• 대한수학회보
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• 제51권6호
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• pp.1561-1577
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• 2014

In this paper, we define a conditional transform with respect to the Gaussian process, the conditional convolution product and the first variation of functionals via the Gaussian process. We then examine various relationships of the conditional transform with respect to the Gaussian process, the conditional convolution product and the first variation for functionals F in $S_{\alpha}$ [5, 8].

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제6권12호
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• pp.3296-3314
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• 2012

We present a novel approach for the simulation of color pencil effects using line integral convolution (LIC) to produce pencil drawings from images. Our key idea is to use a bilateral convolution filter to simulate the various effects of pencil strokes. Our filter resolves the drawbacks of the existing convolution-based schemes, and presents an intuitive control to mimic the properties of pencil strokes. We also present a scheme that determines stroke directions from the shapes to be drawn. Smooth tangent flows are used for the pixels close to feature lines, and partially parallel flows inside regions. The background is rendered using a flow of fixed direction. Using different styles of stroke directions increases the realism of the resulting images. This approach produces convincing pencil drawing effects from photographs.

• 대한기계학회논문집
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• 제15권6호
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• pp.1781-1791
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• 1991

본 연구에서는 천이온도하에 있는 물체의 균열의 거동을 연구하기 위하여 선 적분 형태의 J적분을 유도하고 유한요소법으로 수치계산하여 기존의 결과와 비교한다. 한편 관성항과 재료의 물성치가 J적분값에 미치는 영향을 검토한다.

• International Journal of Naval Architecture and Ocean Engineering
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• 제9권3호
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• pp.266-281
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• 2017

Hydroelastic interactions of a deformable floating body with random waves are investigated in time domain. Both hydroelastic motion and structural dynamics are solved by expansion of elastic modes and Fourier transform for the random waves. A direct and efficient structural analysis in time domain is developed. In particular, an efficient way of obtaining distributive loads for the hydrodynamic integral terms including convolution integral by using Fubini theory is explained. After confirming correctness of respective loading components, calculations of full distributions of loads in random waves are expedited by reformulating all the body loading terms into distributed forms. The method is validated by extensive convergence tests and comparisons against the counterparts of the frequency-domain analysis. Characteristics of motion/deformation responses and stress resultants are investigated through a parametric study with varying bending rigidity and types of random waves. Relative contributions of componential loads are identified. The consequence of elastic-mode resonance is underscored.

• 소음진동
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• 제10권4호
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• pp.679-685
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• 2000

A procedure is presented for calculating the magnitude and shape of impact pulses in a vibro-impact system when an arbitrary input force is applied to a point in the system. The procedure utilizes the condition that the displacements of two contacting point in the primary and secondary system are the same during a contacting period. The displacements of those points are calculated numerically through the convolution integral which involve the impulse response functions and applied forces. The validity of the calculation procedure is demonstrated by using it to calculated the impact forces of a simple system where a theoretical solution is known and also of systems for which other researchers have published results. The agreement between the results derived by the numerical method and the theoretical and also some published results is good.

• Korean Journal of Mathematics
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• 제31권4호
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• pp.521-536
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• 2023

This paper is a further development of the recent results by the author and coworker on the generalized sequential Fourier-Feynman transform for functionals in a Banach algebra Ŝ and some related functionals. We establish existence of the generalized first variation of these functionals. Also we investigate various relationships between the generalized sequential Fourier-Feynman transform, the generalized sequential convolution product and the generalized first variation of the functionals.

• 충청수학회지
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• 제26권2호
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• pp.323-342
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• 2013

Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $Xn:C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}:C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\cdots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\cdots},x(t_n),x(t_{n+1}))$, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n$ < $t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions which have the form $${\int}_{L_2[0,t]}{{\exp}\{i(v,x)\}d{\sigma}(v)}{{\int}_{\mathbb{R}^r}}\;{\exp}\{i{\sum_{j=1}^{r}z_j(v_j,x)\}dp(z_1,{\cdots},z_r)$$ for $x{\in}C[0,t]$, where $\{v_1,{\cdots},v_r\}$ is an orthonormal subset of $L_2[0,t]$ and ${\sigma}$ and ${\rho}$ are the complex Borel measures of bounded variations on $L_2[0,t]$ and $\mathbb{R}^r$, respectively. We then investigate the inverse transforms of the function with their relationships and finally prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the products of the conditional Fourier-Feynman transforms of each function.

• 대한수학회지
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• 제46권3호
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• pp.577-588
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• 2009

In this paper, the author studies the k-th commutators of oscillatory singular integral operators with a BMO function and phases more general than polynomials. For 1 < p < $\infty$, the $L^p$-boundedness of such operators are obtained provided their kernels belong to the spaces $L(log+L)^{k+1}(S^{n-1})$. The results of the corresponding maximal operators are also established.

• Kyungpook Mathematical Journal
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• 제19권1호
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• pp.135-139
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• 1979

We consider the problem that how must the production of certain item vary as a function of time, if for known losses due to depreciation the total amount of the product is to have a constant value. The integral equation associated with the problem is solved by an appeal to the convolution quotients. The production function comes out to be an expression containing the generalized Laguerre polynomials. The loss function and the production function are tabulated for different values of the parameter by using an IBM 370/145 computer.

• 대한수학회지
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• 제38권2호
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• pp.421-435
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• 2001

In this paper we use a general Fubini theorem established in [13] to obtain several Feynman integration formulas involving analytic Fourier-Feynman transforms. Included in these formulas is a general Parseval's relation.