• Journal of applied mathematics & informatics
• /
• 제8권3호
• /
• pp.935-942
• /
• 2001

A finite element approximation of a fourth-order nonlinear boundary value problem is given. In the direct implementation, a nonlinear system will be obtained and also a full size matrix will be introduced when Newton’s method is adopted to solve the system. To avoid this difficulty we introduce an iterative scheme which can be shown to converge the positive solution of the system lying between 0 and $sin{\pi}x$.

• 전자공학회논문지A
• /
• 제32A권12호
• /
• pp.209-219
• /
• 1995

As a new algorithm for RC tree delay estimation, we propose a $\tau$-model of the driver and a moment propagation method. The $\tau$-model represents the driver as a Thevenin equivalent circuit which has a one-time-constant voltage source and a linear resistor. The new driver model estimates the input voltage waveform applied to the RC more accurately than the k-factor model or the 2-piece waveform model. Compared with Elmore method, which is a lst-order approximation, the moment propagation method, which uses $\pi$-model loads to calculate the moments of the voltage waveform on each node of RC trees, gives more accurate results by performing higher-order approximations with the same simple tree walking algorithm. In addition, for the instability problem which is common to all the approximation methods using the moment matching technique, we propose a heuristic method which guarantees a stable and accureate 2nd order approximation. The proposed driver model and the moment propagation method give an accureacy close to SPICE results and more than 1000 times speedup over circuit level simulations for RC trees and FPGA interconnects in which the interconnect delay is dominant.

• 한국컴퓨터정보학회논문지
• /
• 제21권9호
• /
• pp.79-84
• /
• 2016

In this paper we consider the problem of finding the triplet (S,${\pi}$,f), where $S{\subseteq}V$, ${\pi}$ is a sequence of nodes in S and $f:V{\backslash}S{\rightarrow}S$ for a given complete graph G=(V,E). In particular, there exist two costs, $c^V_{uv}$ and $c^D_{uv}$ for $(u,v){\in}E$, and the cost of triplet (S,${\pi}$,f) is defined as $\sum_{i=1}^{{\mid}S{\mid}}c^V_{{\pi}(i){\pi}(i+1)}+2$ ${\sum_{u{\in}V{\backslash}S}c^D_{uf(u)}$. This problem is motivated by the integrated routing of the vehicle and drone for urban delivery services. Since a well-known NP-complete TSP (Traveling Salesman Problem) is a special case of our problem, we cannot expect to have any polynomial-time algorithm unless P=NP. Furthermore, for practical purposes, we may not rely on time-exhaustive enumeration method such as branch-and-bound and branch-and-cut. This paper suggests the simple heuristic which is motivated by the MST (minimum spanning tree)-based approximation algorithm and neighborhood search heuristic for TSP.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2001년도 ICCAS
• /
• pp.151.3-151
• /
• 2001

A design of PI controller to be used to control the first-order lag plus dead time process, such as a flow process, by the coefficient diagram method (CDM) is investigated. The factor of the dead time of process is first approximated to be the first-order by the Pade approximation. The response of the flow control system designed by CDM satisfy both transient and steady state specifications. However, the transient response generally still has long rise time. In order to improve the speed of the system response, a feedforward controller (FFC) is added into the PI control system. The structure of the FFC is a phase lead structure with two designed parameters and one derivative time obtained from the reaction curve of the flow process ...

• 보건의료산업학회지
• /
• 제13권4호
• /
• pp.253-263
• /
• 2019

Objectives: This study evaluated the perception on importance of interprofessional core competencies (PI-ICCP) scale. Methods: Data were collected from 353 college students of health. Content validity was tested using the content validity index for individual items(I-CVI) and for scale(S-CVI). Criterion validity was tested using the professional competencies scale developed by Choi. Reliability was evaluated using Cronbach's coefficient alpha. The goodness-of-fit of the construct validity was determined through exploratory and confirmatory factor analyses. Results: The I-CVI of each item was .8 or higher for all items, and the S-CVI was .98. The reliability of the PI-IPCC was Cronbach's α=.98. The goodness-of-fit indices of the model were χ2=1811.54(p<.001), the comparative fit index (CFI)=.91, and root mean square error of approximation (RMSEA)=.08, which satisfied the criteria. Conclusions: The construct and criterion-related validity of the perception for PI-ICCP scale were a good fit, so the instrument is appropriate for measuring perception on importance of interprofessional core competencies. Further research will be required using this instrument to investigate perception of interprofessional core competencies of health professionals.

• 대한화학회지
• /
• 제14권1호
• /
• pp.1-4
• /
• 1970

The methyl group does not possess an unshared pair of electrons. But F.A. Matsen has introduced the concept of the methyl group as a Pseudo-heteroatom which contributes a pair of electrons to ${\pi}$ system. In this heteroatom model, A. Streitwieser et al have assumed that the electrons in a methyl group behave to their approximation as a single electron pair on a single atom. But the theoretical basis on the heteroatom model hyper-conjugation has not studied yet. In this paper, Linear combination of Bond orbital and group theory is used to investigate the theoretical basis for it.

