• East Asian mathematical journal
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• v.36 no.3
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• pp.425-435
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• 2020

We explore the Pauli table C^(-1) and nonzero Pauli table W. Recurrence rules and interrelationships of any k slope diagonal sums over C^(-1) and W are studied in connection with diagonal sums of the Pascal table C⁽¹⁾. Since diagonal sums of C⁽¹⁾ are Fibonacci numbers, any k slope diagonal sums over C^(-1) and W are explained by Fibonacci numbers.

• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.323-332
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• 2007

We present a new type of portmanteau test in the frequency domain which is derived from the discrete cosine transform(DCT). For the stationary time series, DCT coefficients are asymptotically independent and their variances are expressed by linear combinations of autocovariances. The covariance matrix of DCT coefficients for white noises is diagonal matrix whose diagonal elements is the variance of time series. A simple way to test the independence of time series is that we divide DCT coefficients into two or three parts and then compare sample variances. We also do this by testing the slope in the linear regression model of which the response variables are absolute values or squares of coefficients. Simulation results show that the proposed tests has much higher powers than Ljung-Box test in most cases of our experiments.

• The Journal of the Petrological Society of Korea
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• v.19 no.4
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• pp.283-292
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• 2010

The Suljeongri east three-story stone pagoda in Changnyeong (National Treasure No. 34) has been damaged mainly by lots of cracks. The stones used for this pagoda are medium-granied equigranular pinkish biotite granite. Measured magnetic susceptibility values are of from 2 to 9 (${\times}10^{-3}$ SI unit). From the ${\gamma}$-ray spectrometer mesurement K, eU, and eTh contents of the stones are 3 to 7%, 8 to 19 ppm, and 11 to 35 ppm, respectively. Comparing the petrographical and chemical characteristics between the stones of the pagoda and the country rocks near Suljeongri, it is suggested that the most similar rock could be equigranular biotite granite in the western slope of the Mt. Hwawangsan. Vertical, horizontal and diagonal cracks are intensely developed at the lower part of the stone pagoda. Biotite granite has intrinsic microcracks defined as rift and grain rock cleavages. Both rock cleavages are assumed to have led to the crack growth and consequent mechanical damage of the pagoda. It seems that vertical cracks have been grown parallel to the principal compressional stress, and that horizontal cracks to the reacting tensional stress. Diagonal cracks seems likely to have been resulted from conjugate rift and grain rock cleavages.

• Fashion & Textile Research Journal
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• v.6 no.1
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• pp.17-22
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• 2004

The purpose of this study was to obtain the basic element of patterns, which is the motif, from the existing art works and use it to create and simulate a variety of patterns to show the practical use of the computer. Natural dyed works of geometric shapes like squares and 1/4 of circles, each dyed with a different natural dyes, were produced and motifs were extracted. Then using the 4D box in Adobe Photoshop v.6.0, the developing pattern change and simulation effects when using different patterns and different repetition settings were examined. Observations were made as the motifs were replicated. Different patterns like a diagonal line, a square and a circle appeared. In order to find out the effects according to the changes, the motifs from work's square portions, circle centre, and the composition of eight motifs were extracted and used. The repeated patterns according to the extracted motifs simply showed that in the case of just repeating and arranging, square patterns appeared. By replicating and arranging, the motif and the allophone were matched and patterns with regular lines were formed, like a twill, pointed twill line. By setting the direction to Y and X in the repetition methodes, a typical half-drop arrangement or a brick pattern arrangement were formed according to 1/4, 2/4, 3/4, 1/3, or 2/3 in changes. Also the steepness of the slope changes quickly or in turn slowly as the rhombus shape appears. However in the case of a composed motif, an ogee pattern appeared. Lastly, by 3-D mapping patterns like a slant line, pointed twill patterns, diamond patterns, and the repeat patterns of a motif with a circle and a line combined, and a circle motif, an optical illusion could be observed.

• Structural Engineering and Mechanics
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• v.5 no.5
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• pp.507-521
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• 1997

The ultimate behavior of a reinforced concrete hyperbolic paraboloid saddle shell under uniformly distributed vertical load is investigated using an inelastic, large displacement finite-element program originally developed at North Carolina State University. Unlike with the author's previous study which shows that the saddle shell possesses a tremendous capacity to redistribute the stresses, introducing tension stiffening in the model the cracks developed are no longer through cracks and formed as primarily bending cracks. Even though with small tension stiffening effect, the behavior of the shell is changed markedly from the one without tension stiffening effect. The load-deflection curves are straight and the slope of the curves is quite steep and remains unchanged with varying the tension stiffening parameters. The failure of the shell took place quite suddenly in a cantilever mode initiated by a formation of yield lines in a direction parallel to the support-to-support diagonal. The higher the tension stiffening parameters the higher is the ultimate load. The present study shows that the ultimate behavior of the shell primarily depends on the concrete tensile characteristics, such as tensile strength (before cracking) and the effective tension stiffening (after cracking). As the concrete characteristics would vary over the life of the shell, a degree of uncertainty is involved in deciding a specified ultimate strength of the saddle shell studied. By the present study, however, the overload factors based on ACI 318-95 are larger than unity for all the cases studied except that the tension stiffening parameter is weak by 3 with and without the large displacement effect, which shows that the Lin-Scordelis saddle shell studied here is at least safe.