Runlian Zhang^1,*, Rui Shu¹, Yongzhuang Wei¹, Hailong Zhang², Xiaonian Wu¹

CMC-Computers, Materials & Continua, Vol.76, No.2, pp. 1911-1927, 2023, DOI:10.32604/cmc.2023.041187

Abstract S-boxes can be the core component of block ciphers, and how to efficiently generate S-boxes with strong cryptographic properties appears to be an important task in the design of block ciphers. In this work, an optimized model based on the generative adversarial network (GAN) is proposed to generate 8-bit S-boxes. The central idea of this optimized model is to use loss function constraints for GAN. More specially, the Advanced Encryption Standard (AES) S-box is used to construct the sample dataset via the affine equivalence property. Then, three models are respectively built and cross-trained to generate 8-bit S-boxes based on three… More >

Changshun Liu¹, Yan Liu¹, Jingjing Song^1,*, Taihua Xu^1,2

Intelligent Automation & Soft Computing, Vol.37, No.2, pp. 2059-2075, 2023, DOI:10.32604/iasc.2023.039592

Abstract Attribute reduction, as one of the essential applications of the rough set, has attracted extensive attention from scholars. Information granulation is a key step of attribute reduction, and its efficiency has a significant impact on the overall efficiency of attribute reduction. The information granulation of the existing neighborhood rough set models is usually a single layer, and the construction of each information granule needs to search all the samples in the universe, which is inefficient. To fill such gap, a new neighborhood rough set model is proposed, which aims to improve the efficiency of attribute reduction by means of two-layer… More >

Siqintuya Jin¹, Bai-Ni Guo^2,*, Feng Qi^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.3, pp. 781-799, 2022, DOI:10.32604/cmes.2022.019941

Abstract In the paper, the authors collect, discuss, and find out several connections, equivalences, closed-form formulas, and combinatorial identities concerning partial Bell polynomials, falling factorials, rising factorials, extended binomial coefficients, and the Stirling numbers of the first and second kinds. These results are new, interesting, important, useful, and applicable in combinatorial number theory. More >

H. Hadavinia¹, K. Gordnian¹, J. Karwatzki¹, A. Aboutorabi¹

Structural Durability & Health Monitoring, Vol.2, No.4, pp. 197-206, 2006, DOI:10.3970/sdhm.2006.002.197

Abstract The cylindrical bending of thick laminated sandwich plates under static loading is studied based on the first order shear deformation theory (FSDT). FSDT generally requires a shear correction factor (SCF) to account for the deflection owing to the transverse shear. In this paper the SCF is derived using energy equivalence method. It is shown that depending on the mechanical and geometrical properties of the layers, the contribution of the transverse shear stress to the maximum deflection of the plate is variable and in some cases account for up to around 88% of the total deflection. The effects of non-dimensional parameters… More >

Jing Tang¹, Mei-e Fang^1,*, Guozhao Wang²

CMES-Computer Modeling in Engineering & Sciences, Vol.115, No.2, pp. 263-280, 2018, DOI: 10.3970/cmes.2018.01702

Abstract ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves. In this paper, we further propose a non-stationary subdivision method of hierarchically and efficiently generating ωB-spline curves of arbitrary order of ωB-spline curves and prove its Ck−2-continuity by two kinds of methods. The first method directly prove that the sequence of control polygons of subdivision of order k converges to a Ck−2-continuousωB-spline curve of order k. The second one is based on the theories upon subdivision masks and asymptotic equivalence etc., which is more convenient to be further extended to the case of surface subdivision. And the problem… More >

Shengping Shen¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.1, pp. 91-104, 2004, DOI:10.3970/cmes.2004.006.091

Abstract An atomistic level stress tensor is defined with physical clarity, based on the SPH method. This stress tensor rigorously satisfies the conservation of linear momentum, and is appropriate for both homogeneous and inhomogeneous deformations. The formulation is easier to implement than other stress tensors that have been widely used in atomistic analysis, and is validated by numerical examples. The present formulation is very robust and accurate, and will play an important role in the multiscale simulation, and in molecular dynamics. An equivalent continuum is also defined for the molecular dynamics system, based on the developed definition of atomistic stress and… More >

Mustafa Turkyilmazoglu^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.120, No.1, pp. 63-81, 2019, DOI:10.32604/cmes.2019.06858

Abstract A ratio approach based on the simple ratio test associated with the terms of homotopy series was proposed by the author in the previous publications. It was shown in the latter through various comparative physical models that the ratio approach of identifying the range of the convergence control parameter and also an optimal value for it in the homotopy analysis method is a promising alternative to the classically used h-level curves or to the minimizing the residual (squared) error. A mathematical analysis is targeted here to prove the equivalence of both the ratio approach and the traditional residual approach, especially… More >

W.C. Wang¹, F.L. Chang², Y.L. Liu¹, X. J. Wu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.5, pp. 411-431, 2015, DOI:10.3970/cmes.2015.107.411

Abstract The detection of macroscopic irregularities is an essential procedure during the production of gears, and it helps to guarantee the quality of electromechanical transmission equipment. The working principles of template matching and the image nonequivalence operation are described in detail in this paper. Gray-level transformation, edge-preserving filtering, image segmentation, feature extraction, and pattern recognition were analyzed, leading to the design of a defect detection system based on template matching and the nonequivalence operation, followed by the development of a hardware platform and application software for the system. The experimental results indicate that the proposed detection system could perform fast detection… More >

Hong-Hua Dai^1,2, Matt Schnoor², Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 459-498, 2012, DOI:10.3970/cmes.2012.084.459

Abstract In this study, the harmonic and 1/3 subharmonic oscillations of a single degree of freedom Duffing oscillator with large nonlinearity and large damping are investigated by using a simple point collocation method applied in the time domain over a period of the periodic solution. The relationship between the proposed collocation method and the high dimensional harmonic balance method (HDHB), proposed earlier by Thomas, Dowell, and Hall (2002), is explored. We demonstrate that the HDHB is not a kind of "harmonic balance method" but essentially a cumbersome version of the collocation method. In using the collocation method, the collocation-resulting nonlinear algebraic… More >

Xiaozhong Jin¹, Gang Li², N. R. Aluru³

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 447-462, 2001, DOI:10.3970/cmes.2001.002.447

Abstract Meshless methods using least-squares approximations and kernel approximations are based on non-shifted and shifted polynomial basis, respectively. We show that, mathematically, the shifted and non-shifted polynomial basis give rise to identical interpolation functions when the nodal volumes are set to unity in kernel approximations. This result indicates that mathematically the least-squares and kernel approximations are equivalent. However, for large point distributions or for higher-order polynomial basis the numerical errors with a non-shifted approach grow quickly compared to a shifted approach, resulting in violation of consistency conditions. Hence, a shifted polynomial basis is better suited from a numerical implementation point of… More >