• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.529-531
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• 2011

We show that for all $N{\geq}1$, the modular function field $K(X_0^+(N))$ is generated by j(z)j(Nz) and j(z) + j(Nz) over ${\mathbb{C}}$, where j(z) is the modular invariant. Moreover we derive the defining equation of the the modular function field $K(X_0^+(N))$ from the classical modular polynomial ${\Phi}_N(X, Y )$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1229-1236
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• 2009

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator S$_K$ on a vector-valued Hardy space H$^2$(${\Omega}$, K) is generated by a quasi-inner function, we also provide relationships of quasi-inner functions by comparing rationally invariant subspaces generated by them. Furthermore, we discuss fundamental properties of quasi-inner functions and quasi-inner divisors.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.2
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• pp.94-103
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• 1997

The WCHF-FSJTC (wavelet circular harmonic function frequency selective joint transform correlator) using th wavelet transformed CHF as the reference image in FSJTC is proposed for rotation invariant pattern recognition. Since the wavelet transform has the property of feature extraction, the proposed system can have the better DC (discrimination cpability) and the higher SNR(signal to noise ratio) compared with the conventional CHF-CJTC(circular harmonic function conventional joint transform correlator). And since the structure of the proposed system is FSJTC which can eliminate auto-correlation and cross-correlation between input images, it can eliminate false alarm caused by the overlapping among correlation peaks. The used wavelet functio is the morlet function, which is proper for the reference image used in this paper. the optimal dialation parameter and oscillation frequency of the wavelet function are also achieved with varying the parameters of the wavelet function. The computer simulation shows that the proposed system has the best performance when the dilation parameter is 0.8 and the oscillation frequency is 0.48.

• Journal of the Korean Statistical Society
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• v.18 no.1
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• pp.62-71
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• 1989

We consider a Markov proces ${X_n} on [0,\infty)^k$ which is generated by $X_{n+1} = f(X_n) + \varepsilon_{n+1}$ where f is a continuous, nondecreasing concave function. Sufficient conditions for the existence of a unique invariant probability measure for ${X_n}$ are obtained.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.661-678
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• 1995

In this paper we will estimate from above and below the values of the Bergman, Caratheodory and Kobayashi metrics for a vector X at z, where z is any point near a given point $z_0$ in the boundary of pseudoconvex domains in $C^n$.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.867-874
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• 1995

Linear invariance is closely related to the concept of uniform local univalence. We give a geometric proof that a holomorphic locally univalent function defined on the open unit disk is linearly invariant if and only if it is uniformly locally univalent.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.376-386
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• 1995

Designs for polynomial approximation to the unknown response function are considered. Optimality criteria are monotone functions of the mean squared error matrix of the least squares estimator. They correspond to the classical A-, D-, G- and Q-optimalities. Optimal first order designs are chosen from the invariant designs and then compared with optimal second order designs.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.2
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• pp.392-400
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• 1997

In this paper we porposed WCHF-fSDF filter to obtain a roration and scale-invariant correlation output. WCHF-fSDF filter is synthesized by each single CHF exttracted from scale-changed and wavelet tranformed imagesfor a refereence image as tranining images. The wavelet transform is defined as the correlation of an input image with a wavelet function. Therefore two 4f optical correlation systems are needed for pattern recognition using wavelet transform. We here include the wavelet function for the input image in the process of the proposed filter design and substitute the two 4f optical correlation system with a single 4f optical correlation system. The Performances of the proposed filter are compared with conventional CHF-SDF, POCHF-SDF filters through the computer simulation. The results of computer simulation show that the proposed filter has the rotation and scale-invariant correlation output and it has better performances than thoseof the conventioanl filters.

• Kyungpook Mathematical Journal
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• v.51 no.4
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• pp.385-393
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• 2011

The aim of this paper is to introduce and study the sequence spaces [w, ${\theta}$, F, p, q]$_{\infty}({\Delta}_{\upsilon}^m)$, [w, ${\theta}$, F, p, q]$_1({\Delta}_{\upsilon}^m)$ and [w, ${\theta}$, F, p, q]$_0({\Delta}_{\upsilon}^m)$, which arise from the notions of generalized difference sequence space, lacunary convergence, invariant mean and a sequence of Moduli $F=(f_k)$. We establish some inclusion relations between these spaces under some conditions.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.10
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• pp.2660-2669
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• 1996

In this paper, it is called nonlinear-symbol CPFSK(NCPFSK) which is modulated by the nonlinear function of information carrying phase function within all symbol interval produce time invariant trellis structure. In general, the bit error probability performance of CPFSK modultion scheme within given signal constellation is determined from the number of memory elementsof continuous phase encoder, i.e. number of state. In this paper the number of state of analyticall designed NCPFSK is time invariant. And the nonlinear symbol mapping function of the proposed moudlation produces the nonlinear symbol andthe phase state of the modulation for updating the phase function of NCPFSK. It si shown in this paper nonlinear symbol CPFSK with multiple TCM to make further improvements in d$^{2}$, and analyzed BER performance in AWGN channel envioronments.hannel envioronments.