• Kyungpook Mathematical Journal
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• 제52권4호
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• pp.513-519
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• 2012

For a spanning tree T of a connected graph ${\Gamma}$ and for a labelling ${\phi}$: E(T) ${\rightarrow}$ {+,-},${\phi}$ is called an alternating sign on a spanning tree T of a graph ${\Gamma}$ if for any cotree edge $e{\in}E({\Gamma})-E(T)$, the unique path in T joining both end vertices of e has alternating signs. In the present article, we prove that any graph has a spanning tree T and an alternating sign on T.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제5권
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• pp.523-523
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• 1997

Suppose that G is a group of permutations of a set ${\Omega}$. For a finite subset ${\gamma}$of${\Omega}$, the movement of ${\gamma}$ under the action of G is defined as move(${\gamma}$):=$max\limits_{g{\epsilon}G}|{\Gamma}^{g}{\backslash}{\Gamma}|$, and ${\gamma}$ will be said to have restricted movement if move(${\gamma}$)<|${\gamma}$|. Moreover if, for an infinite subset ${\gamma}$of${\Omega}$, the sets|{\Gamma}^{g}{\backslash}{\Gamma}| are finite and bounded as g runs over all elements of G, then we may define move(${\gamma}$)in the same way as for finite subsets. If move(${\gamma}$)${\leq}$m for all ${\gamma}$${\subseteq}$${\Omega}$, then G is said to have bounded movement and the movement of G move(G) is defined as the maximum of move(${\gamma}$) over all subsets ${\gamma}$ of ${\Omega}$. Having bounded movement is a very strong restriction on a group, but it is natural to ask just which permutation groups have bounded movement m. If move(G)=m then clearly we may assume that G has no fixed points is${\Omega}$, and with this assumption it was shown in [4, Theorem 1]that the number t of G=orbits is at most 2m-1, each G-orbit has length at most 3m, and moreover|${\Omega}$|${\leq}$3m+t-1${\leq}$5m-2. Moreover it has recently been shown by P. S. Kim, J. R. Cho and C. E. Praeger in [1] that essentially the only examples with as many as 2m-1 orbits are elementary abelian 2-groups, and by A. Gardiner, A. Mann and C. E. Praeger in [2,3]that essentially the only transitive examples in a set of maximal size, namely 3m, are groups of exponent 3. (The only exceptions to these general statements occur for small values of m and are known explicitly.) Motivated by these results, we would decide what role if any is played by primes other that 2 and 3 for describing the structure of groups of bounded movement.

• BMB Reports
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• 제52권7호
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• pp.424-433
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• 2019

Autism spectrum disorder (ASD) is a complex neurodevelopmental monogenic disorder with a strong genetic influence. Idiopathic autism could be defined as a type of autism that does not have a specific causative agent. Among signalling cascades, mTOR signalling pathway plays a pivotal role not only in cell cycle, but also in protein synthesis and regulation of brain homeostasis in ASD patients. The present review highlights, underlying mechanism of mTOR and its role in altered signalling cascades as a triggering factor in the onset of idiopathic autism. Further, this review discusses how distorted mTOR signalling pathway stimulates truncated translation in neuronal cells and leads to downregulation of protein synthesis at dendritic spines of the brain. This review concludes by suggesting downstream regulators such as p70S6K, eIF4B, eIF4E of mTOR signalling pathway as promising therapeutic targets for idiopathic autistic individuals.

• The Journal of Asian Finance, Economics and Business
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• 제5권4호
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• pp.101-105
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• 2018

Price discount is one of the commonly used promotion strategies to increase sales and revenue. If a discount is perceived before the purchase (i.e., pre-purchase discount), consumers are likely to perceive it as a potential gain. If it is noticed after making a regular-priced purchase (i.e., post-purchase discount), consumers may develop negative emotions and attitudes. Based on the rising transparency and omnipresence of price and discount information through web and mobile platforms, we attempt to tackle an understudied topic on the negative effect of post-purchase price discount. Specifically, post-purchase discount information may increase consumers' perception of monetary loss, which may affect consumers' decision to return the product, potentially increasing the operating costs borne by retailers. Based on a close scrutinization of the current market environment and previous academic literature, we suggest a novel conceptual framework to understand consumers' perception, attitude, and behavior (perception of loss, willingness to return) upon perceiving various formats of discount promotion (absolute value vs. percentage discount) posterior to the purchase of a product. We also look at the effect of price level (low-priced vs. high-priced). For marketing practitioners, we intend to suggest optimal promotion formats that can alleviate consumers' negative perceptions and prevent additional operation costs.

