• 대한수학회보
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• 제58권3호
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• pp.669-688
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• 2021

The aim of this paper is to prove the existence of an admissible inertial manifold for mild solutions to infinite delay evolution equation of the form $$\{{\frac{du}{dt}}+Au=F(t,\;u_t),\;t{\geq}s,\\\;u_s({\theta})={\phi}({\theta}),\;{\forall}{\theta}{\in}(-{{\infty}},\;0],\;s{\in}{\mathbb{R}},$$ where A is positive definite and self-adjoint with a discrete spectrum, the Lipschitz coefficient of the nonlinear part F may depend on time and belongs to some admissible function space defined on the whole line. The proof is based on the Lyapunov-Perron equation in combination with admissibility and duality estimates.

• 대한수학회지
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• 제35권4호
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• pp.903-931
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• 1998

Since the modular curves X(N) = $\Gamma$(N)\(equation omitted)＊ (N =1,2,3) have genus 0, we have field isomorphisms K(X(l))(equation omitted)C(J), K(X(2))(equation omitted)(λ) and K(X(3))(equation omitted)( $j_3$) where J, λ are the classical modular functions of level 1 and 2, and $j_3$ can be represented as the quotient of reduced Eisenstein series. When N = 4, we see from the genus formula that the curve X(4) is of genus 0 too. Thus the field K(X(4)) is a rational function field over C. We find such a field generator $j_4$(z) = x(z)/y(z) (x(z) = $\theta$$_3$((equation omitted)), y(z) = $\theta$$_4$((equation omitted)) Jacobi theta functions). We also investigate the structures of the spaces $M_{k}$($\Gamma$(4)), $S_{k}$($\Gamma$(4)), M(equation omitted)((equation omitted)(4)) and S(equation omitted)((equation omitted)(4)) in terms of x(z) and y(z). As its application, we apply the above results to quadratic forms.rms.

• 한국해양학회지
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• 제5권2호
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• pp.41-51
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• 1970

수권(Hydrosphere)은 기권(Atmosphere)과 암권(Lithosphere)의 중간에 있으며 이에 대한 연구는 지구 물리학 분야에서 가장 중요하게 다루어 지는 것 중의 하나이다. 특히 수권의 70% 이상을 차지하고 있는 해양에서의 환경 변화를 조사하는 것은 해황의 변동을 예측하여 수산업이나 기타의 해중 시설물을 설치하는 데 중요한 자료를 제공해 주는 기초 적인 분야이다.

• Structural Engineering and Mechanics
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• 제13권6호
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• pp.671-694
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• 2002

This paper presents theoretical investigation on the cross correlation between torsional vibration ($u_{\theta}$) and translation vibration ($u_x$) of asymmetrical structure under white noise excitation. The formula reveals that the cross correlation coefficient (${\rho}$) is a function of uncoupled frequency ratio (${\Omega}={\omega}_{\theta}/{\omega}_x$), eccentricity, and damping ratio (${\xi}$). Simulations involving acceleration records from fifteen different earthquakes show correlation coefficients results similar to the theoretical correlation coefficients. The uncoupled frequency ratio is the dominating parameter to ${\rho}$; generally, ${\rho}$ is positive for ${\omega}_{\theta}/{\omega}_x$ > 1.0, negative for ${\omega}_{\theta}/{\omega}_x$ < 1.0, and close to zero for ${\omega}_{\theta}/{\omega}_x$ = 1.0. When the eccentricity or damping ratio increases, ${\rho}$ increases moderately for small ${\Omega}$ (< 1.0) only. The relation among $u_x$, $u_{\theta}$ and corner displacement are best presented by ${\rho}$; a simple way to hand-calculate the theoretical dynamic corner displacements from $u_x$, $u_{\theta}$ and ${\rho}$ is proposed as an alternative to dynamic analysis.

• 충청수학회지
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• 제22권1호
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• pp.17-23
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• 2009

Let F be a finite real abelian extension of a global function field k with G = Gal(F/k). Assume that F is an extension field of the Hilbert class field $K_e$ of k and is contained in a cyclotomic function field $K_n$. Let $\ell$ be any prime number not dividing $ph_k{\mid}G{\mid}$. In this paper, we show that if $\theta{\in}\mathbb{Z}[G]$ annihilates the Sylow $\ell$-subgroup of ${\mathcal{O}}^{\times}_F/{\mathcal{C}}_F$, then (q-1)$\theta$ annihilates the Sylow $\ell$-subgroup of ${\mathcal{Cl}}_F$.

