• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.733-746
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• 2009

For any integer k $\geq$ 2, let P(c, k + 1;q) be the number of all k+1-tuples with positive integer coordinates ($a_1,a_2,...,a_{k+1}$) such that $1{\leq}a_i{\leq}q$, ($a_i,q$) = 1, $a_1a_2...a_{k+1}{\equiv}$ c (mod q) and 2 $\nmid$ ($a_1+a_2+...+a_{k+1}$), and E(c, k+1; q) = P(c, k+1;q) - $\frac{{\phi}^k(q)}{2}$. The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the r-th hyper-Kloosterman sums Kl(h,k+1,r;q) and E(c,k+1;q), and give an interesting mean value formula.

• East Asian mathematical journal
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• v.18 no.2
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• pp.271-282
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• 2002

Let R be a ring with an endomorphism $\sigma$ and a derivation $\delta$. An ideal I of R is ($\sigma,\;\delta$)-ideal of R if $\sigma(I){\subseteq}I$ and $\delta(I){\subseteq}I$. An ideal P of R is a ($\sigma,\;\delta$)-prime ideal of R if P(${\neq}R$) is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideals I and J of R, $IJ{\subseteq}P$ implies that $I{\subseteq}P$ or $J{\subseteq}P$. An ideal Q of R is ($\sigma,\;\delta$)-semiprime ideal of R if Q is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideal I of R, $I^2{\subseteq}Q$ implies that $I{\subseteq}Q$. The ($\sigma,\;\delta$)-prime radical (resp. prime radical) is defined by the intersection of all ($\sigma,\;\delta$)-prime ideals (resp. prime ideals) of R and is denoted by $P_{(\sigma,\delta)}(R)$(resp. P(R)). In this paper, the following results are obtained: (1) $P_{(\sigma,\delta)}(R)$ is the smallest ($\sigma,\;\delta$)-semiprime ideal of R; (2) For every extended endomorphism $\bar{\sigma}$ of $\sigma$, the $\bar{\sigma}$-prime radical of an Ore extension $P(R[x;\sigma,\delta])$ is equal to $P_{\sigma,\delta}(R)[x;\sigma,\delta]$.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.435-447
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• 2012

Let G be a group. Let R be a G-graded commutative ring with identity and M be a G-graded multiplication module over R. A proper graded submodule Q of M is semiprime if whenever $I^nK{\subseteq}Q$, where $I{\subseteq}h(R)$, n is a positive integer, and $K{\subseteq}h(M)$, then $IK{\subseteq}Q$. We characterize semiprime submodules of M. For example, we show that a proper graded submodule Q of M is semiprime if and only if grad$(Q){\cap}h(M)=Q+{\cap}h(M)$. Furthermore if M is finitely generated then we prove that every proper graded submodule of M is contained in a graded semiprime submodule of M. A proper graded submodule Q of M is said to be almost semiprime if (grad(Q)$\cap$h(M))n(grad$(0_M){\cap}h(M)$) = (Q$\cap$h(M))n(grad$(0_M){\cap}Q{\cap}h(M)$). Let K, Q be graded submodules of M. If K and Q are almost semiprime in M such that Q + K $\neq$ M and $Q{\cap}K{\subseteq}M_g$ for all $g{\in}G$, then we prove that Q + K is almost semiprime in M.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.46 no.4
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• pp.148-156
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• 2009

This paper presents a new image rejection algorithm based on the analysis of the distortion of a single-frequency continuous-wave (CW) signal due to the I/Q mismatch. Existing methods estimated the gain mismatch and phase mismatch on RF receivers and compensated them However, this paper shows that the circular trajectory of a single-frequency CW signal is distorted elliptic-type trajectory due to the I/Q mismatch. Utilizing the analysis, we propose a I/Q mismatch compensation method. It has two processing steps. In the first processing step, the generated signal is rotated to align the major axis of the elliptic-type trajectory diagram with the x-axis. In the second processing step, the Q-channel signal in the regenerated signal is scaled to align the regenerated signal with the transmitted single-frequency CW signal. Simulation results show that a receiver using the proposed image rejection algorithm can achieve an image rejection ratio of more than 70dB. And, simulation results show that the bit error rate performances of receivers using the proposed image rejection algorithm are almost the same as those of conventional coherent demodulators, even in fading channels.

