• School Mathematics
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• v.4 no.3
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• pp.361-373
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• 2002

In this paper, a series of tasks related on polygonal numbers and pyramidal numbers are suggested for using them as teaching unit materials for teaching and learning of sequences in junior high school mathematics. Especially, finding n-th term in those seque-nces, relations among polygonal numbers, and relations among Pyramidal numbers are focused on. A series of tasks related on polygonal numbers and pyramidal numbers have three math-eucational values. First, they have a value as natural materials for teaching and teaming of finding nth term of original sequences using pro-gression of differences. Second, they have a value as materials for teaching and learning of mathematical thinking such as general-ization, analogy, etc. Third, they have a value as materials for teaching and learning of algebraic operation, proof, and connecting mathematical knowledges.

• School Mathematics
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• v.12 no.4
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• pp.619-638
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• 2010

In this paper, we listed and reviewed some properties on polygonal numbers, pyramidal numbers and Pascal's triangle, and Fibonacci sequence. We discussed that the properties of gnomonic numbers, polygonal numbers and pyramidal numbers are explained integratively by introducing the generalized k-dimensional pyramidal numbers. And we also discussed that the properties of those numbers and relationships among generalized k-dimensional pyramidal numbers, Pascal's triangle and Fibonacci sequence are suitable for teaching and learning of mathematical reasoning and connections.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.599-613
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• 2018

We study a generalization of the classical Pentagonal Number Theorem and its applications. We derive new identities for certain infinite series, recurrence relations and convolution sums for certain restricted partitions and divisor sums. We also derive new identities for Bell polynomials.

• Journal of the Korean Society for Heat Treatment
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• v.17 no.2
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• pp.78-86
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• 2004

Effects of the annealing parameters on the formation of ferrites transformed at low temperatures were studied in cold-rolled ultra low carbon steels with niobium and/or chromium. Niobium and chromium were found to be effective in the formation of the low temperature transformation ferrites. The low temperature transformation ferrites more easily formed when both higher annealing temperature and longer annealing time, allowing substitutional alloying elements to distribute between phases, are in combination with faster cooling rate. It was found from EBSD study that the additions of niobium or chromium resulted in the increase in the numbers of high angle grain boundaries and the decrease in those of the low angle grain boundaries in the microstructures. Both granular bainitic ferrite and bainitic ferrite were characterized by the not clearly etched grain boundaries in light microscopy because of the low angle grain boundaries.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.837-847
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• 2011

For an integer $m{\geq}3$, every integer of the form $p_m(x)$ = $\frac{(m-2)x^2(m-4)x}{2}$ with x ${\in}$ $\mathbb{Z}$ is said to be a generalized m-gonal number. Let $a{\leq}b{\leq}c$ and k be positive integers. The quadruple (k, a, b, c) is said to be universal if for every nonnegative integer n there exist integers x, y, z such that n = $ap_k(x)+bp_k(y)+cp_k(z)$. Sun proved in [16] that, when k = 5 or $k{\geq}7$, there are only 20 candidates for universal quadruples, which h listed explicitly and which all involve only the case of pentagonal numbers (k = 5). He veri ed that six of the candidates are in fact universal and conjectured that the remaining ones are as well. In a subsequent paper [3], Ge and Sun established universality for all but seven of the remaining candidates, leaving only (5, 1, 1, t) for t = 6, 8, 9, 10, (5, 1, 2, 8) and (5, 1, 3, s) for s = 7, 8 as candidates. In this article, we prove that the remaining seven quadruples given above are, in fact, universal.

• Korean Journal of Veterinary Research
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• v.46 no.3
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• pp.263-265
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• 2006

A 15-year-old intact female poodle dog was referred to a local animal clinic showing signs of dyspnea. A radiographic examination revealed multiple nodules in the lung. The following day, the animal died and a necropsy examination revealed multiple nodular masses of varying sizes in the lung. Microscopically, the tumor cells were composed of round to polygonal cells resembling adipocytes with little or no collagenous stroma. Most of the cells contained clear cytoplasmic vacuoles with the nucleus at the periphery while the other cells contained varying numbers of smaller vacuoles. The immunohisto-chemical evaluation yielded a positive reaction to S-100 and vimentin. Negative results were obtained for pancytokeratin, smooth muscle actin, desmin, epithelial membrane antigen and CD68. This case was diagnosed as a well-differentiated liposarcoma.

