• Journal of the Korean Mathematical Society
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• v.56 no.2
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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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• v.37 no.3_4
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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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• v.39 no.3_4
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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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• v.39 no.1_2
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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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• v.31 no.3
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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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• v.41 no.6
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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.

• The Korean Journal of Applied Statistics
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• v.14 no.1
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• pp.39-57
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• 2001

Categorical data has sometimes misclassification errors. If this data will be analyzed, then estimated cell probabilities could be biased and the standard Pearson X2 tests may have inflated true type I error rates. On the other hand, if we regard wellclassified data with misclassified one, then we might spend lots of cost and time on adjustment of misclassification. It is a necessary and important step to ask whether categorical data is misclassified before analyzing data. In this paper, when data is misclassified at one of two variables for two-dimensional contingency table and marginal sums of a well-classified variable are fixed. We explore to partition marginal sums into each cells via the concepts of Bound and Collapse of Sebastiani and Ramoni (1997). The double sampling scheme (Tenenbein 1970) is used to obtain informations of misclassification. We propose test statistics in order to solve misclassification problems and examine behaviors of the statistics by simulation studies.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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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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• v.4 no.1_2
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• pp.52-57
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• 1981

I have studied serveral patterns of flowering periods in selected floras of the world since 1969. The total sums and patterns of flowering periods in Netherland, South Germany, France, and Mediterranean and Palestine floras are compared. The total sums of flowering periods of the floras are gradually increased from Netherland to Palestine. The patterns of these flowering periods are characteristic, and divided into two categories; northern temperate and Mediteranean climatic types. The patterns of Netherland, south Germany, and France flora belong to the northern temperate climatic type, and thus the peak of flowering period occur in the month of July. These patterns are particularly belong to the Meditteranean climatic type; and thus the peaks of patterns of flowering period occur in April or May. The Increasing patterns of flowering period from January to April or May seems to be dependent upon the combined factors of satisfactory precipitatiion an dincreasing temperature, while the decreasing patterns since the month of the peak is presumably greatly affected by the scanty precipitation in the high temperature seasons.

• Physical Therapy Korea
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• v.2 no.1
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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.