• 대한수학회지
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• 제51권4호
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• pp.679-702
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• 2014

Investigation of the numerical solution of singularly perturbed turning point problems dates back to late 1970s. However, due to the presence of layers, not many high order schemes could be developed to solve such problems. On the other hand, one could think of applying the convergence acceleration technique to improve the performance of existing numerical methods. However, that itself posed some challenges. To this end, we design and analyze a novel fitted operator finite difference method (FOFDM) to solve this type of problems. Then we develop a fitted mesh finite difference method (FMFDM). Our detailed convergence analysis shows that this FMFDM is robust with respect to the singular perturbation parameter. Then we investigate the effect of Richardson extrapolation on both of these methods. We observe that, the accuracy is improved in both cases whereas the rate of convergence depends on the particular scheme being used.

• 대한수학회논문집
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• 제36권3호
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• pp.465-483
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• 2021

Let 𝓗(𝔻) be the space of analytic functions on the unit disc 𝔻. Let 𝜓 = (𝜓_j)ⁿ_j=0 and 𝚽 = (𝚽_j)ⁿ_j=0 be such that 𝜓_j, 𝚽_j ∈ 𝓗(𝔻). The linear differential operator is defined by T_𝜓(f) = ∑ⁿ_j=0 𝜓_jf^(j), f ∈ 𝓗(𝔻). We characterize the boundedness and compactness of the difference operator (T_𝜓 - T_𝚽)(f) = ∑ⁿ_j=0 (𝜓_j - 𝚽_j) f^(j) between weighted-type spaces of analytic functions. As applications, we obtained boundedness and compactness of the difference of multiplication operators between weighted-type and Bloch-type spaces. Also, we give examples of unbounded (non compact) differential operators such that their difference is bounded (compact).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권3호
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• pp.175-187
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• 2010

This paper presents the numerical valuation of the two-asset step-down equitylinked securities (ELS) option by using the operator-splitting method (OSM). The ELS is one of the most popular financial options. The value of ELS option can be modeled by a modified Black-Scholes partial differential equation. However, regardless of whether there is a closedform solution, it is difficult and not efficient to evaluate the solution because such a solution would be represented by multiple integrations. Thus, a fast and accurate numerical algorithm is needed to value the price of the ELS option. This paper uses a finite difference method to discretize the governing equation and applies the OSM to solve the resulting discrete equations. The OSM is very robust and accurate in evaluating finite difference discretizations. We provide a detailed numerical algorithm and computational results showing the performance of the method for two underlying asset option pricing problems such as cash-or-nothing and stepdown ELS. Final option value of two-asset step-down ELS is obtained by a weighted average value using probability which is estimated by performing a MC simulation.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.125-130
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• 2016

A finite rank difference of two composition operators is studied on a Hilbert Lebesgue space or a Hilbert Hardy space.

• 지구물리와물리탐사
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• 제10권2호
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• pp.111-123
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• 2007

본 논문에서는 파동장 외삽(wavefield extrapolation)의 방향을 단순히 역시간(reverse time)으로 하여 적용하는 기존의 역시간 구조보정법(reverse time migration method)이 아닌, 묵시적으로 가정된 순방향 모델링(forward modeling) 연산자에 대한 정확한 어드조인트(adjoint) 연산자로서의 역시간 구조보정 연산자를 유도한다. 어드조인트 연산자를 얻는 방법으로는 우선 해당하는 순방향 연산자를 명시적인 행렬식의 형태로 정의하고 이에 대한 전치행렬식을 구한 후, 이러한 전치행렬식에 해당하는 연산자를 정의하는 접근법을 사용하였다. 정확한 어드조인트 관계에 있는 역시간 구조보정 연산자는 기존의 역시간 구조보정 연산자와 마찬가지로 구조보정의 목적으로 사용될 수 있을 뿐 아니라, 최소자승 구조보정(Least-squares migration)과 같은 역산을 통해서 지하구조 영상화를 할 때 필요로 하는 어드조인트 연산자를 정확하게 구현 할 수 있어 보다 정확한 역산 결과를 얻게 해준다.

