• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.3
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• pp.215-223
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• 2013

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that the weighted averages of expectations of fuzzy random variables converge. Finally, weak laws of large numbers for weighted sums of strongly tight or identically distributed fuzzy random variables are obtained as corollaries.

• Journal of the Semiconductor & Display Technology
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• v.17 no.2
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• pp.41-46
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• 2018

This paper proposes a new method for the number recognition on dot matrix LED display. The proposed method uses morphological processing that dilates dots of numbers and connects the dots into strokes. The size of numbers is normalized using horizontal projection because the gaps of dots are different according to the size of numbers. The numbers are segmented by connected component analysis and finally, template matching method recognizes the segmented numbers. The proposed method is implemented using C language in Raspberry Pi system with a camera module for a real-time image processing. Experiments were conducted by using various dot matrix LED displays. The results show that the proposed method is successful for the number recognition on dot matrix LED display.

• Journal of Educational Research in Mathematics
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• v.17 no.1
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• pp.1-31
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• 2007

Negative numbers have been one of the most difficult mathematical concepts, and it was only 200 years ago that they were recognized as a real object of mathematics by mathematicians. It was because it took more than 1500 years for human beings to overcome the quantitative notion of numbers and recognize the formality in negative numbers. Understanding negative numbers as formal ones resulted from the Copernican conversion in mathematical way of thinking. we first investigated the historic and the genetic process of the concept of negative numbers. Second, we analyzed the conceptual fields of negative numbers in the aspect of the additive and multiplicative structure. Third, we inquired into the levels of thinking on the concept of negative numbers on the basis of the historical and the psychological analysis in order to understand the formal concept of negative numbers. Fourth, we analyzed Korean mathematics textbooks on the basis of the thinking levels of the concept of negative numbers. Fifth, we investigated and analysed the levels of students' understanding of the concept of negative numbers. Sixth, we analyzed the symbolizing process in the development of mathematical concept. Futhermore, we tried to show a concrete way to teach the formality of the negative numbers concepts on the basis of such theoretical analyses.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.413-423
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• 2014

In this article we study different properties of the statistically convergent and statistically null sequence classes of fuzzy real numbers with fuzzy metric, like completeness, solidness, sequence algebra, symmetricity and convergence free.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.530-535
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• 2001

Variations of temperature field in a Hele-Shaw convection cell (HSC) were measured using a holographic interferometry with varying Rayleigh number. Experimental results show a steady flow pattern at low Rayleigh numbers and a time-dependent periodic flow at high Rayleigh numbers. Especially, the period of oscillation at $Ra = 6.35{\times}10^6$ was 62 seconds. Two different measurement methods of holographic interferometry, double-exposure method and real-time method, were employed to measure the temperature field variations of HSC convective flow. In the double-exposure method, unwanted waves can be eliminated and reconstruction images are clear, but transient flow structure cannot be observed clearly. On the other hand, transient flow can be observed and reconstructed well using the real-time method. However, the fringe patterns reconstructed by the real-time method contain more noise, compared with the double-exposure method. The two holographic interferometer techniques employed complementary in this study were proved to be useful for analyzing the temperature field variations of unsteady thermal fluid flows.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.11
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• pp.1624-1631
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• 2001

Variations of temperature field in a Hele-Shaw convection cell (HSC) were measured using a holographic interferometry with varying Rayleigh number. Experimental results show a steady flow pattern at low Rayleigh numbers and a time-dependent periodic flow at high Rayleigh numbers. Especially, the period of oscillation at Ra = 6.35 $\times$ 10$^{6}$ was 62 seconds. Two different measurement methods of holographic interferometry, double-exposure method and real-time method, were employed to measure the temperature field variations of HSC convective flow. In the double-exposure method, unwanted waves can be eliminated and reconstruction images are clear, but transient flow structure cannot be observed clearly. On the other hand, transient flow can be observed and reconstructed well using the real-time method. However, the fringe patterns reconstructed by the real-time method contain more noise, compared with the double-exposure method. The two holographic interferometer techniques employed complementary in this study were proved to be useful fur analyzing the temperature field variations of unsteady thermal fluid flows.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.417-445
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• 2020

