• Bulletin of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.807-816
• /
• 2007

For the stochastic differential inclusion on infinite dimensional space of the form $dX_t{\in}\sigma(X_t)dW_t+b(X_t)dt$, where ${\sigma}$, b are set-valued maps, W is an infinite dimensional Hilbert space valued Q-Wiener process, we prove the boundedness and continuity of solutions under the assumption that ${\sigma}$ and b are closed convex set-valued satisfying the Lipschitz property using approximation.

• Progress in Superconductivity
• /
• v.9 no.1
• /
• pp.29-34
• /
• 2007

The baseline selection is the first and important step to analyze magnetocardiography (MCG) parameters. There are no difficulties to select the baseline between P- and Q-wave peak (P-Q interval) of MCG wave recorded from healthy subjects because the P-Q intervals of the healthy subjects do not much vary. However, patients with ischemic heart disease often show an unstable P-Q interval which does not seem to be appropriate for the baseline. In this case, T-P interval is alternatively recommended for the baseline. However, there has been no study on the difference made by the baseline selection. In this study, we studied the effect of the different baseline selection. MCG data were analyzed from twenty healthy subjects and twenty one patients whose baselines were alternatively selected in the T-P interval for their inappropriate P-Q interval. Paired T-test was used to compare two set of data. Fifteen parameters derived from the R-wave peak, the T-wave peak, and the period, $T_{max/3}{\sim}T_{max}$ were compared for the different baseline selection. As a result, most parameters did not show significant differences (p>0.05) except few parameters. Therefore, there will be no significant differences if anyone of two intervals were selected for the MCG baseline. However, for the consistent analysis, P-Q interval is strongly recommended for the baseline correction.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.2
• /
• pp.233-239
• /
• 2007

Let $\mathbb{A}=\mathbb{F}_q$[T] be the polynomial ring over a finite field $\mathbb{F}_q$[T] and K=$\mathbb{F}_q$(T) its field of fractions. Let ${\ell}$ be a fixed prime divisor of q-1. Let J be a finite set of monic irreducible polynomials $P{\in}{\mathbb{A}}$ with deg $P{\equiv}0$ (mod ${\ell})$. In this paper we define the group $C_K$ of circular units in K=k$(\{\sqrt[{\ell}]P\;:\;P{\in}J\})$ in the sense of Kucera [4] and compute the index of $C_K$ in the full unit group $O^*_K$.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.1-16
• /
• 1996

Earlier in 1935[12], M. S. Robertson introduced the class of quadrant preserving functions. More precisely, let Q be the class of all functions f(z) analytic in the unit disk $D = {z : $\mid$z$\mid$ < 1}$ such that f(0) = 0, f'(0) = 1, and the range f(z) is in the j-th quadrant whenever z is in the j-th quadrant of D, j = 1,2,3,4. This class Q contains the subclass of normalized, odd univalent functions which have real coefficients. On the other hand, this class Q is contained in the class T of odd typically real functions which was introduced by W. Rogosinski [13]. Clearly, if $f \in Q$, then f(z) is real when z is real and therefore the coefficients of f are all real. Recently, it was observed by Y. Abu-Muhanna and T. H. MacGregor [1] that any function $f \in Q$ is odd. Instead of functions "preserving quadrants", the authors [1] have introduced the notion of "preserving sectors".

• Bulletin of the Korean Mathematical Society
• /
• v.25 no.2
• /
• pp.175-178
• /
• 1988

Let .SIGMA. be a smooth compact manifold without boundary having the same homotopy type as a sphere, which is called a homotopy sphere. Supose a group G acts smoothly on .SIGMA. with the fixed point set .SIGMA.$^{G}$ consists of two isolated fixed points p and q. In this case, tangent spaces $T_{p}$ .SIGMA. and $T_{q}$ .SIGMA. at isolated fixed points, as isotropy representations of G are called Smith equivalent. Moreover .SIGMA. is called a supporting homotopy sphere of Smith equivalent representations $T_{p}$ .SIGMA. and $T_{q}$ .SIGMA.. The study on Smith equivalence has rich history, and for this we refer the reader to [P] or [Su]. The following question of pp.A.Smith [S] motivates the study on Smith equivalence.e.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.2
• /
• pp.399-405
• /
• 2013

We explicitly construct a thin basis for the set $\mathbf{M}$ of monic polynomials in one variable $t$ over a finite field ${\mathbb{F}}_q$.

