• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.04a
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• pp.19-26
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• 1997

In this paper, two dimensional analytical infinite elements which can include multiple wave components to model a underlying half-space are developed. Since these elements are expressed clearly and simply using Legendre polynomials of frequencies in frequency domain, these are very economical and efficient in computing the responses of strip foundations in frequency domain and are easily transformed for SSI analysis in time domain. To prove the behavior of the proposed two dimensional analytical infinite elements, vertical, horizontal, and rocking compliances of a rigid strip foundation in layered soils are analyzed and compared with those of Tzong ' Penzie $n^{(17)}$ and with those which calculated by numerical infinite elemen $t^{(1)}$ in frequency domain, and good agreements are noticed between them. As an application for a further study, a new scheme for SSI analysis in time domain are proposed and verified by comparing the displacement responses of the soil with a underlying rock due to a rectangular impulse loading with those of a soil modeled extended FE meshes.soil modeled extended FE meshes.

• Proceedings of the Korea Society for Simulation Conference
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• 1992.10a
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• pp.7-7
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• 1992

Extending discrete event modelling formalisms to facilitate greater symbol manipulation capabilities is important to further their use in intelligent control and design of high autonomy systems. This paper defines an extension to the DEVS formalism that facilitates symbolic expression of discrete event times by extending the time base from the real numbers to the field of linear polynomials over the reals. A simulation algorithm is developed to generate the branching trajectories resulting from the underlying non-determinism. To efficiently manage linear polynomial constraints based on feasibility checking algorithm borrowed from linear programming. The extended formalism offers a convenient means to conduct multiple, simultaneous explorations of model behaviors. Examples of application are given with consideration on fault model analysis.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.825-831
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• 2021

The derivative of a polynomial p(z) of degree n, with respect to point α is defined by D_αp(z) = np(z) + (α - z)p'(z). Let p(z) be a polynomial having all its zeros in the unit disk |z| ≤ 1. The Sendov conjecture asserts that if all the zeros of a polynomial p(z) lie in the closed unit disk, then there must be a zero of p'(z) within unit distance of each zero. In this paper, we obtain certain results concerning the location of the zeros of D_αp(z) with respect to a specific zero of p(z) and a stronger result than Sendov conjecture is obtained. Further, a result is obtained for zeros of higher derivatives of polynomials having multiple roots.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.3
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• pp.267-275
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• 2009

This paper presents the p-convergent coupling element on the basis of the ESSE(equivalent single layer shell element) and the PLLE(partial-linear layerwise element) to analyze laminated composite plates. The ESSE is formulated by the degenerated shell theory, on the other hand, the assumption of the PLLE is piecewise linear variation of the in-plane displacement and a constant value of lateral displacement across the thickness. The proposed finite element model is based on p-convergence approach. The integrals of Legendre polynomials and Gauss-Lobatto technique are chosen to interpolate displacement fields and to implement numerical quadrature, respectively. This study has been focused on the verification of p-convergent element. For this purpose, various finite element multiple models associated with the combination of ESSE and PLLE elements are tested to show numerical stability. The simple examples such as a cantilever beam subjected vertical load and a plate with tension are adopted to evaluate the performance of proposed element.

• The KIPS Transactions:PartA
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• v.11A no.2
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• pp.115-122
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• 2004

In this paper, the multiple-valued adders and multipliers are implemented by current-mode CMOS. First, we implement the 3-valued T-gate and the 4-valued T-gate using current-mode CMOS which have an effective availability of integrated circuit design. Second we implement the circuits to be realized 2-variable 3-valued addition table and multiplication table over finite fields $GF(3^2)$, and 2-variable 4-valued addition table and multiplication table over finite fields $GF(4^2)$ with the multiple-valued T-gates. Finally, these operation circuits are simulated under $1.5\mutextrm{m}$ CMOS standard technology, $15\mutextrm{A}$ unit current, and 3.3V VDD voltage Spice. The simulation results have shown the satisfying current characteristics. The 3-valued adder and multiplier, and the 4-valued adder and multiplier implemented by current-mode CMOS is simple and regular for wire routing and possesses the property of modularity with cell array. Also, since it is expansible for the addition and multiplication of two polynomials in the finite field with very large m, it is suitable for VLSI implementation.

• Journal of the Korean Mathematical Society
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• v.8 no.1
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• pp.25-30
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• 1971

