• Communications for Statistical Applications and Methods
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• v.11 no.2
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• pp.413-418
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• 2004

Statistically illiterate people seem to believe that there are some strategies for choosing winning numbers in lottery. One seemingly plausible strategy is to select the hot numbers which most frequently appeared in the past. In this article we investigate the existence of hot numbers in the Korean national lottery called Lotto. A numerical method is proposed to estimate the exact sampling distribution of test statistic for checking the existence of hot numbers among 45 possible numbers of choice.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.485-505
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• 2019

In 1935, D. H. Lehmer introduced and investigated generalized Euler numbers $W_n$, defined by $${\frac{3}{e^t+e^{wt}e^{w^2t}}}={\sum\limits_{n=0}^{\infty}}W_n{\frac{t^n}{n!}}$$, where ${\omega}$ is a complex root of $x^2+x+1=0$. In 1875, Glaisher gave several interesting determinant expressions of numbers, including Bernoulli and Euler numbers. These concepts can be generalized to the hypergeometric Bernoulli and Euler numbers by several authors, including Ohno and the second author. In this paper, we study more general numbers in terms of determinants, which involve Bernoulli, Euler and Lehmer's generalized Euler numbers. The motivations and backgrounds of the definition are in an operator related to Graph theory. We also give several expressions and identities by Trudi's and inversion formulae.

• Journal of the Korean Society for Library and Information Science
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• v.28
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• pp.23-70
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• 1995

This study is to survey the present book numbers used in Korean libraries. to analyze their problems. and to suggest improvement in the book numbers. As the results of the survey several suggestions are derived as follows. 1. The education to the librarians about the kinds and the application methods of the book numbers used in Korean libraries should be sufficiently offered. 2. The present book numbers used should be expanded in detail for avoiding the duplication of the call numbers. Also when book numbers are assigned. shelf list cards should be examined one by one not to give the same number. If the book numbers are overlapped in the state not to expand further. libraries should establish a detailed expansion rules according to their respective situation and maintain it consistently. However, it is impossible for libraries operating open stack systems to arrange books on the shelves in call number sequence, therefore libraries can solve the problems as they accept duplication cases. 3. Since the object word of main mark IS a heading In main entry, we must apply cataloging rules to it closely. 4. For expanding book numbers widely it is desirable that the subsidiary mark of the book numbers which is the most prevalent in general and will be the most preferable In the future through the survey should be added and be provided. 5. The book numbers used being changed, we are to assign new book number leaving former materials as they are at the point of adopting a new book number. So aged materials are stored in a repository or on a compact shelf in the stack, will be discarded or weeded according to subjects after a certain period of time. 6. With library automation bringing together all the books of an author in a particular subject or in a particular form and avoiding completely duplication in open stack systems are meaningless. Rather than chronological book numbers, distinguishing clearly new materials from aged materials and controlling the stack spaces mechanically and effectively, can be regarded as the most modern and future-oriented of all the book numbers.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.623-630
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• 2013

In this paper, our aim is finding the term of generalized Eule polynomials. We also obtain some identities and relations involving the Bernoulli numbers, the Euler numbers and the Stirling numbers.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.587-597
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• 2017

In this paper we define the (p, q)-analogue of Bernoulli numbers and polynomials by generalizing the Bernoulli numbers and polynomials, Carlitz's type q-Bernoulli numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with (p, q)-analogue of Bernoulli numbers and polynomials. Finally, we investigate the zeros of the (p, q)-analogue of Bernoulli polynomials by using computer.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.153-162
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• 1998

We study limits of sums of fuzzy numbers with different spreads and different shape functions where addition is defined by the sup-t-norm. We show the existence of the limit of the series of fuzzy numbers and prove the uniform continuity of the limit. Finally we investigate a law of large numbers for sequences of fuzzy numbers.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.259-270
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• 2019

In this paper we define the degenerate Carlitz-type q-Euler polynomials by generalizing the degenerate Euler numbers and polynomials, degenerate Carlitz-type Euler numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with degenerate Carlitz-type q-Euler numbers and polynomials.

• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.129-140
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• 2002

In this paper, we obtain a strong law of large numbers for convex tight random elements taking values in the space of fuzzy numbers in R.

• Journal of the Korean Data and Information Science Society
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• v.7 no.1
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• pp.105-112
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• 1996

Softwares including random number generation are abundant in modern informative society. But it's hard to get directly multivariate multinomial random numbers from existing softwares. Multivariate multinomial random numbers are greatly used in social and medical sciences. In this paper, we show that desired multivariate multinomial random numbers can be easily generated by the aids of existing random number generating software. Some characteristics of multivariate multinomial distribution are surveyd. Measures of association for the generated random numbers were computed and compared with population ones via simulation study.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.535-547
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• 2019

In this paper, by using the lower bound of linear forms in logarithms of Matveev and the theory of continued fractions by means of a variation of a result of Dujella and $Peth{\ddot{o}}$, we find all generalized Fibonacci numbers which are Pell numbers. This paper continues a previous work that searched for Pell numbers in the Fibonacci sequence.