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Rababah, Abedallah,Lee, Byung-Gook,Yoo, Jaechil M. Dekker 2007 Numerical functional analysis and optimization Vol.28 No.9-10
<P> In this article, we find the optimal r times degree reduction of Bézier curves with respect to the Jacobi-weighted L2-norm on the interval [0, 1]. This method describes a simple and efficient algorithm based on matrix computations. Also, our method includes many previous results for the best approximation with L1, L2, and L∞-norms. We give some examples and figures to demonstrate these methods.</P>
Best sextic approximation of circular arcs with thirteen equioscillations
Abedallah Rababah 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.1
We approximate a circular arc using a polynomial curve of degree 6. The approximation has least deviation from the x-axis and the error function is of degree 12; the error function equioscillates 13 times rather than the classical 8 times equioscillations that are mathematically guaranteed by the Borel and Chebyshev theorems without a method to find their approximation.
Generalized Chebyshev polynomials of third kind
Abedallah Rababah,Esraa Hijazi 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.3
In this paper, the generalized third-kind Chebyshev polynomials are considered. Motivated by the fact that the Bernstein polynomial basis is numerically stable, the generalized Chebyshev polynomials of third kind are characterized by writing them in terms of the Bernstein basis. This representation is given in explicit form. Moreover, the weighted denite integrals of the generalized third-kind Chebyshev polynomials multiplied with the Bernstein polynomials are found.
Saja Rababah,Aya Diab The Korean Society of Systems Engineering 2023 시스템엔지니어링학술지 Vol.19 No.2
Implementing Severe Accident Management (SAM) strategies is crucial for enhancing a nuclear power plant's resilience and safety against severe accidents conditions represented in the analysis of Station Blackout (SBO) event. Among these critical approaches, the In-Vessel Retention (IVR) through External Reactor Vessel Cooling (IVR-ERVC) strategy plays a key role in preventing vessel failure. This work is designed to evaluate the efficacy of the IVR strategy for a high-power density reactor APR1400. The APR1400's plant is represented and simulated under steady-state and transient conditions for a station blackout (SBO) accident scenario using the computer code, ASYST. The APR1400's thermal-hydraulic response is analyzed to assess its performance as it progresses toward a severe accident scenario during an extended SBO. The effectiveness of emergency operating procedures (EOPs) and severe accident management guidelines (SAMGs) are systematically examined to assess their ability to mitigate the accident. A group of associated key phenomena selected based on Phenomenon Identification and Ranking Tables (PIRT) and uncertain parameters are identified accordingly and then propagated within DAKOTA Uncertainty Quantification (UQ) framework until a statistically representative sample is obtained and hence determine the uncertainty bands of key system parameters. The Systems Engineering methodology is applied to direct the progression of work, ensuring systematic and efficient execution.
Debugging of Parallel Programs using Distributed Cooperating Components
Mrayyan, Reema Mohammad,Al Rababah, Ahmad AbdulQadir International Journal of Computer ScienceNetwork S 2021 International journal of computer science and netw Vol.21 No.12
Recently, in the field of engineering and scientific and technical calculations, problems of mathematical modeling, real-time problems, there has been a tendency towards rejection of sequential solutions for single-processor computers. Almost all modern application packages created in the above areas are focused on a parallel or distributed computing environment. This is primarily due to the ever-increasing requirements for the reliability of the results obtained and the accuracy of calculations, and hence the multiply increasing volumes of processed data [2,17,41]. In addition, new methods and algorithms for solving problems appear, the implementation of which on single-processor systems would be simply impossible due to increased requirements for the performance of the computing system. The ubiquity of various types of parallel systems also plays a positive role in this process. Simultaneously with the growing demand for parallel programs and the proliferation of multiprocessor, multicore and cluster technologies, the development of parallel programs is becoming more and more urgent, since program users want to make the most of the capabilities of their modern computing equipment[14,39]. The high complexity of the development of parallel programs, which often does not allow the efficient use of the capabilities of high-performance computers, is a generally accepted fact[23,31].
DEGREE REDUCTION OF BEZIER CURVES WITH CHEBYSHEV WEIGHTED G3-CONTINUITY
SALISU IBRAHIM,ABEDALLAH RABABAH 장전수학회 2020 Advanced Studies in Contemporary Mathematics Vol.30 No.4
This paper considers Chebyshev weighted G3-multi-degree reduction of B´ezier curves. Exact degree reduction is not possible, based on this fact, approximative process to reduce a given B´ezier curve of higher degree n to a B´ezier curve of lower degree m, m<n is required. The weight function w[t]=2t(1 − t), t ∈ [0, 1] is used with the L2 -norm in multi degree reduction with G3- continuity at the end points of the curve. Explicit results and comparisons are verified by examples. The numerical result obtained from the new method yields minimum approximation error, improves the approximation in the middle of the curve, and shows up helpful applications to many scientists and engineers on how to design and reconstruct complex systems.
Debugging of Parallel Programs using Distributed Cooperating Components
Mrayyan, Reema Mohammad,Al Rababah, Ahmad AbdulQadir International Journal of Computer ScienceNetwork S 2021 International journal of computer science and netw Vol.21 No.spc12
Recently, in the field of engineering and scientific and technical calculations, problems of mathematical modeling, real-time problems, there has been a tendency towards rejection of sequential solutions for single-processor computers. Almost all modern application packages created in the above areas are focused on a parallel or distributed computing environment. This is primarily due to the ever-increasing requirements for the reliability of the results obtained and the accuracy of calculations, and hence the multiply increasing volumes of processed data [2,17,41]. In addition, new methods and algorithms for solving problems appear, the implementation of which on single-processor systems would be simply impossible due to increased requirements for the performance of the computing system. The ubiquity of various types of parallel systems also plays a positive role in this process. Simultaneously with the growing demand for parallel programs and the proliferation of multiprocessor, multicore and cluster technologies, the development of parallel programs is becoming more and more urgent, since program users want to make the most of the capabilities of their modern computing equipment[14,39]. The high complexity of the development of parallel programs, which often does not allow the efficient use of the capabilities of high-performance computers, is a generally accepted fact[23,31].