• 한국마린엔지니어링학회:학술대회논문집
• /
• 한국마린엔지니어링학회 2001년도 추계학술대회 논문집(Proceeding of the KOSME 2001 Autumn Annual Meeting)
• /
• pp.112-119
• /
• 2001

Parameter tuning methods by Ziegler-Nickels for control systems are generally classified into Z-N(1) and Z-N(2). The purpose of this paper is to describe what relations exist between methods of Z-N(1) and Z-N(2), or how Z-N(1) method can be originated from Z-N(2) method by analyzing one loop control system of P or PI controller and time delay process. The formulas of Z-N(1) consist of process parameters, L(time delay), $K_m$(gain) and $T_m$(time constant), but Z-N(2) method is based only on the ultimate gain $K_u$ and the ultimate period $T_u$ acquired normally by practical trial without any parameters of Z-N(1). In this paper, for the first step to seek mutual relations, the simple formulas of Z-N(2) are transformed into the formulas composed of the same parameters as Z-N(1) which is derived from the analysis of frequency characteristics. Then, the approximation of the actual ultimate frequency is proposed as important premise in the translation between Z-N(1) and (2). Such equalization and approximation brings a simple approximated formula which can explain how Z-N(1) is originated from the Z-N(2) in the form of formula. And a model system is adopted to compare the approximated formula to Z-N(1) and Z-N(2) methods, the results of which show the effectiveness of the proposals.

• 한국컴퓨터정보학회논문지
• /
• 제16권10호
• /
• pp.101-109
• /
• 2011

리만의 제타함수 $\zeta(s)$는 주어진 수 x보다 작은 소수의 개수 $\pi$(x)를 구하는 해답으로 알려져 있으며, 소수정리에서 지금까지 리만의 제타 함수 이외에 $\frac{x}{lnx}$,Li(x)와 R(x)의 근사치 함수가 제안되었다. 여기서 $\pi$(x)와의 오차는 R(x) < Li(x) < $\frac{x}{lnx}$이다. 로그적분함수 Li(x) = $\int_{2}^{x}\frac{1}{lnt}dt$, ~ $\frac{x}{lnx}\sum\limits_{k=0}^{\infty}\frac{k!}{(lnx)^k}=\frac{x}{lnx}(1+\frac{1!}{(lnx)^1}+\frac{2!}{(lnx)^2}+\cdots)$ 이다. 본 논문은 $\pi$(x)는 유한급수��Li(x)로 표현됨을 보이며, 일반화된 $\sqrt{ax}{\pm}{\beta}$의 소수계량함수를 제안한다. 첫 번째로, $\pi$(x)는 $0{\leq}t{\leq}2k$의 유한급수인 $Li_3(x)=\frac{x}{lnx}(\sum\limits_{t=0}^{{\alpha}}\frac{k!}{(lnx)^k}{\pm}{\beta})$와 $Li_4(x)=\lfloor\frac{x}{lnx}(1+{\alpha}\frac{k!}{(lnx)^k}{\pm}{\beta})\rfloor$, $k\geq2$ 함수로 표현됨을 보였다. $Li_3$(x)는 $\pi(x){\simeq}Li_3(x)$가 되도록 ${\alpha}$ 값을 구하고 오차를 보정하는 ${\beta}$ 값을 갖도록 조정하였다. 이 결과 $x=10^k$에 대해 $Li_3(x)=Li_4(x)=\pi(x)$를 얻었다. 일반화된 함수로 $\pi(x)=\sqrt{{\alpha}x}{\pm}{\beta}$를 제안하였다. 제안된 $\pi(x)=\sqrt{{\alpha}x}{\pm}{\beta}$ 함수는 리만의 제타함수에 비해 소수를 월등히 계량할 수 있었다.

• 한국수학사학회지
• /
• 제19권3호
• /
• pp.95-112
• /
• 2006

본 논문은 고대 수학자이며 발명가인 아르키메데스의 ${\ll}$구와 원기둥에 관하여${\gg}$ 에 대해 고찰한다. 3차원의 공간기하학에 관한 ${\ll}$구와 원기둥에 관하여${\gg}$ 에 제시되어 있는 명제들을 통하여 고대 수학자가 어떻게 입체도형을 수학적으로 정복하였으며 이런 고대 수학적 아이디어가 어떻게 현대의 적분개념으로 발달하게 되었는지를 알아보는 것은 현대 수학에 대한 이해를 깊이 있게 함과 동시에 새로운 수학적 아이디어의 개발에 좋은 소재가 될 것으로 기대한다.

• 대한수학교육학회지:학교수학
• /
• 제18권3호
• /
• pp.647-666
• /
• 2016

본 연구는 수학적 표현이 개념적 이해를 형성하는 수단이라는 관점을 토대로 예비교사들의 무리수 개념과 표현 방식에 대한 이해 정도를 조사하여 무리수 개념 지도를 위한 교수학적 시사점을 도출하고자 하였다. 이에 무리수 개념과 표현, 다양한 표현, 표현간 번역 항목을 조사하는 검사도구를 예비교사 48명을 대상으로 적용하였다. 체계적인 분석을 위해 무리수 표현을 비(非)분수, 소수, 기호, 기하, 수직선, 함숫값 표현으로 범주화하여 활용하였다. 분석 결과, 예비교사들은 무리수 정의의 비(非)분수 표현에 내포된 통약불가능성을 명확하게 인식하지 못하였으며, 무리수의 다양한 표현 중에서 기호 표현에 집중 경향을 나타냈고, 다른 표현들을 상대적으로 간과하는 현상을 나타내었다. 특히 규칙성이 있는 비순환 무한소수에 대한 제한된 이해와 무한소수에 대한 일관성 있는 이해의 결여를 확인할 수 있었다. 또한 기호 표현 $\sqrt{5}$에 비해 ${\pi}$를 다른 표현으로 번역하는데 더 큰 어려움을 나타냈으며, ${\pi}$를 번역하는 과정에서 가무한의 관점이 드러나기도 하였다. 이상의 연구결과를 종합하여 무리수 개념 지도는 무리수 정의와 표현의 관계, 다양한 무리수 표현의 이해, 무리수 표현간의 번역에 중점을 두어 지도되어야 함을 주장하였다.