• Korean Journal of Agricultural and Forest Meteorology
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• v.21 no.3
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• pp.196-207
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• 2019

This study was carried out to investigate the effects of C. japonica, D. morbifera, D. macropodum, I. anisatum, Q. glauca and R. indica To investigate the photosynthetic ability, chlorophyll content, chlorophyll fluorescence analysis, and physiological environmental. The photosynthetic rate, cancer respiration rate, stomatal conductance, and rate of evaporation tended to decrease as a result of drying stress in the no-water condition for 28 days. I. anisatum, Q. glauca and R. indica showed a low rate of less than 40% until 28 days of no-treatment. The total chlorophyll contents were decreased in the order of D. macropodum> D. morbifera> C. japonica> Q. glauca> M. thunbergii> R. indica> I. anisatum. Chlorophyll fluorescence analysis showed that there was no change in the qP, but after 28 days no $Fv/F_m$, $F_o$, $R_{fd}$, $NPQ_{_-LSS}$ can be a useful indicator for quantitative estimation within a short period of time with a marked reduction rate of PSII quantum yield ${\Phi}PSII$ in the rectified state by continuous light during the nominal adaptation period. In the case of I. anisatum, Q. glauca and R. indica If water management can be carried out at intervals, it may be possible to plant trees in trees and landscape trees.

• The Journal of Korean Physical Therapy
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• v.26 no.2
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• pp.68-73
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• 2014

Purpose: The purpose of this study was to investigate the effect of closed kinetic chain exercise using EMG-biofeedback for selective training of the vastus medialis oblique on functional ability and Q-angle in subjects with patellofemoral pain syndrome. Methods: Thirty participants who met the criteria were included in this study. Participants were randomly allocated to the control group (Group I, n=10), closed kinetic chain exercise group (Group II, n=10), and closed kinetic chain exercise using EMG-biofeedback group (Group III, n=10). Intervention was performed in three groups, three times per week, for a period of six weeks. Kujala patellofemoral score and Q-angle were measured before and after the experiment. Results: Some significant differences in kujala patellofemoral score were observed in group II and group III, compared with group I (p<0.01). There was no significant difference on in Q-angle at knee flexion angle $0^{\circ}$. However, some significant differences in Q-angle at knee flexion $60^{\circ}$ were observed in group III, compared with group I (p<0.01). Conclusion: Closed kinetic chain exercise using EMG-biofeedback that provides real-time biometric information on selected muscles in order to increase the efficiency of treatment may be helpful in improvement of functional ability and Q-angle in patellofemoral pain syndrome.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.1019-1030
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• 2020

Efficient computation of r-th root in 𝔽_q has many applications in computational number theory and many other related areas. We present a new r-th root formula which generalizes Müller's result on square root, and which provides a possible improvement of the Cipolla-Lehmer type algorithms for general case. More precisely, for given r-th power c ∈ 𝔽_q, we show that there exists α ∈ 𝔽_q^r such that $$Tr{\left(\begin{array}{cccc}{{\alpha}^{{\frac{({\sum}_{i=0}^{r-1}\;q^i)-r}{r^2}}}\atop{\text{ }}}\end{array}\right)}^r=c,$$ where $Tr({\alpha})={\alpha}+{\alpha}^q+{\alpha}^{q^2}+{\cdots}+{\alpha}^{q^{r-1}}$ and α is a root of certain irreducible polynomial of degree r over 𝔽_q.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.381-392
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• 2007

