• East Asian mathematical journal
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• v.35 no.3
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• pp.351-356
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• 2019

In this paper, we investigate Hyers-Ulam-Rassias stability of the general quartic functional equation f(5x + y) - 5f(4x + y) + 10f(3x + y) - 10f(2x + y) + 5f(x + y) - f(y) = 0.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.2
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• pp.125-136
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• 2022

The goal of this paper is to introduce the notion of generalized symmetric bi-f-derivations in lattices and to study some properties of generalized symmetric f-derivations of lattice. Moreover, we consider generalized isotone symmetric bi-f-derivations and fixed sets related to generalized symmetric bi-f-derivations.

• The Journal of the Petrological Society of Korea
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• v.14 no.2 s.40
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• pp.108-115
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• 2005

Gyeonggi metamorphic complex in the Gwangju area include banded biotite gneiss and quartzofeldspathic gneiss. Detailed structural analysis suggests that structural elements in the study area were formed by at least five phase of deformations. Penetrative compositional foliations(S1) formed in the banded gneiss during the first metamorphism and deformation (D1). After intrusion of plutonic rocks, the second deformation (D2) produced S2 foliations in the banded gneiss and quartzofeldspathic gneiss during the second metamorphism. D3 structures are represented by isoclinal folds (F3) whose axial surfaces are parallel to S3 foliations. The N-S oriented shortening (D4) was accommodated by closed upright F4 fold with about 100m of axial surface separation. F4 fold is refolded by regional F5 folding resulting in different orientation and fold style of F4 fold according to the position of F5 fold. The F4 fold with tight interlimb angle is subparallel to the axial surface (north-south) of F5 fold in the core of the F5 fold. In contrast the F4 fold trends northeast in the western limb and northwest in the eastern limb of F5 fold. The interlimb angle is larger in the limbs than that in the core of F5 fold. The trace of foliations is constrained by mainly F4 and F5 folds. Joint fanning around fold is developed in the limbs of F5 fold and bc joints are dominant in the hinge area of F5 fold. A strike-slip fault had developed in tile central part of the study area after F5 folding. The orientation of joint and foliation is rotated anticlockwise about $15^{\circ}$ by the landslide occurred during the Quaternary.

• Journal of Acupuncture Research
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• v.30 no.2
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• pp.9-15
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• 2013

Objectives : This study was done for reporting the effect of moxibustion therapy on Ryodoraku score of the patients with degenerative arthritis of knee joint. Methods : We investigated 65 cases of patients with degenerative arthritis of knee joint, and devided patients into two groups : One group treated by moxibustion therapy, which was not applied to the other group we analyzed of each group the Ryodoraku score(F1, F6) of each group before and after moxibustion therapy and compared it. Results : 1. In moxibustion therapy group compared with baseline, at final, Ryodoraku score(F1, F6) was significantly increased. 2. At final, moxibustion therapy group showed significant increase on Ryodoraku score(F1, F6) score compared with non moxibustion therapy group. Conclusions : It is suggested that Ryodoraku score(F1, F6) should be available for diagnosing degenerative arthritis of knee joint.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.377-391
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• 2013

The main goal of this paper is to present the additional stability results of the following orthogonally additive and orthogonally quadratic functional equation $$f(\frac{x}{2}+y)+f(\frac{x}{2}-y)+f(\frac{x}{2}+z)+f(\frac{x}{2}-z)=\frac{3}{2}f(x)-\frac{1}{2}f(-x)+f(y)+f(-y)+f(z)+f(-z)$$ for all $x,y,z$ with $x{\bot}y$, which has been introduced in the paper [11], in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.

• Phonetics and Speech Sciences
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• v.10 no.3
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• pp.9-18
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• 2018

This paper presents an acoustic and phonological study of the alveolar flaps in American English. Based on the Buckeye Corpus, the flapping tokens produced by twenty men are analyzed at both lexical and post-lexical levels. The data, analyzed with Pratt speech analysis, include duration, F2 and F3 in voicing during the flap, as well as duration, F1, F2, F3, and f0 in the adjacent vowels. The results provide evidence on two issues: (1) The different ways in which voiced and voiceless alveolar stops give rise to neutralized flapping stops by following lexical and post-lexical levels, (2) The extent to which the vowel features (height, frontness, and tenseness) affect flapping sounds. The results show that flaps are affected by pre-consonantal vowel features at the lexical as well as post-lexical levels. Unlike previous studies, this study uses the Praat method to distinguish flapped from unflapped tokens in the Buckeye Corpus and examines connections between the lexical and post-lexical levels.

• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.295-301
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• 2006

We Investigate the relation between the multi-variable bi-additive functional equation f(x+y+z,u+v+w)=f(x,u)+f(x,v)+f(x,w)+f(y,u)+f(y,v)+f(y,w)+f(z,u)+f(z,v)+f(z,w) and the multi-variable quadratic functional equation g(x+y+z)+g(x-y+z)+g(x+y-z)+g(-x+y+z)=4g(x)+4g(y)+4g(z). Furthermore, we find out the general solution of the above two functional equations.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1231-1240
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• 2018

In this paper, we characterize the conformal transformations between two almost regular (${\alpha},{\beta}$)-metrics. Suppose that F is a non-Riemannian (${\alpha},{\beta}$)-metric and is conformally related to ${\widetilde{F}}$, that is, ${\widetilde{F}}=e^{{\kappa}(x)}F$, where ${\kappa}:={\kappa}(x)$ is a scalar function on the manifold. We obtain the necessary and sufficient conditions of the conformal transformation between F and ${\widetilde{F}}$ preserving the mean Landsberg curvature. Further, when both F and ${\widetilde{F}}$ are regular, the conformal transformation between F and ${\widetilde{F}}$ preserving the mean Landsberg curvature must be a homothety.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.371-376
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• 2008

In this paper, it is shown that if f satisfies the following functional inequality (0.1) $${\parallel}\sum\limits_{i,j=1}^3\;f{(xi,yj)}{\parallel}{\leq}{\parallel}f(x_1+x_2+x_3,\;y_1+y_2+y_3){\parallel}$$ then f is a bi-additive mapping. We moreover prove that if f satisfies the following functional inequality (0.2) $${\parallel}2\sum\limits_{j=1}^3\;f{(x_j,\;z)}+2\sum\limits_{j=1}^3\;f{(x_j,\;w)-f(\sum\limits_{j=1}^3\;xj,\;z-w)}{\parallel}{\leq}f(\sum\limits_{j=1}^3\;xj,\;z+w){\parallel}$$ then f is an additive-quadratic mapping.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1079-1089
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• 2009

In this paper, we shall show that for any entire function f, the function of the form $f^m(f^n$ - 1)f' has no non-zero finite Picard value for all positive integers m, n ${\in}\;{\mathbb{N}}$ possibly except for the special case m = n = 1. Furthermore, we shall also show that for any two nonconstant meromorphic functions f and g, if $f^m(f^n$-1)f' and $g^m(g^n$-1)g' share the value 1 weakly, then f $\equiv$ g provided that m and n satisfy some conditions. In particular, if f and g are entire, then the restrictions on m and n could be greatly reduced.