心構造上에 있어서의 정신병리 계층 및 수행론 관찰

원광대학교 종교심성연구반 圓光大學校 圓佛敎學硏究會 1990 圓佛敎學硏究 Vol.20 No.-

생물 종의 개체 수 변화를 기술하는 수학적 모델에 대한 고찰

심성아,Shim, Seong-A 한국수학사학회 2011 Journal for history of mathematics Vol.24 No.2

일정 영역에 서식하는 생물 종의 개체 수가 변화하는 역학적 과정을 이해하고 실질적인 예측을 하는데 도움을 주는 여러가지 수학적 모델이 현재 수학과 생태학 분야에서 활발하게 연구되고 있다. 영국의 경제학자 Malthus가 1798년부터 시작하여 1826년까지 출간한 An Essay on the Principle of Population에서 제안했던 세계인구 변화 모델과 1845년 Verhulst의 한계수용모델은 개체 수 변화에 대한 초기 수학적 모델로서 지수적 형태에 기초한 것이었다. 수리생물학으로 불리는 학문분야는 1920년경 Lotka의 연구에서 본격적으로 시작되었다고 할 수 있다. 이때부터 여러 가지 다양한 수학적 모델들이 제안되어지고 검증되어져 왔다. 이 논문에서는 주로 상미분방정식(ordinary differential equations)으로 표현되는 단일 생물종에 대한 개체 수 변화모델들을 살펴본다. Various mathematical models have been widely studied recently in both fields of mathematics and ecology since they help us understand the dynamical process of population changes in biological species living in a certain habitat and give useful predictions. The world population model proposed by Malthus, a British economist, in his work 'An Essay on the Principle of Population' published in the period of 1789~1826 is one of the early mathematical models on population changes. Malthus' models and the carrying capacity models of Verhulst in 1845 were based on exponential type functions. The independent research field of mathematical ecology has been started from Lotka's works in 1920's. Since then various different mathematical models has been proposed and examined. This article mainly deals with single species population change models expressed in terms of ordinary differential equations.

개체 수 변화에 대한 이산적 모델의 역사적 개요와 컴퓨터 소프트웨어를 이용하는 시각적 분석 방법

심성아,Shim, Seong-A 한국수학사학회 2014 Journal for history of mathematics Vol.27 No.3

Species like insects and fishes have, in many cases, non-overlapping time intervals of one generation and their descendant one. So the population dynamics of such species can be formulated as discrete models. In this paper various discrete population models are introduced in chronological order. The author's investigation starts with the Malthusian model suggested in 1798, and continues through Verhulst model(the discrete logistic model), Ricker model, the Beverton-Holt stock-recruitment model, Shep-herd model, Hassell model and Sigmoid type Beverton-Holt model. We discuss the mathematical and practical significance of each model and analyze its properties. Also the stability properties of stationary solutions of the models are studied analytically and illustratively using GSP, a computer software. The visual outputs generated by GSP are compared with the analytical stability results.

상호작용하는 두 생물 종의 개체 수 변화에 대한 수학적 모델

심성아,Shim, Seong-A 한국수학사학회 2012 Journal for history of mathematics Vol.25 No.1

최근 그 중요성이 인식되면서 수학에서 뿐만 아니라, 생물학, 의학, 면역학 등의 여러 분야에서 세계적으로 광범위하게 연구되어지고 있는 수리 생물학(Mathematical biology) 분야의 학문적 시초이며 그 기초를 제공하는 개체 수 생태학 (population ecology) 은 생물 종 (種) 의 개체 수가 서식지 안의 특정 위치에서 시간에 따라 어떻게 변하는 지를 연구하는 분야이다. 이 논문에서는 두 종류의 생물 종이 한 서식지 안에서 상호작용하는 형태로서 포식자-먹이 관계, 경쟁관계, 협력관계를 나타내는 모델들을 살펴본다. Mathematical biology has been recognized its importance recently and widely studied in the fields of mathematics, biology, medical sciences, and immunology. Mathematical ecology is an academic field that studies how populations of biological species change as times flows at specific locations in their habitats. It was the earliest form of the research field of mathematical biology and has been providing its basis. This article deals with various form of interactions between two biological species in a common habitat. Mathematical models of predator-prey type, competitive type, and simbiotic type are investigated.

