• Geomechanics and Engineering
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• v.24 no.2
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• pp.167-178
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• 2021

Spatial variability is an inherent uncertainty of soil properties. Current reliability analyses generally incorporate random field theory and Monte Carlo simulation (MCS) when dealing with spatial variability, in which the computational efficiency is a significant challenge. This paper proposes a KL-FORM algorithm to improve the computational efficiency. In the proposed KL-FORM, Karhunen-Loeve (KL) expansion is used for discretizing random fields, and first-order reliability method (FORM) is employed for reliability analysis. The KL expansion and FORM can be used in conjunction, through adopting independent standard normal variables in the discretization of KL expansion as the basic variables in the FORM. To illustrate the effectiveness of this KL-FORM, it is applied to a case study of a strip footing in spatially variable unsaturated soil under rainfall, in which the bearing capacity of the footing is computed by numerical simulation. This case study shows that the KL-FORM is accurate and efficient. The parametric analyses suggest that ignoring the spatial variability of the soil may lead to an underestimation of the reliability index of the footing.

• Korean Journal of Computational Design and Engineering
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• v.5 no.3
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• pp.276-284
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• 2000

Usual practice of the transformation of a B-spline curve into a set of piecewise polynomial curves in a power form is done by either a knot refinement followed by basis conversions or applying a Taylor expansion on the B-spline curve for each knot span. Presented in this paper is a new algorithm, called a direct expansion algorithm, for the problem. The algorithm first locates the coefficients of all the linear terms that make up the basis functions in a knot span, and then the algorithm directly obtains the power form representation of basis functions by expanding the summation of products of appropriate linear terms. Then, a polynomial segment of a knot span can be easily obtained by the summation of products of the basis functions within the knot span with corresponding control points. Repeating this operation for each knot span, all of the polynomials of the B-spline curve can be transformed into a power form. The algorithm has been applied to both static and dynamic curves. It turns out that the proposed algorithm outperforms the existing algorithms for the conversion for both types of curves. Especially, the proposed algorithm shows significantly fast performance for the dynamic curves.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.229-234
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• 2009

We find congruences for the t-expansion coefficients of a Drinfeld modular form for ${\Gamma}^+_0$(Q), where Q is a monic irreducible polynomial. As an application we obtain new congruence relations for the t-expansion coefficients of Drinfeld modular forms for ${GL_2}(\mathbb{F}_q[T])$.

• Journal of the Korean Society for Precision Engineering
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• v.33 no.9
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• pp.745-751
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• 2016

This paper presents the acceleration and deceleration control of free-form surfaces. A rapid variation of acceleration (or Deceleration) drives the system into a machine shock, resulting in the inaccuracy of the path control of the NURBS curve. The pattern of acceleration control can be established using the curvature of the NURBS curve. The curvature can be easily calculated from the first and second derivative of the NURBS curve used in Taylor's expansion for NURBS interpolation. However, the derivatives are not used in the recursive method for NURBS interpolation. Hence, we attempted the difference-derivatives for calculating the NURBS curvature. Both, Taylor's expansion and the recursive method, are used jointly for controlling the acceleration in the same interpolation algorithm.

• The Korean Journal of Ecology
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• v.17 no.1
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• pp.37-47
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• 1994

A study was conducted to examine the leaf expansion forms and to analyze the leaf growth in early growing season of 1992 in a temperate deciduous forest in central region of Korea. After the winter bud scale fell off, the expansion forms of 11 woody species were divided into 3 groups, spreading fan form, opening form from half folding, and unrolling form from main vein. The ratios of leaf area at the end of growing season to that of leaf expantion time varied among species, and were related closely to expansion forms. The leaves reached to full size between the third ten days of April and the middle ten days of May, except for a few species. Leaf weight, however, increased steadily during the growing season. Specific leaf area (SLA) increased rapidly for 10-20 days after leaf expansion and decreased rapidly for 10 days after reaching maximum values, and thereafter decreased slowly. The SLA values of trees were smaller than $200cm^2/g$, but those of subtree and shrub were larger than $200cm^2/g$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1047-1057
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• 2015

In [6], it is proved that the lengths of periods occurring in the ${\beta}$-expansion of a rational series r noted by $Per_{\beta}(r)$ depend only on the denominator of the reduced form of r for quadratic Pisot unit series. In this paper, we will show first that every rational r in the unit disk has strictly periodic ${\beta}$-expansion for Pisot or Salem unit basis under some condition. Second, for this basis, if $r=\frac{P}{Q}$ is written in reduced form with |P| < |Q|, we will generalize the curious property "$Per_{\beta}(\frac{P}{Q})=Per_{\beta}(\frac{1}{Q})$".