• Korean Journal of Mathematics
• /
• v.16 no.3
• /
• pp.349-353
• /
• 2008

Let the set of all quasi-class A operators for which $ker(A){\subseteq}ker(A^*)$ be denoted by $A{\in}{\mathcal{Q}}A^*$. In this paper it is proved that an operator $T{\in}{\mathcal{Q}}A^*$ is normal if and only if the Duggal transform of T is normal.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.187-204
• /
• 2018

Let $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}\;R_{\alpha}$ be a graded integral domain, H be the set of nonzero homogeneous elements of R, and ${\star}$ be a semistar operation on R. The purpose of this paper is to study the properties of $quasi-Pr{\ddot{u}}fer$ and UMt-domains of graded integral domains. For this reason we study the graded analogue of ${\star}-quasi-Pr{\ddot{u}}fer$ domains called $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. We study several ring-theoretic properties of $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. As an application we give new characterizations of UMt-domains. In particular it is shown that R is a $gr-t-quasi-Pr{\ddot{u}}fer$ domain if and only if R is a UMt-domain if and only if RP is a $quasi-Pr{\ddot{u}}fer$ domain for each homogeneous maximal t-ideal P of R. We also show that R is a UMt-domain if and only if H is a t-splitting set in R[X] if and only if each prime t-ideal Q in R[X] such that $Q{\cap}H ={\emptyset}$ is a maximal t-ideal.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.41 no.4
• /
• pp.404-414
• /
• 2016

So called quaternary quasi-orthogonal sequence spatial modulation (Q-QOS-SM) has been presented with an advantage of improved throughputs compared to the conventional SM and generalized spatial modulation (GSM) by virtue of a larger set size of QOSs and its minimized correlation value between these QOSs. However the Q-QOS-SM has been originally invented for limited transmit antennas of only powers of two. In this paper, by extending the Q-QOS-SM to any number of transmit antennas, we propose a generalized Q-QOS-SM, referred as G-QO-SM. Unlike the conventional Q-QOS-SM using the Q-QOSs of length of any power of two, the proposed G-QO-SM is constructed based on the Q-QOSs of only the lengths of 2 and 4. The proposed scheme guarantees the transmission of the total $N_t$ spatial bits with $N_t$ transmit antennas, and thus achieves greatly higher throughputs than the other existing schemes including the SM, GSM, Q-QOS-SM, Quadrature-SM, and Enhanced-SM. The performance improvements of the proposed G-QO-SM is justified by comparing the analytically derived BER upper bounds and also the exact Monte Carlo simulation results.

• Journal of Korean Society of Forest Science
• /
• v.85 no.1
• /
• pp.76-83
• /
• 1996

Four natural Quercus stands in Kwangju, Kyonggi-Do, of which ages ranging from 32 to 38 years old, were studied to compare their growth, biomass and net production. Ten $10m{\times}10m$ quadrats were set up and ten sample trees were harvested for dimension analysis in each stand. The largest mean DBH and height were shown by Q. acutissima stand, and followed by Q. variabilis stand, Q. mongolica stand, and Q. dentata stand in descending order. Tree density was the highest at Q. variabilis stand, and followed by Q. dentata stand, Q. mongolica stand, and Q. acutissima stand in descending order. Biomass was the largest at Q. acutissima stand(122.73t/ha), and followed by Q. variabilis stand(87.03t/ha), Q. mongolica stand(72.14t/ha), and Q. dentata stand(38.56t/ha) in descending order. Net production was the greatest at Q. mongolica stand(7.49t/ha/yr.), and followed by Q. variabilis stand(6.47t/ha/yr.), Q. acutissima stand(6.06t/ha/yr.), and Q. dentata stand(3.52t/ha/yr.) in descending order. The highest net assimilation ratio was exhibited by Q. acutissima stand (3.275), and followed by Q. variabilis stand(2.898), Q. mongolica stand(2.888), and Q. dentata stand (1.840) in descending order. The difference in net assimilation ratio and net production among four stands was caused by differences in their leaf biomass. The difference in net production and biomass among four stands was due to that in the distribution of net production among stems, branches and leaves.