The purpose of this article is to continue the study of q, 𝜔-special functions in the spirit of Wolfgang Hahn from the previous papers by Annaby et al. and Varma et al., with emphasis on q, 𝜔-Apostol Bernoulli and Euler polynomials, Ward-𝜔 numbers and multiple q, 𝜔power sums. Like before, the q, 𝜔-module for the alphabet of q, 𝜔-real numbers plays a crucial role, as well as the q, 𝜔-rational numbers and the Ward-𝜔 numbers. There are many more formulas of this type, and the deep symmetric structure of these formulas is described in detail.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.831-846
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• 2011

There are several methods, in the literature, for finding the fuzzy optimal solution of fully fuzzy transportation problems (transportation problems in which all the parameters are represented by fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, a new method (based on fuzzy linear programming formulation) is proposed to find the fuzzy optimal solution of unbalanced fuzzy transportation problems with a new representation of trapezoidal fuzzy numbers. The advantages of the proposed method over existing method are discussed. Also, it is shown that it is better to use the proposed representation of trapezoidal fuzzy numbers instead of existing representation of trapezoidal fuzzy numbers for finding the fuzzy optimal solution of fuzzy transportation problems. To illustrate the proposed method a fuzzy transportation problem (FTP) is solved by using the proposed method and the obtained results are discussed. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems occurring in real life situations.

• Asian-Australasian Journal of Animal Sciences
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• v.24 no.11
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• pp.1552-1559
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• 2011

Real time PCR was used in this study to determine the effect of triticale dried distillers grains with solubles (TDDGS) as a replacement for grain or barley silage in finishing diets on the presence of six classical ruminal bacterial species (Succinivibrio dextrinosolvens, Selenomonas ruminantium, Streptococcus bovis, Megasphaera elsdenii, Prevotella ruminicola and Fibrobacter succinogenes) within the rumen contents of feedlot cattle. This study was divided into a step-wise adaptation experiment (112 days) that examined the effects of adaptation to diets containing increasing levels of TDDGS up to 30% (n = 4), a short-term experiment comparing animals (n = 16) fed control, 20%, 25% or 30% TDDGS diets over 28 days, and a rapid transition experiment (56 days) where animals (n = 4) were rapidly switched from a diet containing 30% TDDGS to a barley-based diet with no TDDGS. It was found that feeding TDDGS as replacement for barley grain (control vs. 20% TDDGS) decreased 16S rRNA copy numbers of starch-fermenting S. ruminantium and S. bovis (p<0.001 and p = 0.04, respectively), but did not alter 16S rRNA copy numbers of the other rumen bacteria. Furthermore, feeding TDDGS as a replacement barley silage (20% vs. 25% and 30% TDDGS) increased 16S rRNA copy numbers of S. ruminantium, M. elsdenii and F. succinogenes (p<0.001; p = 0.03 and p<0.001, respectively), but decreased (p<0.001) the 16S rRNA copy number of P. ruminicola. Upon removal of 30% TDDGS and return to the control diet, 16S rRNA copy numbers of S. ruminantium, M. elsdenii and F. succinogenes decreased (p = 0.01; p = 0.03 and p = 0.01, respectively), but S. dextrinosolvens and S. bovis increased (p = 0.04 and p = 0.009, respectively). The results suggest that replacement of TDDGS for grain reduces 16S rRNA copy numbers of starch-fermenting bacteria, whereas substitution for barley silage increases 16S rRNA copy numbers of bacteria involved in fibre digestion and the metabolism of lactic acid. This outcome supports the contention that the fibre in TDDGS is highly fermentable.

• Education of Primary School Mathematics
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• v.21 no.3
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• pp.289-307
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• 2018

Although mixed calculation of natural numbers is important in that it completes arithmetic calculation of natural numbers in elementary school, few studies have been conducted regarding its instruction methods. Given this, this study analyzed Korean mathematics textbooks (from the fifth textbooks to the 2009 revised textbooks) along with Japanese and Singaporean textbooks in terms of the parentheses and the order of operations regarding mixed calculation of natural numbers. The results of this study showed that there were differences in introducing the parentheses and representing them in an explicit way per textbooks. In the Korean textbooks, the order of operations was presented mostly with the real-life contexts but it was not always in a diagrammatic representation. In contrast, in the Singaporean textbooks, the order of operations was presented without the real-life contexts and the use of calculators was emphasized. In the Japanese textbooks, the order of operations was presented with the real-life contexts and a hierarchy of operations was emphasized. Based on these results, this study suggested several implications of textbook development and instructional methods regarding mixed calculations of natural numbers.