Exact minimization of large fixed polarity dual form of reed-muller functions
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.2006.306532
Dual 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...
FCA interpretation of relation algebra.
Conference Proceeding
Priss, U. (2006)
FCA interpretation of relation algebra. https://doi.org/10.1007/11671404_17
This 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-Schroe...
Dynamic response simulation for a nonlinear system.
Journal Article
Roberts, D., & Hay, N. (2005)
Dynamic response simulation for a nonlinear system. Journal of sound and vibration, 281(3-5), (783-798). doi:10.1016/j.jsv.2004.02.016. ISSN 1095-8568
Laboratory simulation testing has for many years contributed significantly to the durability and quality of motor vehicles. Most sophisticated test rigs use an iterative algor...
On a representation of vector continued fractions.
Journal Article
Roberts, D. E. (1999)
On a representation of vector continued fractions. Journal of Computational and Applied Mathematics, 105(1-2), (453-466). doi:10.1016/S0377-0427(99)00034-5. ISSN 0377-0427
Vector Pade approximants to power series with vector coefficients may be calculated using the three-term recurrence relations of vector continued fractions
if formulated in th...
Modulo correlativity and its application in a multiple valued logic system.
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, 561-570. doi:10.1080/002072198133851. ISSN 0020-7217
Several new concepts such as pseudoprime and correlativity, are presented. Then modulo subtraction and modulo division, which are very useful in computing the canonical expans...
Algebraic properties of multiple-valued modulo systems and their applications to current-mode CMOS circuits.
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. doi:10.1049/ip-cdt:19982204. ISSN 1350-2387
The paper presents the concepts of pseudoprime and modulo correlativity and establishes the relationships among completeness of modulo operations, uniqueness of solution of eq...
A vector Chebysev algorithm.
Journal Article
Roberts, D. (1998)
A vector Chebysev algorithm. Numerical Algorithms, 17(1/2), (33-50). doi:10.1023/A:1011633327892. ISSN 1017-1398
We consider polynomials orthogonal relative to a sequence of vectors and derive their recurrence relations within the framework of Clifford algebras. We state sufficient condi...
On a vector q-d algorithm.
Journal Article
Roberts, D. (1998)
On a vector q-d algorithm. Advances in computational mathematics, 8(3), (193-219). doi:10.1023/A:1018944213562. ISSN 1019-7168
Using the framework provided by Clifford algebras, we consider a noncommutative quotient-difference algorithm for obtaining the elements of a continued fraction corresponding ...
Vector continued fraction algorithms.
Book
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. BioMed Central. doi:10.1007/978-1-4615-8157-4_7
We consider the construction of rational approximations to given power series whose coefficients are vectors. The approximants are in the form of vector-valued continued fract...
On the algebraic foundations of the vector epsilon-algorithm.
Book
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 Academic
We review the Clifford algebraic foundations of versions of the vector epsilon-algorithm. This involves the formation of rational approximants to vector-valued functions defin...