• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.177-182
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• 2019

This study is about the number expressed and the number not expressed in terms of the sum of consecutive natural numbers with a difference of 2k. Since it is difficult to generalize in cases of onsecutive positive integers with a difference of 2k, the table of cases of 4, 6, 8, 10, and 12 was examined to find the normality and to prove the hypothesis through the results. Generalized guesswork through tables was made to establish and prove the hypothesis of the number of possible and impossible numbers that are to all consecutive natural numbers with a difference of 2k. Finally, it was possible to verify the possibility and impossibility of the sum of consecutive cases of 124 and 2010. It is expected to be investigated the sum of consecutive natural numbers with a difference of 2k + 1, as a future research task.

• Communications for Statistical Applications and Methods
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• v.30 no.6
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• pp.631-652
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• 2023

In the two-condition within-subject mediation design, pairs of variables such as mediator and outcome are observed under two treatment conditions. The main objective of the design is to investigate the indirect effects of the condition difference (sum) on the outcome difference (sum) through the mediator difference (sum) for comparison of two treatment conditions. The natural condition variables mean the original variables, while the rotated condition variables mean the difference and the sum of two natural variables. The outcome difference (sum) is expressed as a linear model regressed on two natural (rotated) mediators as a parallel two-mediator design in two condition approaches: the natural condition approach uses regressors as the natural condition variables, while the rotated condition approach uses regressors as the rotated condition variables. In each condition approach, the total indirect effect on the outcome difference (sum) can be expressed as the sum of two individual indirect effects: within- and cross-condition indirect effects. The total indirect effects on the outcome difference (sum) for both condition approaches are the same. The invariance of the total indirect effect makes it possible to analyze the nature of two pairs of individual indirect effects induced from the natural conditions and the rotated conditions. The two-condition within-subject design is extended to the addition of a between-subject moderator. Probing of the conditional indirect effects given the moderator values is implemented by plotting the bootstrap confidence intervals of indirect effects against the moderator values. The expected indirect effect with respect to the moderator is derived to provide the overall effect of moderator on the indirect effect. The model coefficients are estimated by the structural equation modeling approach and their statistical significance is tested using the bias-corrected bootstrap confidence intervals. All procedures are evaluated using function lavaan() of package {lavaan} in R.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.731-739
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• 2010

In this paper, we prove stability of the reciprocal difference functional equation $$r\(\frac{{\sum}_{i=1}^{m}x_i}{m}\)-r\(\sum_{i=1}^{m}x_i\)=\frac{(m-1){\prod}_{i=1}^{m}r(x_i)}{{\sum}_{i=1}^{m}{\prod}_{k{\neq}i,1{\leq}k{\leq}m}r(x_k)$$ and the reciprocal adjoint functional equation $$r\(\frac{{\sum}_{i=1}^{m}x_i}{m}\)+r\(\sum_{i=1}^{m}x_i\)=\frac{(m+1){\prod}_{i=1}^{m}r(x_i)}{{\sum}_{i=1}^{m}{\prod}_{k{\neq}i,1{\leq}k{\leq}m}r(x_k)$$ in m-variables. Stability of the reciprocal difference functional equation and the reciprocal adjoint functional equation in two variables were proved by K. Ravi, J. M. Rassias and B. V. Senthil Kumar [13]. We extend their result to m-variables in similar types.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.959-970
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• 2017

In this paper, we investigate the transcendental meromorphic solutions with finite order of two different types of difference equations $${\sum\limits_{j=1}^{n}}a_jf(z+c_j)={\frac{P(z,f)}{Q(z,f)}}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ and $${\prod\limits_{j=1}^{n}}f(z+c_j)={\frac{P(z,f)}{Q(z,f)}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ that share three distinct values with another meromorphic function. Here $a_j$, $b_k$, $d_l$ are small functions of f and $a_j{\not{\equiv}}(j=1,2,{\ldots},n)$, $b_p{\not{\equiv}}0$, $d_q{\not{\equiv}}0$. $c_j{\neq}0$ are pairwise distinct constants. p, q, n are non-negative integers. P(z, f) and Q(z, f) are two mutually prime polynomials in f.

• Journal of Ocean Engineering and Technology
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• v.20 no.5 s.72
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• pp.30-35
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• 2006

In tire presence of incident waves with different frequencies, there are second order sum and difference frequency wave exciting forces due to the nonlinearity of tire incident waves. Although the magnitude of these nonlinear wave forces are small, they act on TLPs at sum and difference frequencies away from those of the incident waves. So, the second order sum and difference frequency waveexciting forces occurring close to tire natural frequencies of TLPs often give greater contributions to high and law frequency resonant responses. Nonlinear motion responses and tension variations in the time domain are analyzed by solving the motion equations with nonlinear wave exciting forces using tire numerical analysismethod. The numerical results of time domain analysis for the nonlinear wave exciting forces on the ISSC TLP in regular waves are compared with the numerical and experimental ones of frequency domain analysis. The results of this comparison confirmed tire validity of the proposed approach.