• Journal of Digital Convergence
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• v.10 no.10
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• pp.529-538
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• 2012

This study analyzed a variety of different kinds of usage patterns of four-digit personal identification numbers(PINs) based on the data collected from students attending at A-university in 2011. According to the analysis, the 4 digit PINs '1234' was being used most frequently which is similar to the findings of the study by the Daniel Amitay research. In addition, almost 50 percent of the students were using the four-digit PINs closely related to their personal information, and more than 10 percent of them were using it only by the reason of easiness to remember or convenience to use. Number '0' was the most frequently used, and girl students used it more than boys did. According to the result of analysis of four-digit PINs, it was found that number '1' was the most frequently used in the first and the third position. It was also found that number '2' and number '4' were the most frequently used in the second and the forth position respectively. Among students who had used number 3 in third position, around 63.6 percent of those students were using number 4 in the forth position in their PINs which showed highest frequency from analysis of double-digits connected together in each position. The analysis of PINs were represented by the polygonal (type) graph with that X-axis showed from first to forth position and Y-axis showed number had been used at each position. Among many polygonal graphs, the form showed an N-type which was called in type 1 took the first place by 35 percent.

• Applied Biological Chemistry
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• v.30 no.2
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• pp.179-185
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• 1987

The physicochemical properties and characteristics of sweet potato starches which were isolated from the six varieties were investigated. The shapes of starch granules which observed through photomicroscope and scanning electron microscope lucre round and polygonal, but those of the Shinmi were most polygonal, and the average diameters were in the range of $10.4{\sim}14.2$ microns. The amylose contents were between 25% and 28%, and blue values and alkali numbers were in the range of $0.29{\sim}0.36$, $7.0{\sim}12$, respectively. The swelling power and solubility patterns of the starches were negligible until $50^{\circ}C$, thereafter it increased rapidly and the Eunmi showed highest water binding capacity of 211.6%. Amylogram pattern of 6% starch solutions were similar to no peak viscosity, but maximum viscosity varied widely with varieties. A significant positive correlation was observed between amylose content and average gelatinization temperature. Taste and texture of the steam cooked sweet potatoes were negatively and positively correlated with moisture and amylose contents, respectively, while those of the microwave cooked sweet potatoes were only positively correlated with amylose contents.

• Korean Journal of Food Science and Technology
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• v.31 no.6
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• pp.1410-1414
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• 1999

The granular size and shape of durian seed starch were $2.0-10.0\;{\mu}m$ and oval and polygonal. Amylose contents of durian seed, corn, sweet potato and potato starch were 28.3%, 27.5%, 20.3% and 21.7%, respectively. Blue value of durian seed (0.370) higher than that of corn (0.368), sweet potato (0.332), and potato starch (0.338). Alkali numbers of durian seed, corn, sweet potato and potato starch were 7.39, 9.02, 7.08 and 5.43, respectively. Swelling power of durian seed starch was similar to that of sweet potato starch. X-ray diffraction patterns of durian seed starch showed an A-type crystalline structure. According to pasting properties by Rapid Visco-Analyzer, the gelatinization temperature of durian seed starch $(76.6^{circ}C)$ was higher than that of corn $(73.0^{circ}C)$, sweet potato $(72.3^{circ}C)$ and potato starch $(70.2^{circ}C)$. The breakdown of durian seed starch were lower than that of corn, sweet potato and potato starch.

• Journal of the Korean Institute of Intelligent Systems
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• v.25 no.3
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• pp.229-235
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• 2015

This study is investigated the effect of sensitivity upon pattern of the four-digit personal identification numbers(PINs) of A-university students. Under survey 2, PINs were collected after each student had information about his PINs were used in disclose his test scores, But Under survey 1, each student didn't have. Survey 2 is viewed more sensitive situation than survey 1 to students. The rate of occurrences of most common PINs which were created by the reason of easiness to remember or to use without caution, in survey 2 is five times less than survey 1 and using rate of girl students are considerably less than that of boys. By comparing frequencies of digits used at each position, it is found that significant differences exist between two surveys in the first, second and forth position except third. PINs are represented by the polygonal graph with that X-axis shows position and Y-axis shows digits from 0 to 9 used at each position. There are many different figures between two surveys. This study shows that students are more anxious about using the PINs in survey 2 which is viewed more sensitive than survey 1.