Put ($$^*$$) $$G[x,y]={\sum}\limits^{p+q=n}_{p,q=0}[-n]_{p+q}c_{p,q}x^py^q$$, where $[{\lambda}]_m$ is the Pocbhammer symbol and the $c_{p,q}$ are arbitrary constants. Making use of the specialized forms of some of his earlier results (see [8] and [9] the author derives here bilateral generating functions of the type ($$^{**}$$) $${\sum}\limits^{\infty}_{n=0}{\frac{[\lambda]_n}{n!}}_2F_1[\array{{\rho}-n,\;{\alpha};\\{\lambda}+{\rho};}x]\;G[y,z]t^n$$ where ${\alpha}$, ${\rho}$ and ${\lambda}$ are arbitrary complex numbers. In particular, it is shown that when G[y, z] is a double hypergeometric polynomial, the right-band member of ($^{**}$) belongs to a class of general triple hypergeometric functions introduced by the author [7]. An interesting special case of ($^{**}$) when ${\rho}=-m,\;m$ being a nonnegative integer, yields a class of bilateral generating functions for the Jacobi polynomials $\{P_n{^{{\alpha},{\beta}}}(x)\}$ in the form ($$^{***}$$) $${\sum\limits^{\infty}_{n=0}}\(\array{m+n\\n}\)P{^{({\alpha}-n,{\beta}-n)}_{m+n}(x)\;G[y,z]{\frac{t^n}{n!}}$$, which provides a unification of several known results. Further extensions of ($^{**}$) and ($^{***}$) with G[y, z] replaced by an analogous multiple sum $H\[y_1,{\cdots},y_m\]$ are also discussed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.10
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• pp.2150-2158
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• 2002

A recent research and development has the requirement for the optimization to shorten design time of modified or new product model and to obtain more precise engineering solution. General optimization problem must consider many conflicted objective functions simultaneously. Multi-objective optimization treats the multiple objective functions and constraints with design change. But, real engineering problem doesn't describe accurate constraint and objective function owing to the limit of representation. Therefore this study applies variance analysis on the basis of structure analysis and DOE to the vertical roller mill fur portland cement and proposed statistical design model to evaluate the effect of structural modification with design change by performing practical multi-objective optimization considering mass, stress and deflection.

• Journal of the Optical Society of Korea
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• v.10 no.3
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• pp.124-129
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• 2006

We have developed a compact and cost-effective camera module on the basis of wafer-scale-replica processing. A multiple-layered structure of several aspheric lenses in a mobile-phone camera module is first assembled by bonding multiple glass-wafers on which 2-dimensional replica arrays of identical aspheric lenses are UV-embossed, followed by dicing the stacked wafers and packaging them with image sensor chips. This wafer-scale processing leads to at least 95% yield in mass-production, and potentially to a very slim phone with camera-module less than 2 mm in thickness. We have demonstrated a VGA camera module fabricated by the wafer-scale-replica processing with various UV-curable polymers having refractive indices between 1.4 and 1.6, and with three different glass-wafers of which both surfaces are embossed as aspheric lenses having $230{\mu}m$ sag-height and aspheric-coefficients of lens polynomials up to tenth-order. We have found that precise compensation in material shrinkage of the polymer materials is one of the most technical challenges, in orderto achieve a higher resolution in wafer-scaled lenses for mobile-phone camera modules.

• Asian-Australasian Journal of Animal Sciences
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• v.31 no.10
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• pp.1542-1549
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• 2018

Objective: Because lactation periods in dairy cows lengthen with increasing total milk production, it is important to predict individual productivities after 305 days in milk (DIM) to determine the optimal lactation period. We therefore examined whether the random regression (RR) coefficient from 306 to 450 DIM (M2) can be predicted from those during the first 305 DIM (M1) by using a RR model. Methods: We analyzed test-day milk records from 85,690 Holstein cows in their first lactations and 131,727 cows in their later (second to fifth) lactations. Data in M1 and M2 were analyzed separately by using different single-trait RR animal models. We then performed a multiple regression analysis of the RR coefficients of M2 on those of M1 during the first and later lactations. Results: The first-order Legendre polynomials were practical covariates of RR for the milk yields of M2. All RR coefficients for the additive genetic (AG) effect and the intercept for the permanent environmental (PE) effect of M2 had moderate to strong correlations with the intercept for the AG effect of M1. The coefficients of determination for multiple regression of the combined intercepts for the AG and PE effects of M2 on the coefficients for the AG effect of M1 were moderate to high. The daily milk yields of M2 predicted by using the RR coefficients for the AG effect of M1 were highly correlated with those obtained by using the coefficients of M2. Conclusion: Milk production after 305 DIM can be predicted by using the RR coefficient estimates of the AG effect during the first 305 DIM.

• Korean Journal of Weed Science
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• v.4 no.1
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• pp.88-95
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• 1984

The study was intended to analyze the interaction effects of paraquat and oxytluorfen as an orchard herbicide-mixture. Data were prepared from the former report of authors. The algebraic expression for the actions of paraquat and oxyfluorfen on the control percentages of peach orchard weeds, and their interactions were determined from the multiple regression polynomial and plotted in three-dimensional graphs. As a result of treatments by combination of paraquat and oxyfluorfen on the field which was dominated by perennial weeds, the most effective interactions were detected at combination rates of $245\;gHa^{-1}$ paraquat and $470-705\;gHa^{-1}$ oxyfluorfen. However, to develope the long-term weeding-efficacies, the combination rates of paraquat are expected to raise up to $500-700\;gHa^{-1}$, and oxyfluorfen to fit at lower limits of rates, respectively.