Nashed, M.Z., Votruba, G.F.: A unified operator theory of generalized inverses. In: Generalized Inverses and Applications (Proc. Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1973), pp. 1–109. Publication of Mathematics Research Center University Wisconsin, No. 32. Academic...
The result obtained can be parameterized to cover the class of all possible FIR inverses. In addition, by using the computation method of syzygy with the Grbner basis module, the syndrome matrix for a given -D convolutional encoder is shown. Furthermore, the theory of Grbner basis is applied...
representation of a quaternion matrix, we introduce a concept of norm of quaternion matrices, discuss singular values and generalized inverses of a quaternion matrix, study the QLS problem and derive two algebraic methods for finding solutions of the QLS problem in quaternionic quantum theory. ...
This is the first comprehensive textbook that provides a systematic and detailed analysis of initial and boundary value problems for differential-algebraic equations. The analysis is developed from the theory of linear constant coefficient systems via linear variable coefficient systems to general nonlinear...
It is not hard to see, with the above initial A0,G0 and H0, that the SDA_ls still works, again with exactly the same forms and updating formulae for Ak,Bk,Ck,Dk(1),Dk(2) and the inverses of Rk,Sk and Tk. One relevant difference for CAREs is that A0≠A but satisfies, from ...
Some concepts in semigroup theory can be interpreted in several algebraic structures. A generalization fA,B,fA,B(X) = A(X′)B of the complement operator (′) on Boolean matrices is made, where A and B denote any rectangular Boolean matrices. While (′) is an isomorphism between Boolean ...
The NTRU (Number Theory Research Unit) is a prominent post-quantum public key cryptography algorithm and a current focus of research. Although many NTRU variants have been proposed, a comprehensive generalization of these variants is still lacking. To address this issue, we propose the G-NTRU (...
Standard Genetic Code Group theory is the branch of mathematics that is used for studying symmetry. In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. 2.1. The Concept of a Group ...
The algebraic theory of surgery gives a necessary and sufficient chain level condition for a space with n-dimensional Poincare duality to be homotopy equivalent to an n-dimensional topological manifold. A relative version gives a necessary and sufficient chain level condition for a simple homotopy ...
and J.A. Stegun (1965): Handbook of mathematical functions, Dover Publication, New York 1965 Google Scholar Adams, M. and V. Guillemin (1996): Measure theory and probability, 2nd edition, Birkhäuser-Verlag, Basel Boston Berlin 1996 Google Scholar Adelmalek, N.N. (1974): On the ...