Recently, recursive blocked algorithms for solving triangular one-sided and two-sided Sylvester-type equations were introduced by Jonsson and K̊agström. This elegant yet simple technique enables an automatic variable blocking that has the potential of matching the memory hierarchies of today’s HPC systems. The main parts of the computations are performed as level 3 general matrix multiply and ad...

Building on recent work of Jaikin-Zapirain, we provide a homological criterion for ring to be pseudo-Sylvester domain, that is, admit division fractions over which all stably full matrices become invertible. We use the study skew Laurent polynomial rings free ideal (firs). As an application our methods, prove crossed products with free-by-{infinite cyclic} and surface groups are domains uncondi...

AMA Chukwu C, Sunday Ede S, Egbumike J, Nwabueze I, Okoh Ojukwu C. Geriatric physiotherapy care: exploring the state of affairs in southeast Nigeria. Physiotherapy Review. 2023;27(2):5-18. doi:10.5114/phr.2023.128857. APA Chukwu, C., Ede, S., Egbumike, J., Nwabueze, I., Okoh, & Ojukwu, (2023). Review, 27(2), 5-18. https://doi.org/10.5114/phr.2023.128857 Chicago Ceaser Sylvester, Stephen Joseph ...

We consider one of the fundamental problems classical invariant theory - research Hilbert polynomials for algebra invariants Lie group S L 2 . Form gives us important information about structure algebra. Besides, coefficients and degree polynomial play an role in Algebraic Geometry. It is well-known that function n -invariants quasi-polynomial. The Cayley-Sylvester formula calculation values co...

In this paper, the eigenvalues of various non-Sylvester Hadamard matrices constructed by monomial permutation matrices are derived, which shows the relation between the eigenvalues of the newly constructed matrix and Sylvester Hadamard matrix. * The authors are with School of Electrical Engineering and Computer Science, Seoul National University, Seoul, Korea, ([email protected]). Paper No....

X iv :m at h/ 03 10 27 6v 2 [ m at h. N T ] 1 3 M ay 2 00 4 ON THE HEIGHT OF THE SYLVESTER RESULTANT CARLOS D’ANDREA AND KEVIN G. HARE Abstract. Let n be a positive integer. We consider the Sylvester resultant of f and g, where f is a generic polynomial of degree 2 or 3 and g is a generic polynomial of degree n. If f is a quadratic polynomial, we find the resultant’s height. If f is a cubic pol...

Let a and b be two polynomials having numerical coeecients. We consider the question: when are a and b relatively prime? Since the coeecients of a and b are approximant, the question is the same as: when are two polynomials relatively prime, even after small perturbations of the coeecients? In this paper we provide a numeric parameter for determining that two polynomials are prime, even under s...

In 1853 J. Sylvester introduced a family of double sum expressions for two finite sets of indeterminates and showed that some members of the family are essentially the polynomial subresultants of the monic polynomials associated with these sets. In 2009, in a joint work with C. D’Andrea and H. Hong we gave the complete description of all the members of the family as expressions in the coefficie...

Let Vn be the SL2-module of binary forms of degree n and let V = V1 ⊕ V3 ⊕ V4. We show that the minimum number of generators of the algebra R = C[V ]2 of polynomial functions on V invariant under the action of SL2 equals 63. This settles a 142-year old question.

This paper presents a way to construct the Sylvester A-resultant matrix for three bi-degree (m; n) polynomials whose exponent set is cut oo by rectangles at the corners. The paper also shows that the determinant of this matrix does give the resultant of the three polynomials.