• Speech Sciences
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• v.10 no.2
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• pp.249-258
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• 2003

This study attempted to examine a speaker identification method using difference sum and correlation coefficient determined from a pair of intensity level matrices of band-pass-filtered numeric sounds produced by ten female speakers of similar age and height. Subjects recorded three digit numbers at a quiet room at a sampling rate of 22 kHz on a personal computer. Collected data were band-pass-filtered at five different band ranges. Then, matrices of five intensity levels at 100 proportional time points were obtained. Pearson correlation coefficients and the sum of absolute intensity differences between a pair of given matrices were determined within and across the speakers. Results showed that very high correlation coefficient and small difference sum generally occurred within each speaker but some individual variation was also observed. Thus, the matrix pair with a higher coefficient and a smaller difference sum was averaged to form each individual's model. Comparison among the speakers yielded generally low coefficients and large differences, which suggests successful speaker identification, but among them there were a few cases with very high coefficients and small differences. Future studies will focus on finer band ranges and additional spectral parameters at some peak points of the intensity contour at a low frequency band.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.645-651
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• 2010

In this note we study positive solutions of the mth order rational difference equation $x_n=(a_0+\sum{{m\atop{i=1}}a_ix_{n-i}/(b_0+\sum{{m\atop{i=1}}b_ix_{n-i}$, where n = m,m+1,m+2, $\ldots$ and $x_0,\ldots,x_{m-1}$ > 0. We describe a sufficient condition on nonnegative real numbers $a_0,a_1,\ldots,a_m,b_0,b_1,\ldots,b_m$ under which every solution $x_n$ of the above equation tends to the limit $(A-b_0+\sqrt{(A-b_0)^2+4_{a_0}B}$/2B as $n{\rightarrow}{\infty}$, where $A=\sum{{m\atop{i=1}}\;a_i$ and $B=\sum{{m\atop{i=1}}\;b_i$.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.295-303
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• 2007

In this paper we investigate the boundedness character of the positive solutions of the rational difference equation of the form $$x_{n+1}=\frac{a_0+{{\sum}^k_{j=1}}a_jx_{n-j+1}}{b_0+{{\sum}^k_{j=1}}b_jx_{n-j+1}},\;\;n=0,\;1,...$$ where $k{\in}N,\;and\;a_j,b_j,\;j=0,\;1,...,\;k $, are nonnegative numbers such that $b_0+{{\sum}^k_{j=1}}b_jx_{n-j+1}>0$ for every $n{\in}N{\cup}\{0\}$. In passing we confirm several conjectures recently posed in the paper: E. Camouzis, G. Ladas and E. P. Quinn, On third order rational difference equations(part 6), J. Differ. Equations Appl. 11(8)(2005), 759-777.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.4
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• pp.1987-2001
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• 2017

Low-density parity-check (LDPC) codes have attracted a great attention because of their excellent error correction capability with reasonably low decoding complexity. Among decoding algorithms for LDPC codes, the min-sum (MS) algorithm and its modified versions have been widely adopted due to their high efficiency in hardware implementation. In this paper, a self-adaptive MS algorithm using the difference of the first two minima is proposed for faster decoding speed and lower power consumption. Finding the first two minima is an important operation when MS-based LDPC decoders are implemented in hardware, and the found minima are often compressed using the difference of the two values to reduce interconnection complexity and memory usage. It is found that, when these difference values are bounded, decoding is not successfully terminated. Thus, the proposed method dynamically decides whether the termination-checking step will be carried out based on the difference in the two found minima. The simulation results show that the decoding speed is improved by 7%, and the power consumption is reduced by 16.34% by skipping unnecessary steps in the unsuccessful iteration without any loss in error correction performance. In addition, the synthesis results show that the hardware overhead for the proposed method is negligible.

• Journal of Ocean Engineering and Technology
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• v.12 no.2 s.28
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• pp.33-42
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• 1998

In the presence of incident waves with different frequencies, the second order sum and difference frequency waves due to the nonlinearity of the incident waves come into existence. Although the magnitudes of the forces produced on a Tension Leg Platform(TLP) by these nonlinear waves are small, they act on the TLP at sum and difference frequencies away from those of the incident waves. So, the second order sum and difference frequency wave loads produced close to the natural frequencies of TLPs often give greater contributions to high and low frequency resonant responses. The second order wave exciting forces and moments have been obtained by the method based on direct integration of pressure acting on the submerged surface of a TLP. The components of the second order forces which depend on first order quantities have been evaluated using the three dimensional source distribution method. The numerical results of time domain analysis for the nonlinear wave exciting forces in regular waves are compared with the numerical ones of frequency domain analysis. The results of comparison confirmed the validity of the proposed approach.