• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.71-79
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• 2001

The purpose of this paper is to prove new equilibrium existence theorems of social systems with coordination under general conditions on the preference correspondence in locally convex spaces, and we also give an example which the previous existence results on SSC do not work but our theorem can be applied.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.683-689
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• 2000

The convergence rate of the expectation of the logarithm of the first return time R(sub)n with block length n has been investigated for Bernoulli processes. This idea is applied to check the randomness of the digits of the decimal expansion of $\pi$, e and √2.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.347-361
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• 2014

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distribution includes exponential distribution, Pareto or Lomax distribution. In this paper, we established exact expressions and recurrence relations satised by the quotient moments of generalized order statistics for a generalized Pareto distribution. Further the results for quotient moments of order statistics and records are deduced from the relations obtained and a theorem for characterizing this distribution is presented.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1247-1260
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• 2021

We introduce the notion of barycentric transformation of Fano polytopes, from which we can assign a certain type to each Fano polytope. The type can be viewed as a measure of the extent to which the given Fano polytope is close to be Kähler-Einstein. In particular, we expect that every Kähler-Einstein Fano polytope is of type B_∞. We verify this expectation for some low dimensional cases. We emphasize that for a Fano polytope X of dimension 1, 3 or 5, X is Kähler-Einstein if and only if it is of type B_∞.

• Journal of the Korean Statistical Society
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• v.2 no.1
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• pp.3-7
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• 1973

Zellner, Kmenta, Dreze (1966) and later Hedges (1969) showed that consistent estimates of the parameters of Cobb-Douglas or CES production functions can be obtained by the single equation estimation methods if the models incorporate the assumption that firms maximize the mathematical expectation of profits. This note demonstrates that the results of the above-cited works can be extended to a class of VES production function models.

• Journal of Korea Society of Digital Industry and Information Management
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• v.15 no.2
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• pp.71-85
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• 2019

The importance of the NCS(National Competitiveness Standards) is growing as the job market shrinks and more institutions require hiring based on NCS. Of the ten domains of NCS', the most relevant one with the performance of all tasks is basic capability group. The purpose of this study is to investigate the effect of college students' basic capability group(communication capability, mathematical capability) on their career preparation behavior. In this study, we set up a process model to comprehend the effect of college students' basic capability group on career preparation behavior based on social cognitive career theory. For research model testing, 561 questionnaires were used for empirical analysis through structural equations modeling. Empirical analysis showed that communication capability positively influenced college students' career preparation behaviors for employment. But, mathematical capability don't influenced college students' career preparation behaviors for employment. Next, career self-efficacy and career outcome expectation each positively influenced college students' career preparation behaviors for employment. Also, interest in the major positively influenced college students' career preparation behaviors for employment. The academic implications are as follows: Career self-efficacy and interest in the major were important factors in the communication capability. The process of communication capability affecting career preparation behavior and interest in the major was explained through social cognitive career theory and self-efficacy. The practical implications are as follows: Administrative assistance should be provided to improve the career self-efficacy of college students.

• Communications for Statistical Applications and Methods
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• v.18 no.5
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• pp.559-570
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• 2011

The role of jurisprudence is examined in the early history of probability and statistics. From the mid-17th to the early 18th century, Christiaan Huygens and Jacob Bernoulli used mathematical expectation to solve the problems that originated from games of chance. We demonstrate that their concept of expectation as a fair price for participating in a game came from the legal concept of 'fair trade'. In addition, we consider that the probability that Bernoulli defined in his Ars Conjectandi originated from the legal concept of 'degree of certainty'. After considering some contributions of Laplace and Poisson, we examined the history of census and statistical survey in the early 19th century. Contrary to the history of the 17th and 18th century, statistics influenced society and law in the 19th century.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.345-353
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• 2015

Subnormality of bounded weighted composition operators on $L^2({\Sigma})$ of the form $Wf=uf{\circ}T$, where T is a nonsingular measurable transformation on the underlying space X of a ${\sigma}$-finite measure space (X, ${\Sigma}$, ${\mu}$) and u is a weight function on X; is studied. The standard moment sequence characterizations of subnormality of weighted composition operators are given. It is shown that weighted composition operators are subnormal if and only if $\{J_n(x)\}^{+{\infty}}_{n=0}$ is a moment sequence for almost every $x{{\in}}X$, where $J_n=h_nE_n({\mid}u{\mid}^2){\circ}T^{-n}$, $h_n=d{\mu}{\circ}T^{-n}/d{\mu}$ and $E_n$ is the conditional expectation operator with respect to $T^{-n}{\Sigma}$.

• The Mathematical Education
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• v.24 no.2
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• pp.117-125
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• 1986

The education of mathematics in generalized schooling should aim to concentrate on the cultivation of mathematical abilities necessary for social life. Mathemeatical abilities for social life run as follows: A. Utilitarian aspects 1. classification and numbers 2. traffic network and connection of segments of lines 3. expectation of getting the winning number in a lottery 4. interests in dealing in unharvested rice crop B. Aesthetic aspects 1. finding the optimum value and 2. successful candidates in accordance with election methods Every nation has its own peculiar customs and circumstances. Therefore, in order to achieve the expected results, the education of mathematics should develop what every nation has on its own and apply them to school education.

• Journal of Distribution Science
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• v.13 no.8
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• pp.61-71
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• 2015

Purpose - Before the year 2000, the housing prices in Korea were increasing every decade. After 2000, for the first time, Korea experienced a decrease in housing prices, and the repetitive cycle of price fluctuation started. Such a "boom and bust cycle" is a worldwide phenomenon. The current study proposes a mathematical model to explain price fluctuation cycles based on the theory of consumer psychology. Specifically, the model incorporates the effects of buyer expectations of future prices on actual price changes. Based on the model, this study investigates various independent variables affecting the amplitude of price fluctuations in housing markets. Research design, data, and methodology - The study provides theoretical analyses based on a mathematical model. The proposed model uses the following assumptions of the pricing mechanism in housing markets. First, the price of a house at a certain time is affected not only by its current price but also by its expected future price. Second, house investors or buyers cannot predict the exact future price but make a subjective prediction based on observed price changes up to the present. Third, the price is determined by demand changes made in previous time periods. The current study tries to explain the boom-bust cycle in housing markets with a mathematical model and several numerical examples. The model illustrates the effects of consumer price elasticity, consumer sensitivity to price changes, and the sensitivity of prices to demand changes on price fluctuation. Results - The analytical results imply that even without external effects, the boom-bust cycle can occur endogenously due to buyer psychological factors. The model supports the expectation of future price direction as the most important variable causing price fluctuation in housing market. Consumer tendency for making choices based on both the current and expected future price causes repetitive boom-bust cycles in housing markets. Such consumers who respond more sensitively to price changes are shown to make the market more volatile. Consumer price elasticity is shown to be irrelevant to price fluctuations. Conclusions - The mechanism of price fluctuation in the proposed model can be summarized as follows. If a certain external shock causes an initial price increase, consumers perceive it as an ongoing increasing price trend. If the demand increases due to the higher expected price, the price goes up further. However, too high a price cannot be sustained for long, thus the increasing price trend ceases at some point. Once the market loses the momentum of a price increase, the price starts to drop. A price decrease signals a further decrease in a future price, thus the demand decreases further. When the price is perceived as low enough, the direction of the price change is reversed again. Policy makers should be cognizant that the current increase in housing prices due to increased liquidity can pose a serious threat of a sudden price decrease in housing markets.