• 대한인간공학회지
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• 제36권5호
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• pp.447-458
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• 2017

Objective: The purpose of this study is to present the basic guidelines for preventing human error by measuring and analyzing the risk of collision perceived by the ship operator in the collision risk situation by using Korea Coast Guard patrol ships. Background: In the last 5 years, 97.5% of the causes of ship collision occurred at the sea was caused by human factors. However, the rate of marine accidents due to human error has not been reduced yet. Experiments and researches on the ship operators using the ships in actual operation are rarely performed. Method: Using two K.C.G Ships on the sea, the ship measured by 30 persons who are the subject of the ship (ship operator) when both ships approach and the relative distance gradually decreases in four encounter situations, perceived ship collision risk (PSCR) data were analyzed by statistical analysis. Results: The age and boarding career of the ship operator in the situation of ship collision risks encountered a negative impact on perceived collision risk in all four opposing encounter situations S1 ($000^{\circ}$), S2 ($045^{\circ}$), S3 ($090^{\circ}$) and S4 ($135^{\circ}$) respectively. That is, the higher the age of the ship operator, the lower the perceived risk of collision and the lower the age, the higher the risk of collision. Also, there was a difference between the average of group A (20~30 years) and group B (40~50 years) according to age of the ship operators at $000^{\circ}$, $045^{\circ}$ and $090^{\circ}$ and there was no difference at $135^{\circ}$. The mean difference of the experience of boarding career was also significantly different between group A (less than 4 years) and group B (more than 5 years), but there was no significant difference at $135^{\circ}$. Conclusion: The results showed that age and boarding career of the ship operators had negative impact on perceived collision risk and there was a difference in perceived risk of collision according to age and abundance of boarding career. As a result, by focusing on the ship operators who are in the age group of 20~30 years old and have less than 4 years of experience in boarding the ship. It is expected that the effect of prevention of marine accidents can be expected by avoiding collision avoidance. Application: The results of this study can be used as policy data of related organizations to prevent human error of ship operators and as training data of training institutes.

• 대한수학회보
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• 제50권6호
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• pp.2035-2051
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• 2013

In this paper, we study numerical schemes for solving multi-dimensional option pricing problem. We compare the direct solving method and the Operator Splitting Method(OSM) by using finite difference approximations. By varying parameters of the Black-Scholes equations for the maximum on the call option problem, we observed that there is no significant difference between the two methods on the convergence criterion except a huge difference in computation cost. Therefore, the two methods are compatible in practice and one can improve the time efficiency by combining the OSM with parallel computation technique. We show numerical examples including the Equity-Linked Security(ELS) pricing based on either two assets or three assets by using the OSM with the Monte-Carlo Simulation as the benchmark.

• Kyungpook Mathematical Journal
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• 제55권4호
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• pp.909-931
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• 2015

This paper presents some new paranormed sequence spaces $X(r,s,t,p;{\Delta})$ where $X{\in}\{l_{\infty}(p),c(p),c_0(p),l(p)\}$ defined by using generalized means and difference operator. It is shown that these are complete linear metric spaces under suitable paranorms. Furthermore, the ${\alpha}$-, ${\beta}$-, ${\gamma}$-duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from $X(r,s,t,p;{\Delta})$ to X. Finally, it is proved that the sequence space $l(r,s,t,p;{\Delta})$ is rotund when $p_n$ > 1 for all n and has the Kadec-Klee property.

• 전자공학회논문지C
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• 제34C권4호
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• pp.36-44
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• 1997

An efficient context-free multiple-object segmentation using attention operator based on modified generalized symmetry transform is proposed and implemented by modifying a radial basis function network. By using the difference of intensity gradient, instead of te intensity gradient itself, in generalized symmetry tranform so as to make the attention operator to preserve the edges of the objects shape, an efficient context-free multiple-object segementation is proposed in which no a priori shape informtion on the objects is requried. The attention operator is implemented by using a modified radial basis function network which can reflect symmetry, and by using te edge pyramid of the input image, both of the local and the global symmetry of the objects are reflected simultaneously to make the multiple-object with different sizes be segmented with a singel fixed-size $n\timesm$ can be done with O(n) complexity. The simulaton results show that the proposed algorithm can efficiently be used in context-free multiple-object segmentation even for the low contrast IR images as well as for the images from the camera.

• Journal of applied mathematics & informatics
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• 제36권3_4호
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• pp.271-283
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• 2018

In this paper, we introduce various first order (p, q)-difference equations. We investigate solutions to equations which are linear (p, q)-difference equations and nonlinear (p, q)-difference equations. We also find some properties of (p, q)-calculus, exponential functions, and inverse function.