• The Pure and Applied Mathematics
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• v.16 no.4
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• pp.405-416
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• 2009

In this study we are concerned with the problem of approximating a locally unique solution of an equation in a Banach space setting using Newton's and modified Newton's methods. We provide weaker convergence conditions for both methods than before [5]-[7]. Then, we combine Newton's with the modified Newton's method to approximate locally unique solutions of operator equations. Finer error estimates, a larger convergence domain, and a more precise information on the location of the solution are obtained under the same or weaker hypotheses than before [5]-[7]. The results obtained here improve our earlier ones reported in [4]. Numerical examples are also provided.

• International Journal of Reliability and Applications
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• v.2 no.1
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• pp.37-48
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• 2001

This paper presents a new dynamic human reliability analysis method and its application for quantifying the human error probabilities in implementing management action. For comparisons of current HRA methods with the new method, the characteristics of THERP, HCR, and SLIM-MAUD, which are most frequency used method in PSAs, are discussed. The action associated with implementation of the cavity flooding during a station blackout sequence is considered for its application. This method is based on the concepts of the quantified correlation between the performance requirement and performance achievement. The MAAP 3.0B code and Latin Hypercube sampling technique are used to determine the uncertainty of the performance achievement parameter. Meanwhile, the value of the performance requirement parameter is obtained from interviews. Based on these stochastic obtained, human error probabilities are calculated with respect to the various means and variances of the things. It is shown that this method is very flexible in that it can be applied to any kind of the operator actions, including the actions associated with the implementation of accident management strategies.

• Computers and Concrete
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• v.16 no.2
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• pp.329-342
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• 2015

The present paper aims at developing a method to accommodate multi-surface concrete plasticity from the point of view of a consistency concept applied to general tangent operators. The idea is based on a Taylor series expansion of the actual effective stress at the stress point corresponding to the previous accumulated true stresses plus the current increment values, initially taken to be elastic. The proposed algorithm can be generalized for any multi-surface criteria combination and has been tested here for typical cement-based materials. A few examples of application are presented to demonstrate the effectiveness of the multi-surface technique as used to a combination of Rankine and Drucker-Prager yield criteria.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.671-684
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• 2021

The tenacity of the current paper is to find connections between various subclasses of analytic univalent functions by applying certain convolution operator involving generalized hypergeometric distribution series. To be more specific, we examine such connections with the classes of analytic univalent functions k - 𝓤𝓒𝓥^* (𝛽), k - 𝓢^*_p (𝛽), 𝓡 (𝛽), 𝓡^𝜏 (A, B), k - 𝓟𝓤𝓒𝓥^* (𝛽) and k - 𝓟𝓢^*_p (𝛽) in the open unit disc 𝕌.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.859-882
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• 2021

In the proposed paper, a new algorithm based on Nonlinear Feedback Shift Register (NLFSR) and modified RC4A (Rivest Cipher 4A) cipher is introduced. NLFSR is used for image pixel scrambling while modified RC4A algorithm is used for pixel substitution. NLFSR used in this algorithm is of order 27 with maximum period 2^27-1 which was found using Field Programmable Gate Arrays (FPGA), a searching method. Modified RC4A algorithm is the modification of RC4A and is modified by introducing non-linear rotation operator in the Key Scheduling Algorithm (KSA) of RC4A cipher. Analysis of occlusion attack (up to 62.5% pixels), noise (salt and pepper, Poisson) attack and key sensitivity are performed to assess the concreteness of the proposed method. Also, some statistical and security analyses are evaluated on various images of different size to empirically assess the robustness of the proposed scheme.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.621-629
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• 2019

In this paper, we present a local convergence analysis of a three point method with convergence order $1.839{\ldots}$ for approximating a locally unique solution of a nonlinear operator equation in setting of Banach spaces. Using weaker hypotheses than in earlier studies, we obtain: larger radius of convergence and more precise error estimates on the distances involved. Finally, numerical examples are used to show the advantages of the main results over earlier results.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2018.06a
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• pp.198-199
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• 2018

본 논문은 초해상도 기술을 위한 CNN 구조를 제안한다. 제안하는 Gradient-SR 은 고해상도 영상이 고주파 신호와 저주파 신호로 분리될 수 있다는 점을 바탕으로 고역 통과 필터인 Sobel Operator 를 CNN 기반으로 구성한다. Gradient-SR 로부터 생성된 고주파 신호는 목표 크기로 보간 된 저해상도 입력 영상과 더해짐으로 고해상도 영상을 생성한다. 실험 영상은 VDSR 이 사용 한 291 개의 영상과 B100 영상을 이용한다. 제안하는 방법은 스케일 팩터 2 에 대한 초해상도 영상 생성 실험에서 약 200%의 속도 향상을 보인다.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.461-479
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• 2021

This paper includes a general version of Bessel multipliers in Hilbert C∗-modules. In fact, by combining analysis, an operator on the standard Hilbert C∗-module and synthesis, we reach so-called generalized Bessel multipliers. Because of their importance for applications, we are interested to determine cases when generalized multipliers are invertible. We investigate some necessary or sufficient conditions for the invertibility of such operators and also we look at which perturbation of parameters preserve the invertibility of them. Subsequently, our attention is on how to express the inverse of an invertible generalized frame multiplier as a multiplier. In fact, we show that for all frames, the inverse of any invertible frame multiplier with an invertible symbol can always be represented as a multiplier with an invertible symbol and appropriate dual frames of the given ones.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.99-110
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• 2022

The main object of this paper is to provide necessary and sufficient conditions for the generalized Struve functions of first kind to be in the classes 𝒮(k, λ) and 𝒞(k, λ). Furthermore, we give conditions for the integral operator 𝓛(m, c, z) = ∫^z₀(2 - u_p(t))dt to be in the class 𝒞^*(k, λ). Several corollaries and consequences of the main results are also considered.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.329-341
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• 2021

In this study, we consider an efficient and accurate finite difference method for the four underlying asset equity-linked securities (ELS). The numerical method is based on the operator splitting method with non-uniform grids for the underlying assets. Even though the numerical scheme is implicit, we solve the system of discrete equations in explicit manner using the Thomas algorithm for the tri-diagonal matrix resulting from the system of discrete equations. Therefore, we can use a relatively large time step and the computation of the ELS option pricing is fast. We perform characteristic computational test. The numerical test confirm the usefulness of the proposed method for pricing the four underlying asset equity-linked securities.