• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.329-336
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• 2010

In this paper, we introduce a partitioning subsemimodule of a semimodule over a semiring which is useful to develop the quotient structure of semimodule. Indeed we prove : 1) The quotient semimodule M=N(Q) is essentially independent of choice of Q. 2) If f : M ${\rightarrow}$ M' is a maximal R-semimodule homomorphism, then $M/kerf_{(Q)}\;\cong\;M'$. 3) Every partitioning subsemimodule is subtractive. 4) Let N be a Q-subsemimodule of an R-semimodule M. Then A is a subtractive subsemimodule of M with $N{\subseteq}A$ if and only if $A/N_{(Q{\cap}A)}\;=\;\{q+N:q{\in}Q{\cap}A\}$ is a subtractive subsemimodule of $M/N_{(Q)}$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1157-1171
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• 2013

In this paper, by using the $q$-difference analogue of lemma on the logarithmic derivative lemma to re-establish some estimates of Nevanlinna characteristics of $f(qz)$, we deal with the value distribution and uniqueness of certain types of $q$-difference polynomials.

• Phonetics and Speech Sciences
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• v.3 no.3
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• pp.157-165
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• 2011

This study investigated speech rate and intonation slope (least square method; F0, quarter-tone) in normal and CI children's utterances. Each group consisted of 12 people and were divided into groups of children with CI operation (before 3;00), children with CI operation (after 3;00), and normal children. Materials are composed of four kinds of grammatical dialogue sentences which are lacking in respect. Given three groups as independent variables and both speech rate and intonation slope as dependent variables, a one-way ANOVA showed that normal children had faster speech rates and steeper intonation slopes than those of the CI group. More specifically, there was a statistically significant speech rate difference between normal and CI children in all of the sentential patterns but imperative form (p<.01). Additionally, F0 and qtone slope observed in sentential final word showed a significant statistical difference between normal and CI children in imperative form (f0: p<.01; q-tone: p<.05).

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.219-229
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• 2006

Using the integral average method, we establish some oscillation criteria for the nonlinear differential equation with damped term $$a(t)|{x}^{\prime}(t)|^{\sigma-1}{x}^{\prime}(t)^{\prime}+p(t)|{x}^{\prime}(t)|^{\sigma-1}{x}^{\prime}(t)+q(t)f(x(t))=0,\;{\sigma}>1$$, where the functions $a,\;p$ and $q$ are real-valued continuous functions defined on $[t_o,{\infty})$ with $a(t)>0,\;f(x){\in}C^1(\mathbb{R})$ and $\frac{f^{\prime}(u)}{|f^{({\sigma}-1)/{\sigma}}(u)|}{\geq}k>0$ for $u{\neq}0$.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.385-389
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• 2010

In 1997, Exton, by mainly employing a widely-used process of resolving hypergeometric series into odd and even parts, obtained some new and interesting summation formulas with arguments 1 and -1. We aim at showing how easily many summation formulas can be obtained by simply combining some known summation formulas. Indeed, we present 22 results in the form of two generalized summation formulas for the generalized hypergeometric series $_4F_3$, including two Exton's summation formulas for $_4F_3$ as special cases.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.237-272
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• 2021

The main purpose of the present paper is to study the asymptotic behavior near the origin of radial solutions of the equation 𝚫_p u(x) + u^q(x) + f(x) = 0 in ℝ^N\{0}, where p > 2, q > 1, N ≥ 1 and f is a continuous radial function on ℝ^N\{0}. The study depends strongly of the sign of the function f and the asymptotic behavior near the origin of the function |x|^λf(|x|) with suitable conditions on λ > 0.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.1031-1038
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• 2021

The main aim of this article is to study quantitative structure of finite simple exceptional groups F₄(2ⁿ) with n > 1. Here, we prove that the finite simple exceptional groups F₄(2ⁿ), where 2⁴ⁿ + 1 is a prime number with n > 1 a power of 2, can be uniquely determined by their orders and the set of the number of elements with the same order. In conclusion, we give a positive answer to J. G. Thompson's problem for finite simple exceptional groups F₄(2ⁿ).

• Geophysics and Geophysical Exploration
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• v.10 no.3
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• pp.191-202
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• 2007

To identify the detailed attenuation structure in the southern Korean Peninsula, a numerical test was conducted for the Q tomography inversion to be applied to the accumulated dataset until 2005. In particular, the stochastic pointsource ground-motion model (STGM model; Boore, 2003) was adopted for the 2D Q tomography inversion for direct application to simulating the strong ground-motion. Simultaneous inversion of the STGM model parameters with a regional single Q model was performed to evaluate the source and site effects which were necessary to generate an artificial dataset for the numerical test. The artificial dataset consists of simulated Fourier spectra that resemble the real data in the magnitude-distance-frequency-error distribution except replacement of the regional single Q model with a checkerboard type of high and low values of laterally varying Q models. The total number of Q blocks used for the checkerboard test was 75 (grid size of $35{\times}44km^2$ for Q blocks); Q functional form of $Q_0f^{\eta}$ ($Q_0$=100 or 500, 0.0 < ${\eta}$ < 1.0) was assigned to each Q block for the checkerboard test. The checkerboard test has been implemented in three steps. At the first step, the initial values of Q-values for 75 blocks were estimated. At the second step, the site amplification function was estimated by using the initial guess of A(f) which is the mean site amplification functions (Yun and Suh, 2007) for the site class. The last step is to invert the tomographic Q-values of 75 blocks based on the results of the first and second steps. As a result of the checkerboard test, it was demonstrated that Q-values could be robustly estimated by using the 2D Q tomography inversion method even in the presence of perturbed source and site effects from the true input model.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1029-1036
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• 1997

Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.

• The Korean Journal of Ecology
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• v.15 no.2
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• pp.117-125
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• 1992

TWINSPAN(two-way indicator species analysis), DCCA(detrended canonical correspondence analysis) and polar ordination method wee used so as to analyze the the relation between forest vegetation and hibitat of mudungsan(1, 187m) located in kwangju area. Vegetationsurvey consulted 1:25, 000 topographical map, set up 41 quadrats and analyzed from April, 1990 to August, 1991. Forest vegetation of mudungsan was classifild to quercus acutissima community, fraxinus mandshurica community, quercus mongolica community, quercus serrata community, quercus dentata community, quercus variabilis community, and pinus densiflora community by TWINSPANmethod, and this almost coincide with the result of plar ordination. according to DCCA analysis, P. densiflora community was formed in xeric and low altitude region which soil nutrient was poor, compared with other communities. q. variabilis and q. acutissima community wee distributed in the region that low altitude and organic matter content was comparatively low, but q. acutissima community was formed in a damp region while q. variabilis community in a xeric region. q. mongolica and f. mandshurica formed the communities in a high altitude region, especially f. mandshurica cmmunity was distributed in a high humidity region. According to polar ordination analysis, the forest vegetation was classified to 7 communities by means of environmental gradient such as humidity, organic matter, ph, temperature, c.e.c and P2O5.