scholarly journals A Computational Method for Subdivision Depth of Ternary Schemes

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 817
Author(s):  
Faheem Khan ◽  
Ghulam Mustafa ◽  
Aamir Shahzad ◽  
Dumitru Baleanu ◽  
Maysaa M. Al-Qurashi
Keyword(s):  
Error Bounds ◽  
Numerical Experiments ◽  
Computational Method ◽  
Subdivision Schemes ◽  
Practical Applications ◽  
Refinement Procedure ◽  
Subdivision Algorithm ◽  
Subdivision Depth ◽  
Error Distance ◽  
New Framework

Subdivision schemes are extensively used in scientific and practical applications to produce continuous shapes in an iterative way. This paper introduces a framework to compute subdivision depths of ternary schemes. We first use subdivision algorithm in terms of convolution to compute the error bounds between two successive polygons produced by refinement procedure of subdivision schemes. Then, a formula for computing bound between the polygon at k-th stage and the limiting polygon is derived. After that, we predict numerically the number of subdivision steps (depths) required for smooth limiting shape based on the demand of user specified error (distance) tolerance. In addition, extensive numerical experiments were carried out to check the numerical outcomes of this new framework. The proposed methods are more efficient than the method proposed by Song et al.

scholarly journals A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 66 ◽  
Author(s):  
Aamir Shahzad ◽  
Faheem Khan ◽  
Abdul Ghaffar ◽  
Ghulam Mustafa ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Numerical Algorithm ◽  
Subdivision Schemes ◽  
Practical Applications ◽  
Curves And Surfaces ◽  
Geometrical Shapes ◽  
Subdivision Depth ◽  
Subdivision Curves

Subdivision schemes are extensively used in scientific and practical applications to produce continuous geometrical shapes in an iterative manner. We construct a numerical algorithm to estimate subdivision depth between the limit curves/surfaces and their control polygons after k-fold subdivisions. In this paper, the proposed numerical algorithm for subdivision depths of binary subdivision curves and surfaces are obtained after some modification of the results given by Mustafa et al in 2006. This algorithm is very useful for implementation of the parametrization.

scholarly journals A Novel Numerical Method for Computing Subdivision Depth of Quaternary Schemes

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 809
Author(s):  
Aamir Shahzad ◽  
Faheem Khan ◽  
Abdul Ghaffar ◽  
Shao-Wen Yao ◽  
Mustafa Inc ◽  
...  
Keyword(s):  
Numerical Method ◽  
Error Bound ◽  
Error Bounds ◽  
Computational Technique ◽  
Optimal Error ◽  
Subdivision Schemes ◽  
Subdivision Depth

In this paper, an advanced computational technique has been presented to compute the error bounds and subdivision depth of quaternary subdivision schemes. First, the estimation is computed of the error bound between quaternary subdivision limit curves/surfaces and their polygons after kth-level subdivision by using l0 order of convolution. Secondly, by using the error bounds, the subdivision depth of the quaternary schemes has been computed. Moreover, this technique needs fewer iterations (subdivision depth) to get the optimal error bounds of quaternary subdivision schemes as compared to the existing techniques.

scholarly journals Modulation of optical absorption in m-Fe1−xRuxS2 and exploring stability in new m-RuS2

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
H. Joshi ◽  
M. Ram ◽  
N. Limbu ◽  
D. P. Rai ◽  
B. Thapa ◽  
...  
Keyword(s):  
Optical Absorption ◽  
Phonon Dispersion ◽  
Applied Pressure ◽  
Orthorhombic Phase ◽  
Zero Point ◽  
Computational Method ◽  
Crystal Field Theory ◽  
Point Energy ◽  
Practical Applications ◽  
New Phase

AbstractA first-principle computational method has been used to investigate the effects of Ru dopants on the electronic and optical absorption properties of marcasite FeS2. In addition, we have also revealed a new marcasite phase in RuS2, unlike most studied pyrite structures. The new phase has fulfilled all the necessary criteria of structural stability and its practical existence. The transition pressure of 8 GPa drives the structural change from pyrite to orthorhombic phase in RuS2. From the thermodynamical calculation, we have reported the stability of new-phase under various ranges of applied pressure and temperature. Further, from the results of phonon dispersion calculated at Zero Point Energy, pyrite structure exhibits ground state stability and the marcasite phase has all modes of frequencies positive. The newly proposed phase is a semiconductor with a band gap comparable to its pyrite counterpart but vary in optical absorption by around 106 cm−1. The various Ru doped structures have also shown similar optical absorption spectra in the same order of magnitude. We have used crystal field theory to explain high optical absorption which is due to the involvement of different electronic states in formation of electronic and optical band gaps. Lӧwdin charge analysis is used over the customarily Mulliken charges to predict 89% of covalence in the compound. Our results indicate the importance of new phase to enhance the efficiency of photovoltaic materials for practical applications.

