• 대한수학회지
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• 제35권3호
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• pp.559-574
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• 1998

Let the Gel'fand triple (E)$_{\beta}$/ ⊂ ( $L^2$) ⊂ (E)＊$_{\beta}$/ be the framework of white noise distribution theory constructed by Kon-dratiev and Streit. A new class of continuous multiplicative products on (E)$_{\beta}$/ is introduced and associated continuous derivations on (E)$_{\beta}$/ are discussed. Algebraic characterizations of first order differential operators on (E)$_{\beta}$/ are proved. Some applications are also discussed. $\beta$/ are proved. Some applications are also discussed.

• Communications for Statistical Applications and Methods
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• 제5권2호
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• pp.503-515
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• 1998

When a neutral particle beam(NPB) aimed at the object and receive a small number of neutron signals at the detector, it follows approximately Poisson distribution. Under the four assumptions in the presence of errors and uncertainties for the Poisson parameters, an exact probability distribution of neutral particles have been derived. The probability distribution for the neutron signals received by a detector averaged over the three sources of errors is expressed as a four-dimensional integral of certain data. Two of the four integrals can be evaluated analytically and thereby the integral is reduced to a two-dimensional integral. The monotone likelihood ratio(MLR) property of the distribution is proved by using the Cauchy mean value theorem for the univariate distribution and multivariate distribution. Its MLR property can be used to find a criteria for the hypothesis testing problem related to the distribution.

• 대한수학회지
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• 제37권6호
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• pp.1071-1084
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• 2000

We show that a weak solution of the Cauchy problem for he nonlinear Schrodinger equation, {i∂(sub)t u + ∂$^2$(sub)x u = f(u,u), t∈(-T,T), x∈R, u(0,x) = ø(x).} in the negative solbolev space H(sup)s has a smoothing effect up to real analyticity if the initial data only have a single point singularity such as the Dirac delta measure. It is shown that for H(sup)s (R)(s>-3/4) data satisfying the condition (※Equations, See Full-text) the solution is analytic in both space and time variable. The argument is based on the recent progress on the well-posedness result by Bourgain [2] and Kenig-Ponce-Vega [18] and previous work by Kato-Ogawa [12]. We give an improved new argument in the regularity argument.

• Structural Engineering and Mechanics
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• 제51권6호
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• pp.955-971
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• 2014

Large post-buckling behavior of Timoshenko beams subjected to non-follower axial compression loads are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. Two types of support conditions for the beams are considered. In the case of beams subjected to compression loads, load rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of lower-Carbon Steel. In the study, the relationships between deflections, rotational angles, critical buckling loads, post-buckling configuration, Cauchy stress of the beams and load rising are illustrated in detail in post-buckling case.

• 대한수학회지
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• 제51권3호
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• pp.635-654
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• 2014

We consider the Cauchy problem for a Keller-Segel-fluid model with degenerate diffusion for cell density, which is mathematically formulated as a porus medium type of Keller-Segel equations coupled to viscous incompressible fluid equations. We establish the global-in-time existence of weak solutions and bounded weak solutions depending on some conditions of parameters such as chemotactic sensitivity and consumption rate of oxygen for certain range of diffusive exponents of cell density in two and three dimensions.

• 한국통신학회논문지
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• 제18권1호
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• pp.143-149
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• 1993

An approach is presented for efficient numerical integration of the Sormnerfeld type integrals pertinent to the microstrip surface Green's function arising in the problem of an electric current point source on an infinite planar grounded dielectric substrate. This approach, valid for both lossless and lossy dielectric substrates, is based on the deformation of the integration contour via a coordinate transformation and Cauchy's residue theory, and identifies clearly the effects of surface waves. I ts useful application is in a rigorous moment method analysis of micros trip antenna arrays and microstrip guided wave structures. The efficiency and the usefulness of the present approach are emphasized through some numerical calculations of the impedance matrix elements with associated CPU times.

• 항공우주시스템공학회지
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• 제1권1호
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• pp.25-35
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• 2007

In this paper, the interlaminar crack problems of a fiber metal laminate (FML) under generalized plane deformation are studied using the theory of anisotropic elasticity. The crack is considered to be embedded in the matrix interlaminar region (including adhesive zone and resin rich zone) of the FML. Based on Fourier integral transformation and the stress matrix formulation, the current mixed boundary value problem is reduced to solving a system of Cauchy-type singular integral equations of the 1st kind. Within the theory of linear fracture mechanics, the stress intensity factors are defined on terms of the solutions of integral equations and numerical results are obtained for in-plane normal (mode I) crack surface loading. The effects of location and length of crack in the 3/2 and 2/1 ARALL, GLARE or CARE type FML's on the stress intensity factors are illustrated.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권2호
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• pp.91-100
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• 2018

In this paper, we propose a new method for template matching, patch ratio, to inpaint unknown pixels. Before this paper, many inpainting methods used sum of squared differences(SSD) or sum of absolute differences(SAD) to calculate distance between patches and it was very useful for closest patches for the template that we want to fill in. However, those methods don't consider about geometric similarity and that causes unnatural inpainting results for human visuality. Patch ratio can cover the geometric problem and moreover computational cost is less than using SSD or SAD. It is guaranteed about finding the most similar patches by Cauchy-Schwarz inequality. For ignoring unnecessary process, we compare only selected candidates by priority calculations. Exeperimental results show that the proposed algorithm is more efficent than Criminisi's one.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.339-350
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• 2005

A space-time fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the first-order time derivative is replaced with Caputo derivative of order $\alpha{\in}(0,1]$, and the second-order space derivative is replaced with a Riesz-Feller derivative of order $\beta{\in}0,2]$. We derive the solution of its Cauchy problem in terms of the Green functions and the representations of the Green function by applying its Fourier-Laplace transforms. The Green function also can be interpreted as a spatial probability density function (pdf) evolving in time. We do the same on another kind of space-time fractional advection-dispersion equation whose space and time derivatives both replacing with Caputo derivatives.

• International Journal of Ocean System Engineering
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• 제1권1호
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• pp.28-31
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• 2011

An attempt was made to compute the free surface deformation due to the impact of a water droplet. The Cauchy Poisson, i.e. the initial value problem, was solved with the kinematic and dynamic free surface boundary conditions linearized. The zero order Hankel transformation and Laplace transform were applied to the related equations. The initial condition for the free surface profile was derived from a captured video image. The effect of the surface tension was not significant with the water mass used in this investigation. The computed and observed free surface deformations were compared.