• Korean Journal of Mathematics
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• 제23권4호
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• pp.601-605
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• 2015

In the present note, provided $T{\in}{\mathfrak{L}}({\mathfrak{H}})$ is biquasitriangular and Browder's theorem hold for T, we show that the spectrum ${\sigma}$ is continuous at T if and only if the essential spectrum ${\sigma}_e$ is continuous at T.

• 호남수학학술지
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• 제29권4호
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• pp.535-542
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• 2007

In this paper, for each natural number n, we construct a polynomial $p_n$(x) of degree n so that $p_n(x)\;\leq\;p_{n+1}(x)\;\leq\;e^x$ for $x\;\geq\;-1$. These polynomials are optimal in the sense that if p(x) is a polynomial of degree n with $p_{n-l}(x)\;\leq\;p(x)\;\leq\;e^x$, then $p(x)\;\leq\;p_n(x)$.

• Korean Journal of Mathematics
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• 제30권4호
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• pp.653-663
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• 2022

We study cyclic codes of length n over 𝔽_2^t. Cyclic codes can be viewed as ideals in 𝓡_n = 𝔽_2^t [x]/(xⁿ − 1). It is known that there is a unique generating idempotent for each ideal. Let e(x) ∈ 𝓡_n. If t = 1 or t = 2, then there is a necessary and sufficient condition that e(x) is an idempotent. But there is no known similar result for t ≥ 3. In this paper we give an answer for this problem.

• Journal of applied mathematics & informatics
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• 제36권3_4호
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• pp.237-244
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• 2018

Let ${\mathcal{H}}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let L be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in ${\mathcal{L}}$. Let p and q be natural numbers (p < q). Let ${\mathcal{A}}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $T_{(p,q)}=0$ for all T in ${\mathcal{A}}$. If ${\mathcal{A}}$ is a Lie ideal, then $T_{(p,p)}=T_{(p+1,p+1)}={\cdots}=T_{(q,q)}$ and $T_{(i,j)}=0$, $p{\eqslantless}i{\eqslantless}q$ and i < $j{\eqslantless}q$ for all T in ${\mathcal{A}}$.

• Journal of Positioning, Navigation, and Timing
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• 제9권4호
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• pp.337-345
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• 2020

In this paper, an efficient signal tracking method to simultaneously track both GPS L1 C/A and Galileo E1B CBOC(6,1,1/11) using a low cost GPU is proposed. In the existing method that each GNSS signal is processed within 1 ms, more than 2 ms processing time is required in GPU to process 4 ms CBOC signal. It means that real time operation is possible if only Galileo E1B CBOC signal is concerned. But when both GPS C/A and Galileo CBOC is required, it cannot process GPS C/A signal in real time. To process 1 ms GPS C/A and 4 ms Galileo CBOC signal in real time, 4 ms Galileo CBOC signal is divided into 4 by 1 ms signal block in the proposed method. Specially, a buffer that simultaneously manages 1 ms and 4 ms signals is designed. In addition, a module that accumulates the 1 ms correlation value of the Galileo CBOC by 4 ms and passes it to the PLL and DLL is implemented. The operation and performance are evaluated with real measurements in the GPU based SDR. The experimental results show that tracking of more than 16 satellites of GPS C/A and Galileo E1B is possible using the proposed method.

• 한국운동역학회지
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• 제25권1호
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• pp.57-64
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• 2015

Purpose : The purpose of this study was to analyze setter toss motion kinematically according to toss types. Method : Dependent variables were elapsed time, vertical displacement of the body center, the projected speed of the ball, and differences of the joint angle to the target for four setters positioning. Result : There was no significant difference in the time but the ball contact time was shorter when the toss distance of P3 was longer. There was significant difference in the vertical displacement of COM (p<.05). The vertical displacement of COM showed that the vertical movement gradually decreased when the quick distance was longer. The vertical displacement of COM was difference (p<.05), also there was difference of the ball speed (p<.001) at the Release point(E4). There was significant difference in the knee joint angle at a certain moment among the Release(E4) and Landing point(E5)(p<.05). The hip joint was significant difference among the Apex(E2), Ball Touch(E3), Release(E4), and the Landing point(E5) on the surface(E2, E3, E4 p<.05; E5 p<.005). The shoulder angle was significant difference among the Ball Touch(E3), Release(E4) and the Landing point(E5) on the surface(E3, E4 p<.05; E5 p<.001). The elbow was significant difference in the Apex(E2) (p<.05). The wrist was significant difference in the Release(E4) (p<.05). Conclusion : If we find the clue to expect the direction of the setter's ball, we have to fine the clues in the Apex(E2) that hip join and elbow, Ball Touch(E3) that hip joint and shoulder joint, Release(E4) that wrist, elbow, hip joint, and knee joint.