scholarly journals Improved Qrginv Algorithm for Computing Moore-Penrose Inverse Matrices

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Alireza Ataei
Keyword(s):  
Numerical Experiments ◽  
Computation Time ◽  
Computational Method ◽  
Real Matrix ◽  
Pseudoinverse Matrix ◽  
Arbitrary Matrix ◽  
Pseudo Inverse

Katsikis et al. presented a computational method in order to calculate the Moore-Penrose inverse of an arbitrary matrix (including singular and rectangular) (2011). In this paper, an improved version of this method is presented for computing the pseudo inverse of an m×n real matrix A with rank r>0. Numerical experiments show that the resulting pseudoinverse matrix is reasonably accurate and its computation time is significantly less than that obtained by Katsikis et al.

scholarly journals (2n-1)-Point Ternary Approximating and Interpolating Subdivision Schemes

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Muhammad Aslam ◽  
Ghulam Mustafa ◽  
Abdul Ghaffar
Keyword(s):  
Explicit Formula ◽  
Error Bounds ◽  
Computational Cost ◽  
Subdivision Schemes ◽  
Special Cases ◽  
Better Than

We present an explicit formula which unifies the mask of(2n-1)-point ternary interpolating as well as approximating subdivision schemes. We observe that the odd point ternary interpolating and approximating schemes introduced by Lian (2009), Siddiqi and Rehan (2010, 2009) and Hassan and Dodgson (2003) are special cases of our proposed masks/schemes. Moreover, schemes introduced by Zheng et al. (2009) can easily be generated by our proposed masks. It is also proved from comparison that(2n-1)-point schemes are better than2n-scheme in the sense of computational cost, support and error bounds.

scholarly journals Bernoulli multi-armed bandit problem under delayed feedback

2021 ◽  
pp. 20-26
Author(s):  
A. S. Dzhoha
Keyword(s):  
Clinical Trials ◽  
Online Learning ◽  
Numerical Experiments ◽  
Upper Bounds ◽  
Delayed Feedback ◽  
Software Framework ◽  
Bernoulli Distribution ◽  
Bandit Problem ◽  
Practical Applications ◽  
Theoretical Results

Online learning under delayed feedback has been recently gaining increasing attention. Learning with delays is more natural in most practical applications since the feedback from the environment is not immediate. For example, the response to a drug in clinical trials could take a while. In this paper, we study the multi-armed bandit problem with Bernoulli distribution in the environment with delays by evaluating the Explore-First algorithm. We obtain the upper bounds of the algorithm, the theoretical results are applied to develop the software framework for conducting numerical experiments.

scholarly journals An intelligent cross-border transaction system based on consortium blockchain: A case study in Shenzhen, China

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0252489
Author(s):  
Zhengtang Fu ◽  
Peiwu Dong ◽  
Siyao Li ◽  
Yanbing Ju
Keyword(s):  
Numerical Experiments ◽  
Critical Issue ◽  
Allocation System ◽  
Cross Border ◽  
Blockchain Technology ◽  
Profit Allocation ◽  
Smart Contract ◽  
The World ◽  
New Framework

Cross-border transactions have been more and more popular around the world. However, the current cross-border transactions still have risks and challenges, e.g., differences in regulation policies and unbalanced profits of banks. To address this critical issue, we construct a new framework for the transaction system with the support of blockchain technology. In this paper, we propose a new consortium blockchain system, namely asymmetric consortium blockchain (ACB), to ensure the implementation of cross-border transactions. Different from traditional consortium blockchain, the new blockchain system could support the supernode to regulate all the transactions timely. Furthermore, the new smart contract is designed to lower the opportunity loss for each node and make the profits allocation system fairer. In the end, the numerical experiments were carried out based on the transactions of Shenzhen and Hong Kong. The results show that the proposed ACB system is efficient to make the profit allocation fairer for the participants and keep intelligent for the new cross-border transaction system.

