• Title/Summary/Keyword: closed formulas

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An Analysis of the Student's Algebra Word Problem Solving Process (대수 문장제 해결을 위한 학생들의 풀이 과정 분석: 일련의 표시(Chain of signification) 관점의 사례연구)

  • Park, Hyun-Jeong;Lee, Chong-Hee
    • School Mathematics
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    • v.9 no.1
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    • pp.141-160
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    • 2007
  • The purpose of this paper was to evaluate how students apply prior knowledge or experience in solving algebra word problems from the chain of signification-based perspective. Three middle school students were evaluated in this case study. The results showed that the subjects formed similarities in the process of applying knowledge needed for solving a problem. The student A and C used semi-open-end formulas and closed formulas as solutions. They then formed concrete shape for each solution using the chain of signification that was applied for solution by forming procedural similarity. At this time, the chain of signification could be the combination of numbers, words, and pictures (such as diagrams or graphs) or just numbers or words. On the other hand, the student C who recognized closed formulas and her own rule as a solution method could not formulate completely procedural similarity due to many errors arising from number information. Nonetheless, all of the subjects showed something in common in the process of coming up with a algorithm that was semi-open-end formula or closed formula.

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Closed Form Formulas for Equivalent Damping Ratios of a Linear Structure Equipped with Damping Devices (제진장치가 설치된 구조물의 등가감쇠비)

  • Hwang, Jae-Seung;Lee, Sang-Hyun;Min, Kyung-Won
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2002.10a
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    • pp.370-377
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    • 2002
  • Hwang et al (2001) proposed a new method for an evaluation of equivalent damping ratios of a linear structure with linear or nonlinear damping devices. This procedure has a disadvantage that it requires time history analysis for the whole system including damping devices, which may be troublesome for practical application. To tackle this problem closed form formulas for equivalent damping ratios are proposed in this study. It is assumed that the responses of MDOF system can be reproduced by an equivalent SDOF system which vibrates in a fundamental mode. The numerical analyses of a ten-story building equipped with linear viscous damper or active mass damper or friction damper show the effectiveness of equivalent SDOF model and closed form formulas.

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PRICING OF QUANTO CHAINED OPTIONS

  • Kim, Geonwoo
    • Communications of the Korean Mathematical Society
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    • v.31 no.1
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    • pp.199-207
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    • 2016
  • A chained option is a barrier option activated in the event that the underlying asset price crosses barrier or barriers prior to maturity in a specified order. In this paper, we study the pricing of chained options with the quanto property called the "Quanto chained option". A quanto chained option is a chained option starting at time when the foreign exchange rate has the multiple crossing of specified barriers. We provide closed-form formulas for valuing the quanto chained options based on probabilistic approach.

Efficient Design of 2-D FIR Fan Filters Using Formulas for MaClellan Transform Parameters (새로운 맥클레란변환 계수 공식을 이용한 2차원 Fan 유한응답여파기의 효율적 설계)

  • 송영석;이용훈
    • Proceedings of the Korean Society of Broadcast Engineers Conference
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    • 1995.06a
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    • pp.155-157
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    • 1995
  • New formulas for McClellan transform parameters for the design of 2-D Zero-phase FIR fan filters are optimally derived under the integral squared error(ISE) criterion. By imposing the constraint that F(0,0)=coswc, where F($.$) is the McClellan transform and w is the cutoff frequency of the 1-D prototype filter, the ISE is directly minimized without modifying it and, as a consequence, closed-form formulas for the McClellan transform parameters are obtained. It is shows that these formulas lead to a very efficient design for 2-D zero-phase FIR fan filters.

Efficient Design of 2-D FIR Fan Filters Using New Formulas for McClellan Transform Parameters

  • Song, Young-Seog;Lee, Yong-Hoon
    • Journal of Electrical Engineering and information Science
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    • v.1 no.1
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    • pp.160-163
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    • 1996
  • New formulas for McClellan transform parameters for the design of 2-D zero-phase FIR fan filters are optimally derived under the integral squared error(ISE) criterion. By imposing the constraint that F(0, 0)=\ulcorner, where F($.$) is the McClellan transform and $\omega$\ulcorner is the cutoff frequency of the 1-D prototype filter, the ISE is directly minimized without modifying it and, as a consequence, closed-form formulas for the McClellan transform parameters are obtained. It is shown that these formulas lead to a very efficient design for 2-D zero-phase FIR fan filters.

