• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.10
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• pp.188-198
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• 2013

Maximally flat (MAXFLAT) half-band filters usually have wider transition band than other filters. This is due to the fact that the maximum possible number of zeros at $z={\pm}1$ is imposed, which leaves no degree of freedom, and thus no independent parameters for direct control of the frequency response. This paper describes a novel method for the design of FIR halfband filters with an explicit control of the transition-band width. The proposed method is based on a generalized Lagrange halfband polynomial (g-LHBP) with coefficients parametizing a 0-th coefficient $h_0$, and allows the frequency response of this filter type to be controllable by adjusting $h_0$. Then, $h_0$ is modeled as a steepness parameter of the transition band and this is accomplished through theoretically analyzing a polynomial recurrence relation of the g-LHBP. This method also provides explicit formulas for direct computation of design parameters related to choosing a desired filter characteristic (by trade-off between the transition-band sharpness and passband & stopband flatness). The examples are shown to provide a complete and accurate solution for the design of such filters with relatively sharper transition-band steepness than MAXFLAT half-band filters.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.3
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• pp.83-97
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• 1995

The aim of this study is to derive a simple formula for predicting ultimate strength of hull girders under vertical bending moment. The existing formulas have been reviewed and classified into analytical approach, empirical approach and linear approximate approach. It is known that the ship hull will reach the ultimate limit state if both collapse of the compression flange and yielding of the tension flange occur. Side shells in the vicinity of the compression and tension flanges will often fail also, but the material around the final neutral axis will remain in the elastic state. Based on this observation, a credible distribution of longitudinal stresses around the hull section at the overall collapse state is assumed, and an explicit analytical formula is derived. The accuracy of the formula has been verified by a comparison of the experimental and the numerical results.

• Journal of the Society of Naval Architects of Korea
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• v.42 no.6 s.144
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• pp.644-653
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• 2005

In general the loads due to ocean wave are considered as main design parameters governing the global structural safety of VLFS (Very Large Floating Structure). In order to predict design wave loads accurately, hydro-elastic analysis must be conducted considering the initial global flexural rigidity of VLFS. However, in order to determine the structural scantling of major members (deck, bottom, side panels and longitudinal / transverse BHD etc.), static load and design wave loads must be given as explicit form generally. Therefore in order to determine a proper structural arrangement and scantlings of VLFS at initial design stage, both calculations of structural scantling and hydro-elastic analysis for wave conditions must be conducted iteratively and the convergence of their results must be checked. On this paper, based on the case design of a 500×300 m size's floating marina resort, the details of structural design technique using hydro-elastic analysis are explained and discussed. At first, the environmental conditions and the system requirements of the design of marina resort are described. The scantling formulas for the major members of pontoon type VLFS are proposed from the local and global design points of view. Considering the design wave loads as well as static design loads, the structural safety is checked iteratively.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.619-636
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• 2012

The main purpose of this study was to explore the process of generalization generated by mathematically gifted students. Specifically, this study probed how fourth, fifth, and sixth graders might generalize geometric patterns and represent such generalization. The subjects of this study were a total of 30 students from gifted classes of one elementary school in Korea. The results of this study showed that on the question of the launch stage, students used a lot of recursive strategies that built mainly on a few specific numbers in the given pattern in order to decide the number of successive differences. On the question of the towards a working generalization stage, however, upper graders tend to use a contextual strategy of looking for a pattern or making an equation based on the given information. The more difficult task, more students used recursive strategies or concrete strategies such as drawing or skip-counting. On the question of the towards an explicit generalization stage, students tended to describe patterns linguistically. However, upper graders used more frequently algebraic representations (symbols or formulas) than lower graders did. This tendency was consistent with regard to the question of the towards a justification stage. This result implies that mathematically gifted students use similar strategies in the process of generalizing a geometric pattern but upper graders prefer to use algebraic representations to demonstrate their thinking process more concisely. As this study examines the strategies students use to generalize a geometric pattern, it can provoke discussion on what kinds of prompts may be useful to promote a generalization ability of gifted students and what sorts of teaching strategies are possible to move from linguistic representations to algebraic representations.

• Tunnel and Underground Space
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• v.34 no.4
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• pp.355-373
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• 2024

The Generalized Hoek-Brown (GHB) criterion is a nonlinear failure criterion specialized for rock engineering applications and has recently seen increased usage. However, the GHB criterion expresses the relationship between minimum and maximum principal stresses at failure, and when GSI≠100, it has disadvantage of being difficult to express as an explicit relationship between the normal and shear stresses acting on the failure plane, i.e., as a Mohr failure envelope. This disadvantage makes it challenging to apply the GHB criterion in numerical analysis techniques such as limit equilibrium analysis, upper-bound limit analysis, and the critical plane approach. Consequently, recent studies have attempted to express the GHB Mohr failure envelope as an approximate analytical formula, and there is still a need for continued interest in related research. This study presents improved formulations for the approximate GHB Mohr failure envelope, offering higher accuracy in predicting shear strength compared to existing formulas. The improved formulation process employs a method to enhance the approximation accuracy of the tangential friction angle and utilizes the tangent line equation of the nonlinear GHB failure envelope to improve the accuracy of shear strength approximation. In the latter part of this paper, the advantages and limitations of the proposed approximate GHB failure envelopes in terms of shear strength prediction accuracy and calculation time are discussed.