scholarly journals Transient frequency response based leak detection in water supply pipeline systems with branched and looped junctions

2016 ◽  
Vol 19 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Huan-Feng Duan
Keyword(s):  
Water Supply ◽  
Frequency Response ◽  
Numerical Experiments ◽  
Detection Method ◽  
Leak Detection ◽  
Transient Responses ◽  
Practical Applications ◽  
Supply Pipe ◽  
Pipeline Systems ◽  
Water Supply Pipeline

The transient frequency response (TFR) method has been widely developed and applied in the literature to identify and detect potential defects such as leakage and blockage in water supply pipe systems. This type of method was found to be efficient, economic and non-intrusive for pipeline condition assessment and diagnosis, but its applications so far are mainly limited to single and simple pipeline systems. This paper aims to extend the TFR-based leak detection method to relatively more complex pipeline connection situations. The branched and looped pipe junctions are firstly investigated for their influences to the system TFR, so that their effects can be characterized and separated from the effect of other components and potential leakage defects in the system. The leak-induced patterns of transient responses are derived analytically using the transfer matrix method for systems with different pipe junctions, which thereafter are used for the analysis of pipe leakage conditions in the system. The developed method is validated through different numerical experiments in this study. Based on the analytical analysis and numerical results, the applicability and accuracy as well as the limitations of the developed TFR-based leak detection method are discussed for practical applications in the paper.

scholarly journals MGRL: Predicting Drug-Disease Associations Based on Multi-Graph Representation Learning

2021 ◽  
Vol 12 ◽  
Author(s):  
Bo-Wei Zhao ◽  
Zhu-Hong You ◽  
Leon Wong ◽  
Ping Zhang ◽  
Hao-Yuan Li ◽  
...  
Keyword(s):  
High Efficiency ◽  
Drug Repositioning ◽  
Representation Learning ◽  
Computational Method ◽  
Graph Representation ◽  
Practical Applications ◽  
Study Results ◽  
Disease Associations ◽  
Better Than

Drug repositioning is an application-based solution based on mining existing drugs to find new targets, quickly discovering new drug-disease associations, and reducing the risk of drug discovery in traditional medicine and biology. Therefore, it is of great significance to design a computational model with high efficiency and accuracy. In this paper, we propose a novel computational method MGRL to predict drug-disease associations based on multi-graph representation learning. More specifically, MGRL first uses the graph convolution network to learn the graph representation of drugs and diseases from their self-attributes. Then, the graph embedding algorithm is used to represent the relationships between drugs and diseases. Finally, the two kinds of graph representation learning features were put into the random forest classifier for training. To the best of our knowledge, this is the first work to construct a multi-graph to extract the characteristics of drugs and diseases to predict drug-disease associations. The experiments show that the MGRL can achieve a higher AUC of 0.8506 based on five-fold cross-validation, which is significantly better than other existing methods. Case study results show the reliability of the proposed method, which is of great significance for practical applications.

scholarly journals A New Method (FTDCDF) for Blade Design of Axial/Mixed-Flow Compressors and its Applications

1987 ◽  
Author(s):  
Chuan-Gang Gu
Keyword(s):  
Good Accuracy ◽  
Design Method ◽  
Computational Method ◽  
Blade Design ◽  
Mixed Flow ◽  
Practical Applications ◽  
Controlled Diffusion ◽  
Aerodynamic Properties ◽  
Design Requirements ◽  
Design Result

A new design method with unequal work along the height of the blade in the axial/mixed-flow compressors, called The Flow-Type Design of Controlled Diffusion Factors (FTDCDF), has been developed in this paper. The idea of the method is to control the distribution of the diffusion factors along the height of the blade in the vaneless space in order to design the blade with good aerodynamic properties. The theoretical basis of FTDCDF and its computational method are studied in detail. The corresponding computer program has been developed and worked out with good results. Comparison between the results of this method and those of other one is made and discussed. It shows that the FTDCDF and program have good accuracy and convergence. On the basis of the author’s recent works, the practical applications of the FTDCDF for blade design and the choosing of distribution of diffusion factors are described in detail and the matching between the distributions of the diffusion factors and C1u(r1) is discussed. A better design result of FTDCDF satisfying various design requirements is presented.

Sign in / Sign up

Export Citation Format

Share Document