We consider a special case of the problem of computing the Galois group of a system of linear ordinary differential equations Y ′ = MY, M ∈ C(x)n×n. We assume that C is a computable, characteristic-zero, algebraically closed constant field with factorization algorithm. There exists a decision procedure, due to Compoint and Singer, to compute the group in case the system is completely reducible....

Let M be a simple manifold, and F be a component of ∂M of genus two. For a slope γ on F , we denote by M(γ) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of γ on F . In this paper, we shall prove that there is at most one separating slope γ on F so that M(γ) is ∂-reducible.

Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...

We study the relation between zero loci of Bernstein-Sato ideals and roots b-functions obtain a criterion to guarantee that reducible polynomial are determined by locus associated ideal. Applying together with result Maisonobe we prove set b-function free hyperplane arrangement is its intersection lattice. also relative characteristic cycles for arbitrary central arrangements. multivariable n/d...

Let M be a simple 3-manifold such that one component of ∂M , say F , has genus at least two. For a slope α on F , we denote by M(α) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of α on F . If M(α) is reducible, then α is called a reducing slope. In this paper, we shall prove that the distance between two separating, reducing slopes on F is at most 4.

The conversion of the reducible divalent cross-links in collagen to non-reducible multivalent cross-links in mature collagen has resulted in the identification of several new amino acids as the putative mature cross-link. None of these compounds has completely satisfied the necessary criteria. We have now isolated an amino acid of high Mr, derived from lysine, that is only present in high-Mr pe...

We introduce a practical synchronous stream cipher with provable security named QUAD. The cipher relies on the iteration of a multivariate quadratic system of m equations in n < m unknowns over a finite field. The security of QUAD is provably reducible to the conjectured intractability of the MQ problem, namely solving a multivariate system of quadratic equations.

Let S be a Heegaard splitting surface of a compact orientable 3-manifold M. If S is strongly irreducible, the manner in which it can intersect a ball or a solid torus in M is very constrained and the allowable configurations are simple and useful. Splitting surfaces not conforming to these simple local pictures must be weakly reducible.

It is shown that if M is a compact, connected, orientable hyperbolic 3-manifold whose boundary is a torus, and 7‘1, FZ are two slopes on i7M whose associated fillings are respectively a reducible manifold and one containing an essential torus, then the distance between these slopes is bounded above by 4. Under additional hypotheses this bound is improved Consequently the cabling conjecture is s...