• 응용통계연구
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• 제7권2호
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• pp.113-130
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• 1994

본 논문에서는 Oh and Berger (1993)의 알고리즘을 확장하여, Oh and Berger의 알고리즘으로 효율적 처리가 어려웠던 복잡한 모양을 가진 다차원 함수의 적분에 보다 더 일반적으로 적용될 수 있는 알고리즘을 제시한다. 예를 들면 다봉함수이면서 동시에 기울어진 모양을 갖는 함수나 모든 극대점들이 다 파악되지 못한 경우 등이다. 제시된 알고리즘은 Oh and Berger의 알고리즘을 단계적으로 수행해 가면서 각 단계마다 새로운 부확률밀도 함수 (component density functin)를 함성 밀도 함수(mixture importance function) 형태인 중요함 수 (importance function에 더해 감으로써 중요함수를 적분 함수에 접근시킨다.

• 대한수학회논문집
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• 제39권2호
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• pp.345-352
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• 2024

We introduce a new class of bi-partition function c_k(n), which counts the number of bi-color partitions of n in which the second color only appears at the parts that are multiples of k. We consider two partitions to be the same if they can be obtained by switching the color of parts that are congruent to zero modulo k. We show that the generating function for c_k(n) involves the partial theta function and obtain the following congruences: c₂(27n + 26) ≡ 0 (mod 3) and c₃(4n + 2) ≡ 0 (mod 2).

• 한국안광학회지
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• 제10권4호
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• pp.273-281
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• 2005

착용한 안경의 무게가 코의 형상에 따라 코 면을 수직으로 누르는 힘과 코의 경사면으로 분해되는 분력을 코 면의 경사도를 결정짓는 경사각 ${\Psi}$을 포함한 공식으로 유도하였다. 경사각 ${\Psi}$는 정면 및 측면에서 측정한 코의 경사각 ${\theta}$ 및 ${\Phi}$의 함수로서 구해지며 $sin{\Psi}$, $cos{\Psi}$, $cot{\Psi}$의 수지 해석 프로그램을 사용하여 안경의 코 받침이 코 면에서 미끄러지거나/미끄러지지 않는 ${\theta}$, ${\Phi}$값의 범위 및 코 면과 코 받침 사이의 마찰계수 변화에 따른 ${\theta}$, ${\Phi}$의 범위를 예측하였다. ${\theta}$ 값이 일정할 때 ${\Phi}$ 값이 증가할수록 안경이 코 받침에 의해 코 면을 누르는 압력은 증가하고 미끄럼 분력은 감소하며, ${\Phi}$값을 고정시키면 ${\theta}$값 변화에 따라 마찬가지 효과가 발생한다.

• 천문학회지
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• 제33권2호
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• pp.89-95
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• 2000

As an efficient method to detect blending of general gravitational microlensing events, it is proposed to measure the shift of source star image centroid caused by microlensing. The conventional method to detect blending by this method is measuring the difference between the positions of the source star image point spread function measured on the images taken before and during the event (the PSF centroid shift, ${\delta}{\theta}$c,PSF). In this paper, we investigate the difference between the centroid positions measured on the reference and the subtracted images obtained by using the difference image analysis method (DIA centroid shift, ${\delta}{\theta}$c.DIA), and evaluate its relative usefulness in detecting blending over the conventional method based on ${\delta}{\theta}$c,PSF measurements. From this investigation, we find that the DIA centroid shift of an event is always larger than the PSF centroid shift. We also find that while ${\delta}{\theta}$c,PSF becomes smaller as the event amplification decreases, ${\delta}{\theta}$c.DIA remains constant regardless of the amplification. In addition, while ${\delta}{\theta}$c,DIA linearly increases with the increasing value of the blended light fraction, ${\delta}{\theta}$c,PSF peaks at a certain value of the blended light fraction and then eventually decreases as the fraction further increases. Therefore, measurements of ${\delta}{\theta}$c,DIA instead of ${\delta}{\theta}$c,PSF will be an even more efficient method to detect the blending effect of especially of highly blended events, for which the uncertainties in the determined time scales are high, as well as of low amplification events, for which the current method is highly inefficient.

• 대한수학회지
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• 제41권2호
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• pp.265-294
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• 2004

In this paper, using a simple formula, we evaluate the conditional Fourier-Feynman transforms and the conditional convolution products of cylinder type functions, and show that the conditional Fourier-Feynman transform of the conditional convolution product is expressed as a product of the conditional Fourier-Feynman transforms. Also, we evaluate the conditional Fourier-Feynman transforms of the functions of the forms exp {$\int_{O}^{T}$ $\theta$(s,$\chi$(s))ds}, exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))ds}$\Phi$($\chi$(T)), exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))d${\zeta}$(s)}, exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))d${\zeta}$(s)}$\Phi$($\chi$(T)) which are of interest in Feynman integration theories and quantum mechanics.