• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.19-34
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• 2011

A bounded linear operator T on a complex Banach space X is said to have property (I) provided that T has Bishop's property (${\beta}$) and there exists an integer p > 0 such that for a closed subset F of ${\mathbb{C}}$ ${X_T}(F)={E_T}(F)=\bigcap_{{\lambda}{\in}{\mathbb{C}}{\backslash}F}(T-{\lambda})^PX$ for all closed sets $F{\subseteq}{\mathbb{C}}$, where $X_T$(F) denote the analytic spectral subspace and $E_T$(F) denote the algebraic spectral subspace of T. Easy examples are provided by normal operators and hyponormal operators in Hilbert spaces, and more generally, generalized scalar operators and subscalar operators in Banach spaces. In this paper, we prove that if T has property (I), then the quasi-nilpotent part $H_0$(T) of T is given by $$KerT^P=\{x{\in}X:r_T(x)=0\}={\bigcap_{{\lambda}{\neq}0}(T-{\lambda})^PX$$ for all sufficiently large integers p, where ${r_T(x)}=lim\;sup_{n{\rightarrow}{\infty}}{\parallel}T^nx{\parallel}^{\frac{1}{n}}$. We also prove that if T has property (I) and the spectrum ${\sigma}$(T) is finite, then T is algebraic. Finally, we prove that if $T{\in}L$(X) has property (I) and has decomposition property (${\delta}$) then T has a non-trivial invariant closed linear subspace.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.387-400
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• 2014

We prove that the set of k-type nonwandering points of a Z2-action T can be decomposed into a disjoint union of closed and T-invariant sets $B_1,{\ldots},B_l$ such that $T|B_i$ is topologically k-type transitive for each $i=1,2,{\ldots},l$, if T is expansive and has the shadowing property.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.1-5
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• 2009

Let {$X_n,\;n{\geq}1}$ be a sequence of independent identically distributed(i.i.d.) sequence of positive random variables with common absolutely continuous distribution function(cdf) F(x) and probability density function(pdf) f(x) and $E(X^2)<{\infty}$. The random variables $\frac{X_i{\cdot}X_j}{(\Sigma^n_{k=1}X_k)^{2}}$ and $\Sigma^n_{k=1}X_k$ are independent for $1{\leq}i if and only if {$X_n,\;n{\geq}1}$ have gamma distribution.

• Journal of Korea Multimedia Society
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• v.3 no.5
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• pp.454-460
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• 2000

To retrieve complex data such as images, the content-based retrieval method rather than keyword based method is required. In this paper, we implemented a content-based image retrieval system which retrieves object of user query effectively using invariant moments which have invariant properties about linear transformation like position transition, rotation and scaling. To extract the shape feature of objects in an image, we propose a labeling algorithm that extracts objects from an image and apply invariant moments to each object. Hashing method is also applied to reduce a retrieval time and index images effectively. The experimental results demonstrate the high retrieval efficiency i.e precision 85%, recall 23%. Consequently, our retrieval system shows better performance than the conventional system that cannot express the shale of objects exactly.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.7-10
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• 1985

For each a.mem.S and f.mem.m(S), denote by $l_{a}$ f(s)=f(as) for all s.mem.S. If A is a norm closed left translation invariant subalgebra of m(S) (i.e. $l_{a}$ f.mem.A whenever f.mem.A and a.mem.S) containing 1, the constant ont function on S and .phi..mem. $A^{*}$, the dual of A, then .phi. is a mean on A if .phi.(f).geq.0 for f.geq.0 and .phi.(1) = 1, .phi. is multiplicative if .phi. (fg)=.phi.(f).phi.(g) for all f, g.mem.A; .phi. is left invariant if .phi.(1sf)=.phi.(f) for all s.mem.S and f.mem.A. It is well known that the set of multiplicative means on m(S) is precisely .betha.S, the Stone-Cech compactification of S[7]. A subalgebra of m(S) is (extremely) left amenable, denoted by (ELA)LA if it is nom closed, left translation invariant containing contants and has a multiplicative left invariant mean (LIM). A semigroup S is (ELA) LA, if m(S) is (ELA)LA. A subset E.contnd.S is left thick (T. Mitchell, [4]) if for any finite subser F.contnd.S, there exists s.mem.S such that $F_{s}$ .contnd.E or equivalently, the family { $s^{-1}$ E : s.mem.S} has finite intersection property.y.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.157-163
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• 2014

Let {$X_i$, $1{\leq}i{\leq}n$} be a sequence of i.i.d. sequence of positive random variables with common absolutely continuous cumulative distribution function F(x) and probability density function f(x) and $E(X^2)$ < ${\infty}$. The random variables X + Y and $\frac{(X-Y)^2}{(X+Y)^2}$ are independent if and only if X and Y have gamma distributions. In addition, the random variables $S_n$ and $\frac{\sum_{i=1}^{m}(X_i)^2}{(S_n)^2}$ with $S_n=\sum_{i=1}^{n}X_i$ are independent for $1{\leq}m$ < n if and only if $X_i$ has gamma distribution for $i=1,{\cdots},n$.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.127-144
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• 2009

