성화에너지보다 낮았다. 이는 이산화탄소 발생 호흡량이 산소소비 호흡량에 비해 온도의 영향을 많이 받고, 산소감소와 이산화탄소 증가에 따른 호흡량 감소 효과는 저온에 비해 고온에서 커지는 경향이었다. 이는 산소소비와 이산화탄소 발생의 $K_m$과 $K_i$값 비교에 의한 예측과 일치하는 결과이다. 이상의 간을 근거로 하여 각 온도별 MA포장 내 공기조성 변화의 예측하였고, 또한 실제 실험으로 조사된 값은 일치하였다. 따라서 단감의 최적 MA 포장조건설정에 있어서 효소반응속도론에 근거한 호흡모델이 타당한 것으로 판단되었다.

• 대한조선학회논문집
• /
• 제48권3호
• /
• pp.200-206
• /
• 2011

The mechanical properties of the most widely used cryogenic materials, i.e. austenitic stainless steel (ASS), aluminum alloy and invar steel, strongly depend on temperatures and strain rates. These phenomena show very complicated non-linear behaviors and cannot be expressed by general constitutive equation. In this study, an unified constitutive equation was proposed to represent the effect of temperature and strain rate on the materials. The proposed constitutive equation has been based on Tomita/Iwamoto and Bodner/Partom model for the expression of 2nd hardening due to martensite phase transformation of ASS. To simulate ductile fracture, modified Bodner/Chan damage model was additionally applied to the model and the model validity was verified by comparison of experimental and simulation results.

• 한국해안해양공학회지
• /
• 제19권4호
• /
• pp.303-312
• /
• 2007

주파수영역에서 쇄파로 인한 에너지 소산에 관한 그 동안의 논쟁은 주파수의 함수인 소산항의 구체적 형태를 중심으로 진행되어왔다. 본 연구에서는 추계학적 쇄파모형과 이에 기초한 스펙트럼으로부터 소산항을 유추하였다. 기존의 인식과는 상이하게 소산항은 주파수의 삼차함수인 것으로 판단된다. 검증작업은 SUPERTANK Laboratory Data Collection Project(Krauss et al., 1992)에서 축적된 실험자료를 기초로 진행되었다. 추가적인 검증을 위해 단조해안에서의 Cnoidal 파랑의 천수과정을 스펙트럼 파랑모형과 제시된 쇄파모형을 차용하여 수치모의하였다. 그 결과 쇄패대역에서 진행되는 파랑의 왜도와 비대칭성의 진화과정이 비교적 정확히 모의되는 성과를 얻었다.