• 한국수학사학회지
• /
• 제29권6호
• /
• pp.335-351
• /
• 2016

Spherical convexity may be defined in different ways. It depends on which statement we take as a definition among several statements that can be all used as a definition of convexity of subsets in an affine space. In this article, we consider this question from various perspectives. We compare several different definitions of spherical convexity which are found in mathematical papers. In particular, we focus our discussion on the definitions of J. P. $Benz{\acute{e}}cri$ and N. H. Kuiper who built a solid foundation for theory of convex bodies and convex affine(projective) structures on manifolds.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제7권1호
• /
• pp.41-47
• /
• 2000

Johnson and Skoug [Pacific J. Math. 83(1979), 157-176] introduced the concept of scale-invariant measurability in Wiener space. And the applied their results in the theory of the Feynman integral. A converse measurability theorem for Wiener space due to the $K{\ddot{o}}ehler$ and Yeh-Wiener space due to Skoug[Proc. Amer. Math. Soc 57(1976), 304-310] is one of the key concept to their discussion. In this paper, we will extend the results on converse measurability in Wiener space which Chang and Ryu[Proc. Amer. Math, Soc. 104(1998), 835-839] obtained to abstract Wiener space.

• 품질경영학회지
• /
• 제23권2호
• /
• pp.10-27
• /
• 1995

This paper illustrates a method of developing a function of quality costs in manufacturing systems. It begins with a discussion of the problem statement of this research. A review of existing literatures related to quality costs and economic design of quality inspection methods are discussed. Next mathematical models that quantify the production cycle time and quality costs are formulated. This paper ends with an example that demonstrates the usefulness of the model and highlights the importance of using a system approach. The main contribution of this work is the more realistic considerations of the four types of quality costs (prevention cost, appraisal cost, internal failure cost, external failure cost) in manufacturing systems.

• Korean Journal of Mathematics
• /
• 제24권2호
• /
• pp.139-168
• /
• 2016

In this work, we rst introduce a class of analytic functions involving the Dziok-Srivastava linear operator that generalizes the class of uniformly starlike functions with respect to symmetric points. We then establish the closure of certain well-known integral transforms under this analytic function class. This behaviour leads to various radius results for these integral transforms. Some of the interesting consequences of these results are outlined. Further, the lower bounds for the ratio between the functions f(z) in the class under discussion, their partial sums $f_m(z)$ and the corresponding derivative functions f'(z) and $f^{\prime}_m(z)$ are determined by using the coecient estimates.

• 한국통신학회논문지
• /
• 제29권8B호
• /
• pp.730-738
• /
• 2004

본 논문에서는 요구할당 다중접속 방식을 사용하는 패킷 위성통신에서 스팟빔 스위칭 능력과 신호처리 능력을 가진 위성체의 관찰중인 특정 하향링크 출력포트에 초점을 두어 시스템의 처리량(Throughput)과 블로킹 확률(Blocking Probability) 그리고 전송지연(Delay)을 요구트래픽과 채널의 서비스종료 확률에 따란 분석하였다. 수학적 검증을 통해 각 채널 서비스 종료 확률에 따라 전송지연 대 처리량 곡선을 요구트래픽 파라미터 함수로 구하였으며, 처리량에 따른 전송지연의 상대적인 차이를 비교하였다.

• 한국수학사학회지
• /
• 제30권5호
• /
• pp.289-304
• /
• 2017

The interdisciplinary study explores the discussion of actual infinity between Georg Cantor and Roman Catholic Church. Regarding the actual infinity, we first trace the theological background of Cantor by interpreting his correspondence and major works including ${\ddot{U}}ber$ die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche(1885) and Mitteilungen zur Lehre vom Transfiniten (1887), and then investigate his argumentation for two points at issue: (1) pantheism and (2) inconsistency of the necessity with freedom of God. In terms of mathematics and theology, Cantor defined the actual infinity(aphorismenon) as characterized by (1) the transfinite infinity(Transfinitum) and (2) the absolute infinity(Absolutum). Transfinitum is conceptualized here in mathematical terms as a multipliable actual infinity, whereas Absolutum is not as a multipliable actual infinity. The results imply that Cantor's own concept of Transfinitum and Absolutum is adequate for Roman Catholic theology as well as mathematics including the reflection principle.

• 한국추진공학회:학술대회논문집
• /
• 한국추진공학회 2004년도 제22회 춘계학술대회논문집
• /
• pp.528-531
• /
• 2004

For a simple one-dimensional ignition problem a mathematical model is described to investigate the difficulties in numerical simulations. Some computation results are obtained and comparison is made with analytical solution. Discussions are made on topics such as 1) coordinate transformation, 2) gas-phase and solid-phase analysis; (divergence form of the governing system, a finite-volume discretization, implicit time integration, upwind split flux, spatial accuracy improvement are described. Mass, reagent mass, and energy conservations are solved.), and 3) method to determine quantities on the burning surface (matching). Results obtained for small values of the non-dimensional pressure show a steady-combustion and good agreement with the analytical solution. Numerical instability appeared for larger values of the pressure, discussion on the cause of the problem is made. This effort is a part of a study of flame spread phenomena on solid propellant surface.

• 한국수학사학회지
• /
• 제30권2호
• /
• pp.101-119
• /
• 2017

This paper is a follow up study of [2]. In this paper we analyse the contents of middle school mathematics textbooks published in the 1st National Curriculum Period centered on the concept 'straight line' and discuss how they are different from contemporary mathematics textbooks in view of connectedness of contents, mathematical terms, textbook as a learning material vs. teaching material, relationship between contents of national curriculum and textbooks, and some topics related to direct proportion, function, method of equivalence as a method for solving simultaneous linear equations and so on. The results of our analysis and discussion suggest implications for reforming mathematics curriculum and developing mathematics textbooks.

• International Journal of Advanced Culture Technology
• /
• 제7권3호
• /
• pp.116-119
• /
• 2019

"Science" journal is one of the world's top academic journals. Many researchers are trying to publish their work in Science, and only a few selected novel papers are accepted. However, we think that this kind of process cannot continue forever. In this paper, we show that there is a limit to the number of Science papers that can be written. Therefore, the day will come when Science cannot publish new papers anymore. Using a similar method, we estimate the maximum limit on the number of pop songs that can be composed. By extending our discussion to all kinds of digital contents, we derive a mathematical expression for the maximum number of digital contents of a certain type that can be created. These results imply that someday man will not be able to produce new papers or new digital contents anymore. This conclusion raises deep philosophical questions.

• Korean Journal of Mathematics
• /
• 제29권2호
• /
• pp.371-386
• /
• 2021

This paper investigates two discrete time queueing inventory models with positive service time and lead time. Customers arrive according to a Bernoulli process and service time and lead time follow geometric distributions. The first model under discussion based on replenishment of order upto S policy where as the second model is based on order placement by a fixed quantity Q, where Q = S - s, whenever the inventory level falls to s. We analyse this queueing systems using the matrix geometric method and derive an explicit expression for the stability condition. We obtain the steady-state behaviour of these systems and several system performance measures. The influence of various parameters on the systems performance measures and comparison on the cost analysis are also discussed through numerical example.