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Boolean function 1

Boolean logic algebra system 1

Clifford Fourier transform (CFT) 1

Clifford algebra 1

Order eigenvalue matrix 1

Sparse fast Clifford Fourier transform (SFCFT) 1

Sparse fast Fourier transform (sFFT) 1

Symmetric variable 1

Truth table 1

algebra equations 1

approximation space of generalization 1

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Approximation Space of Generalization and Rough Classification Algebra

Liu Yonghong

Strategic Study of CAE 2006, Volume 8, Issue 3,   Pages 39-48

Abstract: set, bit space set, protocol relation, rough set function of protocol relation, rough classification algebra, rough simple algebra, etc. , and a guess is also proposed.Based on the protocol relation, the rough quotient algebra and the rough subalgebra are constructed.

Keywords: approximation space of generalization     rough set     rough classification algebra     protocol relation     roughsimple algebra     rough quotient algebra     rough subalgebra    

Calculation of Cohesive Stress Along the Fictitious Crack Zone in Concrete Materials

Xu Shilang,Wang Limin

Strategic Study of CAE 2002, Volume 4, Issue 5,   Pages 53-58

Abstract: Similarly, two algebra equations for solving the two undefined parameters also for controlling the cohesive

Keywords: concrete     crack opening displacement     fictitious crack cohesive force     algebra equations    

An algorithm for identifying symmetric variables based on the order eigenvalue matrix Article

Xiao-hua LI, Ji-zhong SHEN

Frontiers of Information Technology & Electronic Engineering 2017, Volume 18, Issue 10,   Pages 1644-1653 doi: 10.1631/FITEE.1601052

Abstract: To simplify the process for identifying 12 types of symmetric variables in Boolean functions, we propose a new symmetry detection algorithm based on minterm expansion or the truth table. First, the order eigenvalue matrix based on a truth table is defined according to the symmetry definition of a logic variable. By analyzing the constraint conditions of the order eigenvalue matrix for 12 types of symmetric variables, an algorithm is proposed for identifying symmetric variables of the Boolean function. This algorithm can be applied to identify the symmetric variables of Boolean functions with or without don’t-care terms. The proposed method avoids the restriction by the number of logic variables of the graphical method, spectral coefficient methods, and AND-XOR expansion coefficient methods, and solves the problem of completeness in the fast compu-tation method. The algorithm has been implemented in C language and tested on MCNC91 benchmarks. The application results show that, compared with the traditional methods, the new algorithm is an optimal detection method in terms of the applicability of the number of logic variables, the Boolean function including don’t-care terms, detection type, and complexity of the identification process.

Keywords: Boolean function     Symmetric variable     Boolean logic algebra system     Order eigenvalue matrix     Truth table    

Sparse fast Clifford Fourier transform Article

Rui WANG, Yi-xuan ZHOU, Yan-liang JIN, Wen-ming CAO

Frontiers of Information Technology & Electronic Engineering 2017, Volume 18, Issue 8,   Pages 1131-1141 doi: 10.1631/FITEE.1500452

Abstract: The Clifford Fourier transform (CFT) can be applied to both vector and scalar fields. However, due to problems with big data, CFT is not efficient, because the algorithm is calculated in each semaphore. The sparse fast Fourier transform (sFFT) theory deals with the big data problem by using input data selectively. This has inspired us to create a new algorithm called sparse fast CFT (SFCFT), which can greatly improve the computing performance in scalar and vector fields. The experiments are implemented using the scalar field and grayscale and color images, and the results are compared with those using FFT, CFT, and sFFT. The results demonstrate that SFCFT can effectively improve the performance of multivector signal processing.

Keywords: (sFFT)     Clifford Fourier transform (CFT)     Sparse fast Clifford Fourier transform (SFCFT)     Clifford algebra    

Title Author Date Type Operation

Approximation Space of Generalization and Rough Classification Algebra

Liu Yonghong

Journal Article

Calculation of Cohesive Stress Along the Fictitious Crack Zone in Concrete Materials

Xu Shilang,Wang Limin

Journal Article

An algorithm for identifying symmetric variables based on the order eigenvalue matrix

Xiao-hua LI, Ji-zhong SHEN

Journal Article

Sparse fast Clifford Fourier transform

Rui WANG, Yi-xuan ZHOU, Yan-liang JIN, Wen-ming CAO

Journal Article