CONVERGENCE RESULTS FOR THE COOPERATIVE CROSS-DIFFUSION SYSTEM WITH WEAK COOPERATIONS

심성아 한국수학교육학회 2017 純粹 및 應用數學 Vol.24 No.4

We prove convergence properties of the global solutions to the cooperative cross-diffusion system with the intra-specific cooperative pressures dominated by the inter-speci¯c competition pressures and the inter-speci¯c cooperative pres- sures dominated by intra-speci¯c competition pressures. Under these conditions the W1 2 -bound and the time global existence of the solution for the cooperative cross- diffusion system have been obtained in [10]. In the present paper the convergence of the global solution is established for the cooperative cross-diffusion system with large diffusion coefficients.

생물 종의 개체 수 변화를 기술하는 수학적 모델의 확산현상 표현에 대한 역사적 고찰

심성아,Shim, Seong-A 한국수학사학회 2016 Journal for history of mathematics Vol.29 No.6

In mathematical population ecology which is an academic field that studies how populations of biological species change as times flows at specific locations in their habitats, PDE models have been studied in many aspects and found to have different properties from the classical ODE models. And different approaches to PDE type models in mathematical biology are still being tried currently. This article investigate various forms to express diffusion effects and review the history of PDE models involving diffusion terms in mathematical ecology. Semi-linear systems representing the spatial movements of each individual as random simple diffusion and quasi-linear systems describing more complex diffusions reflecting interspecific interactions are studied. Also it introduce a few of important problems to be solved in this field.

Global Existence of Solutions to the Prey-Predator System with a Single Cross-Diffusion

심성아 대한수학회 2006 대한수학회보 Vol.43 No.2

The prey-predator system with a single cross-diusionpressure is known to possess a local solution with the maximalexistence timeT 1 . By obtaining the bounds of W12 -norms ofthe local solution independent of T we establish the global existenceof the solution. And the long-time behaviors of the global solutionare analyzed when the diusion rates d1 and d2 are suciently large.

사이클로이드 곡선의 역사와 그 특성에 대한 증명

심성아,Shim, Seong-A 한국수학사학회 2015 Journal for history of mathematics Vol.28 No.1

The cycloid curve had been studied by many mathematicians in the period from the 16th century to the 18th century. The results of those studies played important roles in the birth and development of Analytic Geometry, Calculus, and Variational Calculus. In this period mathematicians frequently used the cycloid as an example to apply when they presented their new mathematical methods and ideas. This paper overviews the history of mathematics on the cycloid curve and presents proofs of its important properties.

CONVERGENCE PROPERTIES OF PREDATOR-PREY SYSTEMS WITH FUNCTIONAL RESPONSE

심성아 호남수학회 2008 호남수학학술지 Vol.30 No.3

In the field of population dynamics and chemical reaction the possibility of the existence of spatially and temporally nonhomogeneous solutions is a very important problem. For last 50 years or so there have been many results on the pattern formation of chemical reaction systems studying reaction systems with or without diffusions to explain instabilities and nonhomogeneous states arising in biological situations. In this paper we study timedependent properties of a predator-prey system with functional response and give sufficient conditions that guarantee the existence of stable limit cycles.

STABILITY ANALYSIS FOR PREDATOR-PREY SYSTEMS

심성아 한국수학교육학회 2010 純粹 및 應用數學 Vol.17 No.3

Various types of predator-prey systems are studied in terms of the sta-bilities of their steady-states. Necessary conditions for the existences of non-negative constant steady-states for those systems are obtained. The linearized stabilities of the non-negative constant steady-states for the predator-prey system with monotone response functions are analyzed. The predator-prey system with non-monotone re-sponse functions are also investigated for the linearized stabilities of the positive constant steady-states.