• 대한수학회지
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• 제56권2호
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• pp.457-473
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• 2019

In this paper, we investigate weak laws of large numbers for weighted coordinatewise pairwise negative quadrant dependence random vectors in Hilbert spaces in the case that the decay order of tail probability is r for some 0 < r < 2. Moreover, we extend results concerning Pareto-Zipf distributions and St. Petersburg game.

• Journal of applied mathematics & informatics
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• 제37권3_4호
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• pp.317-328
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• 2019

This paper defines Carlitz's type (p, q)-Genocchi polynomials and Carlitz's type (h, p, q)-Genocchi polynomials, and explains fourteen properties which can be complemented by Carlitz's type (p, q)-Genocchi polynomials and Carlitz's type (h, p, q)-Genocchi polynomials, including distribution relation, symmetric property, and property of complement. Also, it explores alternating powers sums by proving symmetric property related to Carlitz's type (p, q)-Genocchi polynomials.

• Journal of applied mathematics & informatics
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• 제39권3_4호
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• pp.359-380
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• 2021

The main purpose and motivation of this work is to investigate and provide some new results for coefficients derived from eta quotients related to 3. The result of this paper involve some restricted divisor numbers and their convolution sums. Also, our results give relation between the coefficients derived from infinite product, infinite sum and the convolution sum of restricted divisor functions.

• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.145-153
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• 2021

When {Xni|1 ≤ i ≤ n, n ≥ 1} be an array of rowwise negatively superadditive dependent(NSD) for semi-Gaussian random variables and {ani|1 ≤ i ≤ n, n ≥ 1} is an array of constants, we study the almost sure convergence of weighted sums ∑ni=1 aniXni under some appropriate conditions and we obtain some corollaries.

• Korean Journal of Mathematics
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• 제31권3호
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• pp.295-303
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• 2023

This paper introduces a novel method for obtaining umbrella matrices, which are defined as orthogonal matrices with row sums of one, using skew-symmetric matrices and Cayley's Formula. This method is presented for the first time in this paper. We also investigate the kinematic properties and applications of umbrella matrices, demonstrating their usefulness as a tool in geometry and kinematics. Our findings provide new insights into the connections between matrix theory and geometric applications.

• Journal of applied mathematics & informatics
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• 제41권6호
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• pp.1227-1235
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• 2023

The study of convolution sums for divisor functions is an area that has been extensively researched by many mathematicians including Ramanujan. The aim of this paper is to find the formula for convolution sum of divisor functions with coprime conditions.

• 응용통계연구
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• 제14권1호
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• pp.39-57
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• 2001

범주형 자료에서 오분류는 자료를 수집하는 과정에서 발생될 수 있다. 오분류되어 있는 자료를 정확한 자료로 간주하여 분석한다면 추정결과에 편의가 발생하고 검정력이 약화되는 결과를 초래하게 되며, 정확하게 분류된 자료를 오분류하고 판단한다면 오분류의 수정을 위해 불필요한 비용과 시간을 낭비해야 할 것이다. 따라서 정확하게 분류된 표본인지 오분류된 표본인지를 판정하는 것은 자료를 분석하기 전에 이루어져야할 매우 중요한 과정이다. 본 논문은 I$\times$J 분할표로 주어지는 범주형 자료에서 두 변수 중 하나의 변수에서만 오분류가 발생되는 경우에 오분류 여부를 검정하기 위해서 오분류 가능성이 없는 변수에 대한 주변합은 고정시키고, 오분류 여부를 가능성이 있는 변수의 주변합을 Sebastiani와 Ramoni(1997)가 제안한 Bound와 외부정보로 표현되는 Collapse의 개념, 그리고 베이지안 방법을 확장하여 자료에 적합한 모형과 사전정보를 고려한 사전모수를 다양하게 설정하면서 재분류하는 연구를 하였다. 오분류에 대한 정보를 얻기 위해서 Tenenbein(1970)에 의해 연구된 이중추출법을 이용하여 오분류 검정을 위한 새로운 통계량을 제안하였으며, 제안된 오분류 검정통계량에 관한 분포를 다양한 모의실험을 통하여 연구하였다.

