We pose a conjecture for the expected number of generators of the ideal of the union C of s general rational irreducible curves in P r. By using the computer we prove the conjecture for C of low degree d (e.g. if s = 1 for d 80 and if s 10 for d 40).

Given a right ideal I in ring R, the idealizer of R is largest subring which becomes two-sided ideal. In this paper we consider idealizers second Weyl algebra A2, differential operators on k[x,y] (in characteristic 0). Specifically, let f be polynomial x and y defines an irreducible curve whose singularities are all cusps. We show that fA2 A2 always left noetherian, extending work McCaffrey.

We investigate Sharifan and Moradi’s closed neighborhood ideal of a finite simple graph, which is square-free monomial in polynomial ring over field. explicitly describe the minimal irreducible decompositions these ideals. also characterize trees whose ideals are Cohen–Macaulay; particular, this property for characteristic independent.

Traumatic dislocation of the knee is an uncommon but serious injury, associated with extensive soft-tissue damage and the danger ofneurological and vascular involvement. Kennedy (1963) described twenty-two cases, discussing the mechanism of production and the high incidence of popliteal artery involvement, particularly in anterior dislocations. Griswold ( 195 1 ) and Quinlan and Sharrard ( 1958...

This article investigates the codimension of commutator spaces [I, B(H)] of operator ideals on a separable Hilbert space, i.e., “How many traces can an ideal support?” We conjecture that the codimension can be only zero, one, or infinity. Using the arithmetic mean (am) operations on ideals introduced in [13] and the analogous arithmetic mean operations at infinity (am-∞) that we develop extensi...

We investigate the symmetry component of the center variety of polynomial differential systems, corresponding to systems with an axis of symmetry in the real plane. We give a general algorithm to find this component, compute its dimension and show that it is irreducible. We show that our methods provide a simple way to compute the radical of the ideal generated by the focus quantities and, ther...

In this paper, we present a modular strategy which describes key properties of the absolute primary decomposition of an equidimensional polynomial ideal defined by polynomials with rational coefficients. The algorithm we design is based on the classical technique of elimination of variables and colon ideals and uses a tricky choice of prime integers to work with. Thanks to this technique, we ca...

In the last twenty years several methods for computing primary decompositions of ideals in multivariate polynomial rings over fields (Seidenberg (1974), Lazard (1985), Kredel (1987), Eisenbud et al. (1992)), the integers (Seidenberg, 1978), factorially closed principal ideal domains (Ayoub (1982), Gianni et al. (1988)) and more general rings (Seidenberg, 1984) have been proposed. A related prob...

Distal interphalangeal joint dislocations are only rarely complex and irreducible. We present a case and illustrate our approach to management of this problem. Open reduction is necessary, and preferred approach is volar. It is imperative to identify the injured soft tissue and repair them as is feasible.

The diagonal in a product of projective spaces is cut out by the ideal of 2×2-minors of a matrix of unknowns. The multigraded Hilbert scheme which classifies its degenerations has a unique Borel-fixed ideal. This Hilbert scheme is generally reducible, and its main component is a compactification of PGL(d)/PGL(d). For n = 2 we recover the manifold of complete collineations. For projective lines ...