• Journal of the Korean Ceramic Society
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• v.37 no.6
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• pp.576-582
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• 2000

Two type of expanding cement generally referred to as CSA with Hauyne(3CaO 3Al2O3 CaSO4) and Quick lime(CaO). Hauyne is formed to ettringite when there are presented with CaO and CaSO4, and CaO reacts wtih water to form Ca(OH)2. REcently, the mechanism of compensation and expand mortar or concrete tend to same and it has been used improving on its shrink property. The volume of cement paste varies with its water content shrink with drying and re-wetting. Concrete and mortar works are required shrinking compensation and expansion properties to reduce of potential crack. The use of expansion cement may improve on its shrinking volume changes. CSA dosages for shrinking compensation limited by cement weight, but obtained difference expansion rate with varied W/C or inorganic admixture. This paper studies expansion rate according to expansion cement dosages, water and inorganic admixtures as Silica fume. Therefor, the expansion factor has to considered before the application.

• Korean Journal of Mathematics
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• v.31 no.2
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• pp.189-201
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• 2023

In this article, we establish Hilbert-type integral inequalities with the help of a non-homogeneous kernel of hyperbolic function with best constant factor. We also study the obtained inequalities's equivalent form. Additionaly, several specific Hilbert's type inequalities with constant factors in the term of the rational fraction expansion of higher order derivatives of cotangent and cosine functions are presented.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.5 s.248
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• pp.528-532
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• 2006

In the aerospace industry, Cold expansion has been used the most important method that is retarded of crack initiation from fastener hole surface. Cold expansion method(CEM) is that a oversized tapered mandrel goes through the hole in order to develop a compressive residual stress as the passing of the mandrel around the hole. Therefore, because of characteristic of mandrel inserting, Residual Stress Distributions (RSD) are differently generated form Entry, Mid and Exit position of the plate. Also, it is respected that RSD are changed as distances between holes. In this paper, It is performed a FE analysis of RSD by CEM and it is respectively shown RSD in the Entry, Mid and Exit position. It is compared residual stress results form the cold expansion in these two cases: the concurrent CEM and the sequential CEM. From this research, it has been found that compressive residual stress of Entry position is lower than other positions. Also, the concurrent CE of adjacent holes leads to much higher compressive residual stress than the sequential CE. In addition, in the sequential CE case, a compressive RSD of 1 step's hole around is lower than compressive RSD of 2 step's hole around.

• Journal of the Korean Ceramic Society
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• v.23 no.4
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• pp.41-46
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• 1986

When barium titanate was synthesized in solid-solid reaction the abnormal expansion occurred from 90$0^{\circ}C$ to 110$0^{\circ}C$. The equi molecular mixture of $BaCo_3$ and $TiO_2$ was sintered from 90$0^{\circ}C$ to 130$0^{\circ}C$ on the condition of air vacuum and $CO_2$ atomosphere. After that the specimens were tested closely with XDR Dilatometer and SEM The result indicated that: 1, Volume expansion to be synthesized barium titanate in solid-solid reaction was affected by atomosphere sintering. 2. The solid reaction ot fiorm barium titanate in vacuum atomosphere occurred faster than that in air atomosphere. In vacuum atomosphere the maxium volume expansion was about 30% at 90$0^{\circ}C$ for 2hrs, 3. The solid reaction to form barium titanate in 4CO_2$ atomosphere occurred slower than that in air atomosphere. In $CO_2$ atomosphere the maximum volume expansion was 13% at 100$0^{\circ}C$ for 2 hrs. 4. According to the result of x-ray the expanison was caused by the reaction to form $BaTiO_3$ and change $Ba_2TiO_4$ into 4BaTiO_3$.