• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1079-1095
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• 2021

In this paper, we give new congruences with the generalized Catalan numbers and harmonic numbers modulo p². One of our results is as follows: for prime number p > 3, $${\sum\limits_{k=(p+1)/2}^{p-1}}\;k^2B_{p,k}B_{p,k-(p-1)/2}H_k{\equiv}(-1)^{(p-1)/2}\(-{\frac{521}{36}}p-{\frac{1}{p}}-{\frac{41}{12}}+pH^2_{3(p-1)/2}-10pq^2_p(2)+4\({\frac{10}{3}}p+1\)q_p(2)\)\;(mod\;p^2),$$ where q_p(2) is Fermat quotient.

• Korean Journal of Plant Taxonomy
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• v.51 no.3
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• pp.192-197
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• 2021

In the flora of Korea, Carex L. is one of the most species-rich genera. Among nearly 157 Carex taxa, less than 30 have had chromosome numbers reported. We report the meiotic chromosome numbers of eight Carex taxa from Korean populations, which include the first count for C. accrescens Ohwi (n = 37_II) and the first chromosome investigations of Korea populations for three taxa: C. bostrychostigma Maxim. (n = 22_II), C. lanceolata Boott (n = 36_II), and C. paxii Kuk. (n = 38_II). In most species, chromosome counts observed in the study are included in the variation ranges of previous chromosome numbers. However, C. bostrychostigma Maxim. (n = 22_II) and C. planiculmis Kom. (n = 29_II) are assigned new chromosome numbers. Carex is known to have holocentric chromosomes, lacking visible primary constrictions and exhibiting great variance in its chromosome number. Further investigations of the diversity of Carex chromosomes will provide basic information with which to understand the high species diversity of the genus.

• 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 applied mathematics & informatics
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• v.39 no.1_2
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• pp.45-56
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• 2021

D.S. Kim et al. [9] considered some identities and relations for Korobov type numbers and polynomials. In this work, we investigate the degenerate Korobov type Changhee polynomials and the (p,q)-poly-Korobov polynomials. We give a generalization of the Korobov type Changhee polynomials and the (p,q) poly-Korobov polynomials. We prove some properties and identities and explicit relations for these polynomials.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.931-957
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• 2023

For an arbitrary integer x, an integer of the form $$T(x)={\frac{x^2+x}{2}}$$ is called a triangular number. Let α₁, ... , α_k be positive integers. A sum ${\Delta}_{{\alpha}_1,{\ldots},{\alpha}_k}(x_1,\,{\ldots},\,x_k)=\{\alpha}_1T(x_1)+\,{\cdots}\,+{\alpha}_kT(x_k)$ of triangular numbers is said to be almost universal with one exception if the Diophantine equation ${\Delta}_{{\alpha}_1,{\ldots},{\alpha}_k}(x_1,\,{\ldots},\,x_k)=n$ has an integer solution (x₁, ... , x_k) ∊ ℤ^k for any nonnegative integer n except a single one. In this article, we classify all almost universal sums of triangular numbers with one exception. Furthermore, we provide an effective criterion on almost universality with one exception of an arbitrary sum of triangular numbers, which is a generalization of "15-theorem" of Conway, Miller, and Schneeberger.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.753-763
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• 2023

In this paper, we introduce a fully modified (p, q)-poly tangent polynomials and numbers of the first type. We investigate analytic properties that is related with (p, q)-Gaussian binomial coefficients. We also define (p, q)-Stirling numbers of the second kind and fully modified (p, q)-poly tangent polynomials and numbers of the first type with two variables. Moreover, we derive some identities are concerned with the modified tangent polynomials and the (p, q)-Stirling numbers.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.97-103
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• 2024

This study is about digits of numbers in system logic B₃. Any real number is written as digits in the binary system, in the ternary system. The numbers in base two and base three are also written in the B₃ system ternary logic. These two writing methods are transferred into the third method. The real numbers 0,1 and 0, 1, 2 are written as digits. The same real numbers are written as digits of elements of the set -1, 0, 1 in base B₃. The periods here are investigated. The relationship between these digits is analysed.

• Journal of Astronomy and Space Sciences
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• v.30 no.3
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• pp.163-168
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• 2013

Parameters associated with solar minimum have been studied to relate them to solar activity at solar maximum so that one could possibly predict behaviors of an upcoming solar cycle. The number of active days has been known as a reliable indicator of solar activity around solar minimum. Active days are days with sunspots reported on the solar disk. In this work, we have explored the relationship between the sunspot numbers at solar maximum and the characteristics of the monthly number of active days. Specifically, we have statistically examined how the maximum monthly sunspot number of a given solar cycle is correlated with the slope of the linear relationship between monthly sunspot numbers and the monthly number of active days for the corresponding solar cycle. We have calculated the linear correlation coefficient r and the Spearman rank-order correlation coefficient $r_s$ for data sets prepared under various conditions. Even though marginal correlations are found, they turn out to be insufficiently significant (r ~ 0.3). Nonetheless, we have confirmed that the slope of the linear relationship between monthly sunspot numbers and the monthly number of active days is less steep when solar cycles belonging to the "Modern Maximum" are considered compared with rests of solar cycles. We conclude, therefore, that the slope of the linear relationship between monthly sunspot numbers and the monthly number of active days is indeed dependent on the solar activity at its maxima, but that this simple relationship should be insufficient as a valid method to predict the following solar activity amplitude.

• Journal of the Korea Society of Computer and Information
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• v.9 no.3
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• pp.121-125
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• 2004

In the most of recognizing systems of hand-written numbers. extraction of feature shape by using character elements shapes and a method of morphological analysis by using then extraction of feature shapes were usually used. In this paper, however, peculiar chain-code is used, and differential code which gets minimal value by differentiating the chain-code which is generated by the peculiar chain-code is made. We found this differential code is very successful in discriminating hand-written numbers according to the result of applying to most of the hand-written numbers. Testing recognition of hand-written numbers by HMM network. From the results, we can recognize of 96.1 percentage hand-written numbers but can not recognize extremely distorted hand-written numbers.

• International Journal of Contents
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• v.13 no.3
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• pp.1-8
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• 2017

Rice plant numbers and density are key factors for yield and quality of rice grains. Precise and properly estimated rice plant numbers and density can assure high yield from rice fields. The main objective of this study was to automatically detect and count rice plants using images of usual field condition from an unmanned aerial vehicle (UAV). We proposed an automatic image processing method based on morphological operation and boundaries of the connected component to count rice plant numbers after transplanting. We converted RGB images to binary images and applied adaptive median filter to remove distortion and noises. Then we applied a morphological operation to the binary image and draw boundaries to the connected component to count rice plants using those images. The result reveals the algorithm can conduct a performance of 89% by the F-measure, corresponding to a Precision of 87% and a Recall of 91%. The best fit image gives a performance of 93% by the F-measure, corresponding to a Precision of 91% and a Recall of 96%. Comparison between the numbers of rice plants detected and counted by the naked eye and the numbers of rice plants found by the proposed method provided viable and acceptable results. The $R^2$ value was approximately 0.893.