• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.199-213
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• 2006

We compute the holomorphic derivative of the harmonic measure associated to a $C^\infty$bounded domain in the plane and show that the exact Bergman kernel function associated to a $C^\infty$ bounded domain in the plane relates the derivatives of the Ahlfors map and the Szego kernel in an explicit way. We find several formulas for the exact Bergman kernel and the Szego kernel and the harmonic measure. Finally we survey some other properties of the holomorphic derivative of the harmonic measure.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.195-203
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• 2005

We show that the exact Bergman kernel function associated to a $C^{\infty}$ bounded domain in the plane relates the derivatives of the Ahlfors map in an explicit way. And we find several formulas relating the exact Bergman kernel to classical kernel functions in potential theory.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.101-108
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• 1998

For a smoothly bounded n-connected domain $\Omega$ in C, we get a formula representing the relation between the Szego" kernel associated with $\Omega$ and holomorphic mappings obtained from harmonic measure functions. By using it, we show that the coefficient of the above holomorphic map is zero in doubly connected domains.

• International Journal of Reliability and Applications
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• v.6 no.1
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• pp.1-12
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• 2005

A new test for testing that a life distribution is exponential against the alternative that it is harmonic new better (worse) than used in expectation upper tail HNBUET (HNWUET), but not exponential is presented based on the highly popular 'Kernel methods' of curve fitting. This new procedure is competitive with old one in the sense of Pitman's asymptotic relative efficiency, easy to compute and does not depend on the choice of either the band width or kernel. It also enjoys good power.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.449-457
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• 2003

On the setting of the upper half-space of the Euclidean space $R^{n}$, we show that to each weighted harmonic Bergman function $u\;\epsilon\;b^p_{\alpha}$, there corresponds a unique conjugate system ($upsilon$_1,…, $upsilon_{n-1}$) of u satisfying $upsilon_j{\epsilon}\;b^p_{\alpha}$ with an appropriate norm bound.

• International Journal of Reliability and Applications
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• v.7 no.2
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• pp.89-99
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• 2006

A new classes of life distribution, namely harmonic used better than aged in expectation in upper tail (HUBAEUT) is introduced. Testing exponentiality against this class is investigated using kernel method. The limiting null and nonnull distribution of the test statistics is normal and the null variance is calculated exactly. Selected critical values are tabulated for sample sizes of 5(1)40. Power of the test are estimated by simulation. the efficacies of the test statistics used for testing against HUBAEUT are calculated for som common alternatives and are compared to some other procedures. It is shown that proposed test is simple, has high relative efficiency and power for some commonly used alternatives. The set of real data are used as an examples to elucidate the use of the proposed test statistics for practical reliability.

• Speech Sciences
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• v.12 no.4
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• pp.17-29
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• 2005

Time-frequency representation reveals some useful information about instantaneous frequency, instantaneous bandwidth and boundary of each AM-FM component of a speech signal. In many cases, the instantaneous frequency of each component is not constant. The variability of instantaneous frequency causes degradation of resolution in time-frequency representation. This paper presents a method of adaptively adjusting the transform kernel for preventing degradation of resolution due to time-varying instantaneous frequency. The transform kernel is the form of frequency modulated function. The modulation function in the transform kernel is determined by the estimate of instantaneous frequency which is approximated by first order polynomial at each time instance. Also, the window function is modulated by the estimated instantaneous. frequency for mitigation of fringing. effect. In the proposed method, not only the transform kernel but also the shape and the length of. the window function are adaptively adjusted by the instantaneous frequency of a speech signal.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.975-1002
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• 2005

On the setting of the upper half-space H of the Eu­clidean n-space, we show the boundedness of weighted Bergman projection for 1 < p < $\infty$ and nonorthogonal projections for 1 $\leq$ p < $\infty$ . Using these results, we show that Bergman norm is equiva­ lent to the normal derivative norms on weighted harmonic Bergman spaces. Finally, we find the dual of b$\_{$^{1}$.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.469-483
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• 2001

The configuration space and phase space oscillatory path integrals are computed in the case of the stochastic Schrodinger equation for the harmonic oscillator with a stochastic term of the form (K$\psi$(sub)t)(x) o dW(sub)t, where K is either the position operator or the momentum operator, and W(sub)t is the Wiener process. In this way formulae are derived for the stochastic analogues of the Mehler kernel.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.269-278
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• 2008

Let ${\partial}D$ be the boundary of the open unit disk D in the complex plane and $L^p({\partial}D)$ the class of all complex, Lebesgue measurable function f for which $\{\frac{1}{2\pi}{\int}_{-\pi}^{\pi}{\mid}f(\theta){\mid}^pd\theta\}^{1/p}<{\infty}$. Let P be the orthogonal projection from $L^p({\partial}D)$ onto ${\cap}_{n<0}$ ker $a_n$. For $f{\in}L^1({\partial}D)$, ${\hat{f}}(z)=\frac{1}{2\pi}{\int}_{-\pi}^{\pi}P_r(t-\theta)f(\theta)d{\theta}$ is the harmonic extension of f. Let ${\hat{P}}$ be the composition of P with the harmonic extension. In this paper, we will show that if $1, then ${\hat{P}}:L^p({\partial}D){\rightarrow}H^p(D)$ is bounded. In particular, we will show that ${\hat{P}}$ is unbounded on $L^{\infty}({\partial}D)$.