• 대한수학회논문집
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• 제25권1호
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• pp.119-128
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• 2010

Let ${X_n,\;n\geq1}$ be a sequence of independent identically distributed (i.i.d.) random variables (r.vs.), defined on a probability space ($\Omega$,A,P), and let ${N_n,\;n\geq1}$ be a sequence of positive integer-valued r.vs., defined on the same probability space ($\Omega$,A,P). Furthermore, we assume that the r.vs. $N_n$, $n\geq1$ are independent of all r.vs. $X_n$, $n\geq1$. In present paper we are interested in asymptotic behaviors of the random sum $S_{N_n}=X_1+X_2+\cdots+X_{N_n}$, $S_0=0$, where the r.vs. $N_n$, $n\geq1$ obey some defined probability laws. Since the appearance of the Robbins's results in 1948 ([8]), the random sums $S_{N_n}$ have been investigated in the theory probability and stochastic processes for quite some time (see [1], [4], [2], [3], [5]). Recently, the random sum approach is used in some applied problems of stochastic processes, stochastic modeling, random walk, queue theory, theory of network or theory of estimation (see [10], [12]). The main aim of this paper is to establish some results related to the asymptotic behaviors of the random sum $S_{N_n}$, in cases when the $N_n$, $n\geq1$ are assumed to follow concrete probability laws as Poisson, Bernoulli, binomial or geometry.

• The Korean Journal of Ecology
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• 제4권1_2호
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• pp.52-57
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• 1981

1969년이래 세계명국의 식물상화기형에 대한 연구를 하여왔다. 금번의 화기형은 화란, 독일, 불란서, 지중해연안, 희랍과 파레스타인의 식물상화기형을 밝힌것이다. 월별 화기율의 총화는 화란에서 독일, 불란서, 희랍, 지중해연안과 파레스타인의 식물상순으로 점차 증가현상을 보였다. 그리고 화기형이 2형으로 나누어지는 것을 볼 수가 있었다. 즉 화란, 독일 및 불란서와 같이 화기율의 월별 피-크가 7월에 나타나는 북온대형이 있고 지중해연안, 희랍 및 파레스타인과 같이 화기율의 피-크가 4월 또는 5월에 나타나는 지중해형이 있다. 북온대형은 주로 기온곡선과 관련이 큰점을 보게되고 지중해형은 특히 우량곡선과 큰 관련이 있는 것을 볼 수가 있었다.

• 한국전문물리치료학회지
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• 제2권1호
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• pp.51-61
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• 1995

In general, research in isokinetic exercise has focussed on studies of peak torque. However, peak torque is not always sufficient to assess the real amount of motion or to determine endurance. In this study, the subjects were 54 healthy students who performed continuous maximal isokinetic knee flexion and extension until their total work per time reached 50% of their maximal total work. Isokinetic curves were then plotted. Total work sums, exercise durations in seconds, and the numbers of repetitions were compared with reference to subject gender, angular velocity and muscle group. The relationship between total work sum, duration and number of repetition and thigh circumference plus leg length was computed. In addition, the characteristics of total work per second and total work per time were calculated. Results showed the total work sums differed greatly from muscle group to muscle group and with different angular velocities. The duration in seconds and the numbers of repetition differed only at higher angular velocity. Males achieved higher levels in every category except for some duration in seconds and some numbers of repetitions. Thigh circumference and leg length were deciding fators in every case, but duration in seconds and number of repetitions were not. These results suggest that measures of endurance should be included along with measures of total work when isokinetic studies are done. Measures of endurance in seconds are more accurate when isokinetic exercise is performed at lower angular velocities and numbers of repetitions at higher angular velocities.