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Closed-form optimum tuning formulas for passive Tuned Mass Dampers under benchmark excitations

  • Salvi, Jonathan;Rizzi, Egidio
    • Smart Structures and Systems
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    • v.17 no.2
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    • pp.231-256
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    • 2016
  • This study concerns the derivation of optimum tuning formulas for a passive Tuned Mass Damper (TMD) device, for the case of benchmark ideal excitations acting on a single-degree-of-freedom (SDOF) damped primary structure. The free TMD parameters are tuned first through a non-linear gradient-based optimisation algorithm, for the case of harmonic or white noise excitations, acting either as force on the SDOF primary structure or as base acceleration. The achieved optimum TMD parameters are successively interpolated according to appropriate analytical fitting proposals, by non-linear least squares, in order to produce simple and effective TMD tuning formulas. In particular, two fitting models are presented. The main proposal is composed of a simple polynomial relationship, refined within the fitting process, and constitutes the optimum choice. A second model refers to proper modifications of literature formulas for the case of an undamped primary structure. The results in terms of final (interpolated) optimum TMD parameters and of device effectiveness in reducing the structural dynamic response are finally displayed and discussed in detail, showing the wide and ready-to-use validity of the proposed optimisation procedure and achieved tuning formulas. Several post-tuning trials have been carried out as well on SDOF and MDOF shear-type frame buildings, by confirming the effective benefit provided by the proposed optimum TMD.

TWISTED QUADRATIC MOMENTS FOR DIRICHLET L-FUNCTIONS

  • LOUBOUTIN, STEPHANE R.
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.6
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    • pp.2095-2105
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    • 2015
  • Given c, a positive integer, we set. $$M(f,c):=\frac{2}{{\phi}(f)}\sum_{{\chi}{\in}X^-_f}{\chi}(c)|L(1,{\chi})|^2$$, where $X^-_f$ is the set of the $\phi$(f)/2 odd Dirichlet characters mod f > 2, with gcd(f, c) = 1. We point out several mistakes in recently published papers and we give explicit closed formulas for the f's such that their prime divisors are all equal to ${\pm}1$ modulo c. As a Corollary, we obtain closed formulas for M(f, c) for c $\in$ {1, 2, 3, 4, 5, 6, 8, 10}. We also discuss the case of twisted quadratic moments for primitive characters.

Evaluation of the Equivalent First Modal Damping Ratio of a Structure with Additional Damping Devices (부가감쇠 장치가 설치된 구조물의 1차 모드 등가 감쇠비 산정)

  • Lee, Sang-Hyun;Min, Kyung-Won;Hwang, Jae-Seung;Lee, Young-Cheol
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2002.10a
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    • pp.459-466
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    • 2002
  • The purpose of this study is to propose a new method for evaluating equivalent damping ratios of a structure with supplemental damping devices to assess their control effect quantitatively. A MDOF system is transformed to an equivalent SDOF system based on the assumption that the first mode dominates structural response. Approximate closed-form formulas for the evaluation of the first damping ratio are presented for various damping devices. Through numerical analysis of a ten-story building equipped with damping devices, the effectiveness of equivalent SDOF model and closed form formulas are verified.

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Geometrical Construction of the S Matrix and Multichannel Quantum Defect Theory for the two Open and One Closed Channel System

  • Lee, Chun-Woo
    • Bulletin of the Korean Chemical Society
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    • v.23 no.7
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    • pp.971-984
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    • 2002
  • The multichannel quantum defect theory (MQDT) is reformulated into the form of the configuration mixing (CM) method using the geometrical construction of the S matrix developed for the system involving two open and one closed channels. The reformulation is done by the phase renormalization method of Giusti-Suzor and Fano. The rather unconventional short-range reactance matrix K whose diagonal elements are not zero is obtained though the Lu-Fano plot becomes symmetrical. The reformulation of MQDT yields the partial cross section formulas analogous to Fano's resonance formula, which has not easily been available in other's work.

EXPONENTIALLY FITTED INTERPOLATION FORMULAS INVOLVING FIRST AND HIGHER-ORDER DERIVATIVES

  • Kim, Kyung Joong
    • Journal of applied mathematics & informatics
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    • v.31 no.5_6
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    • pp.677-693
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    • 2013
  • We construct exponentially fitted interpolation formulas using the values of the ${\omega}$-dependent function $f$ as well as its derivatives up to the $n$th order at a finite number of nodes on a closed interval ${\Omega}$. The function $f$ is of the form, $$f(x)=f_1(x)cos({\omega}x)+f_2(x)sin({\omega}x),x{\in}{\Omega}$$, where $f_1$ and $f_2$ are smooth enough to be approximated by polynomials on ${\Omega}$. Some properties of the formulas are newly found. The properties are numerically investigated and reexamined by producing some figures.