Let f be a diffeomorphism of a compact $C^{\infty}$ manifold, and let p be a hyperbolic periodic point of f. In this paper we introduce the notion of $C^1$-stable inverse shadowing for a closed f-invariant set, and prove that (i) the chain recurrent set $\cal{R}(f)$ of f has $C^1$-stable inverse shadowing property if and only if f satisfies both Axiom A and no-cycle condition, (ii) $C^1$-generically, the chain component $C_f(p)$ of f associated to p is hyperbolic if and only if $C_f(p)$ has the $C^1$-stable inverse shadowing property.

• Magazine of the Korean Society of Agricultural Engineers
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• v.37 no.3_4
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• pp.34-47
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• 1995

It is experienced fact as a regular annual event that the structure to he designed on unreasonable flood for the agricultural structures including reservoirs have been brought not only loss of lives, but also enormous property damage. For the solution of this problem at issue, this study was conducted to develop an optimal runoff hydrograph model by comparison of the peak flows and time to peak between observed and simulated flows derived by linear time-invariant and linear time-variant models under the condition of having a short duration of heavy rainfall with uniform rainfall intensity at nine small watersheds which are within the range of 55.9 to 140.7 square kilometers in area in Han, Geum, Nagdong and Yeongsan Rivers. The results obtained through this study can be summarized as follows. 1. Storage constants and Gamma function arguments were calculated within the range of 1.2 to 6.42 and of 1.28 to 8.05 respectively by the moment method as the parameters for the analysis of runoff hydrograph based on linear time-invariant model. 2. Parameters for both linear time-invariant and linear time-variant models were calibrated with nine gaged watershed data, using a trial and error method. The resulting parameters including Gamma function argument, N and storage constant, K for linear time-invariant model were related statistically to watershed characteristic variables such as area, slope, length of main stream and the centroid length of the basin. 3. Average relative errors of the simulated peak discharge of calibrated runoff hydrographs by using linear time-variant and linear time-invariant models were shown to be 0.75 and 5.42 percent respectively to the peak of observed runoff hydrographs. Correlation coefficients for the statistical analysis in the same condition were shown to be 0.999 and 0.978 with a high significance respectively. Therefore, it can be concluded that the accuracy of a linear time-variant model is approaching more closely to the observed runoff hydrograph than that of a linear time-invariant model in the applied watersheds. 4. Average relative errors of the time to peak of calibrated runoff hydrographs by using linear time-variant and linear time-invariant models were shown to be 16.44 and 19.89 percent respectively to the time to peak of observed runoff hydrographs. Correlation coefficients in the same condition were also shown to be 0.999 and 0.886 with a high significance respectively. 5. It can be seen that the shape of simulated hydrograph based on a linear time- variant model is getting closer to the observed runoff hydrograph than that of a linear time-invariant model in the applied watersheds. 6. Two different models were verified with different rainfall-runoff events from data for the calibration by relative error and correlation analysis. Consequently, it can be generally concluded that verification results for the peak discharge and time to peak of simulated runoff hydrographs were in good agreement with those of calibrated runoff hydrographs.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.536-539
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• 2004

In this paper, a brief discussion on I-PD position controller design for step motor drive is presented. The proposed method mainly focuses on the robustness property of the controller, which is very important for this type of system in which the variation of external load affects plant parameters. It is considered in this paper that two types of controller design methods namely; Coefficient Diagram Method (CDM), and arbitrary Pole Assignment Method (PAM) are treated and compared them. The control plant chosen for our study is a SM inherently is comprised of some non-linear elements. A the scope of the design method is limited to only linear time invariant systems, the SM modeling is approximated to linear system.

• East Asian mathematical journal
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• v.34 no.3
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• pp.305-316
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• 2018

Let R be a ring with identity. A right ideal ideal I of a ring R is called ref lexive (resp. completely ref lexive) if $aRb{\subseteq}I$ implies that $bRa{\subseteq}I$ (resp. if $ab{\subseteq}I$ implies that $ba{\subseteq}I$) for any $a,\;b{\in}R$. R is called ref lexive (resp. completely ref lexive) if the zero ideal of R is a reflexive ideal (resp. a completely reflexive ideal). Let K(R) (called the ref lexive radical of R) be the intersection of all reflexive ideals of R. In this paper, the following are investigated: (1) Some equivalent conditions on an reflexive ideal of a ring are obtained; (2) reflexive (resp. completely reflexive) property is Morita invariant; (3) For any ring R, we have $K(M_n(R))=M_n(K(R))$ where $M_n(R)$ is the ring of all n by n matrices over R; (4) For a ring R, we have $K(R)[x]{\subseteq}K(R[x])$; in particular, if R is quasi-Armendaritz, then R is reflexive if and only if R[x] is reflexive.