Combining FCA software and Sage.
(2010)
Presentation / Conference Contribution
Priss, U. (2010, October). Combining FCA software and Sage. Presented at International Conference on Concept Lattices and Their Applications
Techniques for dual forms of Reed-Muller expansion conversion. (2008)
Journal Article
Yang, M., Wang, L. Y., Tong, J. R., & Almaini, A. E. A. (2008). Techniques for dual forms of Reed-Muller expansion conversion. Integration, the VSLI Journal, 41, 113-122. https://doi.org/10.1016/j.vlsi.2007.02.001Dual forms of Reed-Muller (DFRM) are implemented in OR/XNOR forms, which are based on the features of coincidence operation. Map folding and transformation techniques are proposed for the conversion between Boolean and DFRM expansions. However, map t... Read More about Techniques for dual forms of Reed-Muller expansion conversion..
Exact minimization of large fixed polarity dual form of reed-muller functions (2007)
Journal Article
Yang, M., Xu, H., Wang, L. Y., Tong, J. R., & Almaini, A. E. A. (2007). Exact minimization of large fixed polarity dual form of reed-muller functions. Solid-State and Integrated Circuit Technology, 1931-1933. https://doi.org/10.1109/ICSICT.2006.306532Dual form of Reed-Muller (DFRM) expansions are implemented in OX/XNOR logic, which are based on the features of coincidence operation and are known as fixed polarity Canonical OR-Coincidence (COC) expansions. An efficient minimization method is propo... Read More about Exact minimization of large fixed polarity dual form of reed-muller functions.
FCA interpretation of relation algebra. (2006)
Presentation / Conference Contribution
Priss, U. (2006, February). FCA interpretation of relation algebra. Presented at 4th International Conference on Formal Concept AnalysisThis paper discusses an interpretation of relation algebra and fork algebra with respect to FCA contexts. In this case, "relation algebra" refers to the DeMorgan-Peirce-Schroeder-Tarski algebra and not to the "relational algebra" as described by Codd... Read More about FCA interpretation of relation algebra..
Novel synthesis method of mixed polarity reed-muller functions. (2005)
Presentation / Conference Contribution
Xia, Y., Ye, X., Wang, L. Y., Zou, Z., & Almaini, A. E. A. (2005, October). Novel synthesis method of mixed polarity reed-muller functions. Presented at Third IASTED International Conference on Circuits, Signals and Systems, CSS 2005In this paper a new approach is proposed to obtain a compact mixed polarity Reed-Muller form, starting from a fixed polarity Reed-Muller expression; a fixed polarity Reed-Muller function is expressed into a truth vector, the truth vector is shrunk an... Read More about Novel synthesis method of mixed polarity reed-muller functions..
Dynamic response simulation for a nonlinear system. (2005)
Journal Article
Roberts, D., & Hay, N. (2005). Dynamic response simulation for a nonlinear system. Journal of sound and vibration, 281(3-5), 783-798. https://doi.org/10.1016/j.jsv.2004.02.016Laboratory simulation testing has for many years contributed significantly to the durability and quality of motor vehicles. Most sophisticated test rigs use an iterative algorithm that generates the input drive files that reproduce service environmen... Read More about Dynamic response simulation for a nonlinear system..
On a representation of vector continued fractions. (1999)
Journal Article
Roberts, D. E. (1999). On a representation of vector continued fractions. Journal of Computational and Applied Mathematics, 105(1-2), 453-466. https://doi.org/10.1016/S0377-0427%2899%2900034-5Vector Pade approximants to power series with vector coefficients may be calculated using the three-term recurrence relations of vector continued fractions
if formulated in the framework of Clifford algebras. We show that the numerator and denominat... Read More about On a representation of vector continued fractions..
Modulo correlativity and its application in a multiple valued logic system (1998)
Journal Article
Wang, L. Y., Chen, X., & Almaini, A. E. A. (1998). Modulo correlativity and its application in a multiple valued logic system. International Journal of Electronics, 85(5), 561-570. https://doi.org/10.1080/002072198133851Several new concepts such as pseudoprime and correlativity, are presented. Then modulo subtraction and modulo division, which are very useful in computing the canonical expansion, are proposed in a multiple valued modulo algebra system with either a... Read More about Modulo correlativity and its application in a multiple valued logic system.
Algebraic properties of multiple-valued modulo systems and their applications to current-mode CMOS circuits. (1998)
Journal Article
Wang, L. Y., Chen, X., & Almaini, A. E. A. (1998). Algebraic properties of multiple-valued modulo systems and their applications to current-mode CMOS circuits. IEE proceedings. Computers and digital techniques, 145, 364-368. https://doi.org/10.1049/ip-cdt%3A19982204The paper presents the concepts of pseudoprime and modulo correlativity and establishes the relationships among completeness of modulo operations, uniqueness of solution of equations, invertibility of a square matrix, and correlativity of vectors in... Read More about Algebraic properties of multiple-valued modulo systems and their applications to current-mode CMOS circuits..
A vector Chebysev algorithm. (1998)
Journal Article
Roberts, D. (1998). A vector Chebysev algorithm. Numerical Algorithms, 17(1/2), 33-50. https://doi.org/10.1023/A%3A1011633327892We consider polynomials orthogonal relative to a sequence of vectors and derive their recurrence relations within the framework of Clifford algebras. We state sufficient conditions for the existence of a system of such polynomials. The coefficients i... Read More about A vector Chebysev algorithm..
On a vector q-d algorithm. (1998)
Journal Article
Roberts, D. (1998). On a vector q-d algorithm. Advances in computational mathematics, 8(3), 193-219. https://doi.org/10.1023/A%3A1018944213562Using the framework provided by Clifford algebras, we consider a noncommutative quotient-difference algorithm for obtaining the elements of a continued fraction corresponding to a given vector-valued power series. We
demonstrate that these elements... Read More about On a vector q-d algorithm..
Vector continued fraction algorithms. (1996)
Book Chapter
Roberts, D. E. (1996). Vector continued fraction algorithms. In R. Ablamowicz, P. Lounesto, & J. M. Parra (Eds.), Clifford algebras with numeric and symbolic computations (111-119). Birkhauser Verlag AG. https://doi.org/10.1007/978-1-4615-8157-4_7We consider the construction of rational approximations to given power series whose coefficients are vectors. The approximants are in the form of vector-valued continued fractions which may be used to obtain vector Pade
approximants using recurrence... Read More about Vector continued fraction algorithms..
On the algebraic foundations of the vector epsilon-algorithm. (1995)
Book Chapter
Roberts, D. E. (1995). On the algebraic foundations of the vector epsilon-algorithm. In R. Ablamowicz, & P. Lounesto (Eds.), Clifford algebras and spinor structures: A special volume dedicated to the memory of Albert Crumeyrolle (1919-1992) (343-361). Kluwer AcademicWe review the Clifford algebraic foundations of versions of the vector epsilon-algorithm. This involves the formation of rational approximants to vector-valued functions defined by a power series. We summarise their properties and demonstrate how a s... Read More about On the algebraic foundations of the vector epsilon-algorithm..