For a number of computational search problems the existence of a polynomial time algorithm for the problem implies that a polynomial time algorithm for the problem is constructively known Some instances of such self witnessing polynomial time complexity are presented Our main result demonstrates this property for the problem of computing the prime factorization of a positive integer based on a ...

We study the complexity of the isomorphism and automorphism problems for finite rings with unity. We show that both integer factorization and graph isomorphism reduce to the problem of counting automorphisms of rings. The problem is shown to be in the complexity class AM ∩ coAM and hence is not NP-complete unless the polynomial hierarchy collapses. Integer factorization also reduces to the prob...

The amount of fill-in occurring in the factorization can vary from zero to complete fill, and can be controlled by specifying either the maximum level of fill LFILL, or the drop tolerance DTOL. The factorization may be modified in order to preserve row sums, and the diagonal elements may be perturbed to ensure that the preconditioner is positive-definite. Diagonal pivoting may optionally be emp...

The amount of fill-in occurring in the factorization can vary from zero to complete fill, and can be controlled by specifying either the maximum level of fill LFILL, or the drop tolerance DTOL. The factorization may be modified in order to preserve row sums, and the diagonal elements may be perturbed to ensure that the preconditioner is positive-definite. Diagonal pivoting may optionally be emp...

A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (J. Zak, Phys. Today, 23 (2), 51 (1970)), and related representations termed q1q2 representations (together with their conjugates) are analysed, as well a...

LetF be a 2-factorization of the complete graphKv admitting an automorphism groupG acting primitively on the set of vertices. IfF consists of Hamiltonian cycles, thenF is the unique, up to isomorphisms, 2-factorization ofKpn admitting an automorphism group which acts 2-transitively on the vertex-set, see [A. Bonisoli, M. Buratti, G. Mazzuoccolo, Doubly transitive 2-factorizations, J. Combin.Des...

Determining shape and structure of moving objects from a single-camera video of their motion has been an active research area. Good, robust solutions to this problem enable, for example, the detection of hand gestures and facial expressions of a human subject by observation from a single camera. The aim of this project is to study how feature tracking and motion factorization can be coupled to ...

Abstract We associate a complete intersection singularity to graded matrix factorization of size two polynomial in three variables. show that we get an inverse the reduction singularities considered by C. T. Wall. study this for full strongly exceptional collections triangulated category factorizations constructed H. Kajiura, K. Saito, and second author.

in this paper, we study the arens regularity properties of module actions and we extend some proposition from baker, dales, lau and others into general situations. we establish some relationships between the topological centers of module actions and factorization properties of them with some results in group algebras. in 1951 arens shows that the second dual of banach algebra endowed with the e...

Students who have been taught new ideas need to develop their skills by carrying out further work in own time. This often consists of a series exercises which must be completed. While students can choose themselves from online sources, they will learn more quickly and easily if the are specifically tailored needs. A good teacher always aim do this, but with large groups typically take advantage...