In 1906, da Rios, a student of Leivi-Civita, wrote a master's thesis modeling the motion of a vortex in a viscous fluid by the motion of a curve propagating in $R^3$, in the direction of its binormal with a speed equal to its curvature. Much later, in 1971 Hasimoto showed the equivalence of this system with the non-linear Schr$\ddot{o}$dinger equation (NLS) $$q_t=i(q_{ss}+\frac{1}{2}{\mid}q{\mid}^2q$$. In this paper, we use the same idea as Terng used in her lecture notes but different technique to extend the above relation to the case of $R^3$, and obtained an analogous equation that $$q_t=i[q_{ss}+(\frac{1}{2}{\mid}q{\mid}^2+1)q]$$.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.193-200
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• 2017

Given a pair p, q of relative prime positive integers, we have uniquely determined positive integers x, y, u and v such that vx-uy = 1, p = x + y and q = u + v. Using this property, we show that$${\sum\limits_{1{\leq}i{\leq}x,1{\leq}j{\leq}v}}\;{t^{(i-1)q+(j-1)p}\;-\;{\sum\limits_{1{\leq}k{\leq}y,1{\leq}l{\leq}u}}\;t^{1+(k-1)q+(l-1)p}$$ is the Alexander polynomial ${\Delta}_{p,q}(t)$ of a torus knot t(p, q). Hence the number $N_{p,q}$ of non-zero terms of ${\Delta}_{p,q}(t)$ is equal to vx + uy = 2vx - 1. Owing to well known results in knot Floer homology theory, our expanding formula of the Alexander polynomial of a torus knot provides a method of algorithmically determining the total rank of its knot Floer homology or equivalently the complexity of its (1,1)-diagram. In particular we prove (see Corollary 2.8); Let q be a positive integer> 1 and let k be a positive integer. Then we have $$\begin{array}{rccl}(1)&N_{kq}+1,q&=&2k(q-1)+1\\(2)&N_{kq}+q-1,q&=&2(k+1)(q-1)-1\\(3)&N_{kq}+2,q&=&{\frac{1}{2}}k(q^2-1)+q\\(4)&N_{kq}+q-2,q&=&{\frac{1}{2}}(k+1)(q^2-1)-q\end{array}$$ where we further assume q is odd in formula (3) and (4). Consequently we confirm that the complexities of (1,1)-diagrams of torus knots of type t(kq + 2, q) and t(kq + q - 2, q) in [5] agree with $N_{kq+2,q}$ and $N_{kq+q-2,q}$ respectively.

• BMB Reports
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• v.37 no.5
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• pp.552-555
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• 2004

Several studies have demonstrated the importance of angiotensin-converting enzyme (ACE) insertion (I)/deletion (D) polymorphisms in the pathogenesis of hypertension. This study sought to determine the association between the ACE I/D polymorphism and essential hypertension in young Pakistanis. The frequency of the ACE I/D polymorphism was established by a comparative cross-sectional survey of Pakistani patients suffering from essential hypertension and ethnically matched normotensive controls. Samples were collected from tertiary care hospitals in northern Pakistan. Hypertensive individuals were defined as those with a systolic blood pressure > 140 mmHg and/or diastolic blood pressure > 90 mmHg on three separate occasions, or those currently receiving one, or more, anti-hypertensive agents. DNA samples obtained from hypertensive (n=211) and normotensive (n=108) individuals were typed by PCR. The frequency of the ACE I/I genotype was significantly higher in hypertensive patients, aged 20-40 years, than in normotensive controls of the same age group ($\chi^2$ = 4.0, P = 0.041). Whereas no overall significant differences were observed between the I/I, I/D and D/D ACE genotypes (One way ANOVA, F=0.672; P=0.413). The association between the ACE I/I genotype and essential hypertension in individuals aged $\leq$ 40 years suggests that ACE has a role in early onset essential hypertension in Pakistan.