Intersection Of Classes Research Articles

Gorenstein liaison of 0-dimensional schemes

The theory of Gorenstein liaison has been developed during the last 3 years to generalize liaison theory of codimension 2 schemes to schemes of codimension ≥ 3 in a projective space. One of the main open questions in Gorenstein liaison theory is whether any arithmetically Cohen-Macaulay subscheme of ℙn is in the Gorenstein liaison class of a complete intersection. In this paper we prove that any set of general points lying on a rational normal scroll surface is in the Gorenstein liaison class of a complete intersection.

Graphs and Balanced Simplicial Complexes

We introduce for each directed graph G on n vertices a generalized notion of shellability of balanced (n−1)-dimensional simplicial complexes. In all cases, the closed cone generated by the flag f-vectors of all G-shellable complexes turns out to be an orthant, and we obtain similar descriptions for certain intersections of G-shellability classes. Our results depend in part on the fact that every interval of a partial order induced by leaks along the edges of a graph is an upper semidistributive lattice. The Mobius inversion formula for these intervals, together with further graph-theoretic observations, yield “graphical generalizations” of the sieve formula.

Fixed point spaces in actions of exceptional algebraic groups

Let G be a simple algebraic group of exceptional type acting transitively on an algebraic variety. We provide estimates for the dimensions of the subvarieties of fixed points of elements of G. These translate into estimates for the dimensions of intersections of conjugacy classes of G with closed subgroups.

Diagnostic Methodology for the Detection of Safety Problems at Intersections

There is an established consensus among traffic safety researchers that a nonlinear relationship exists between traffic exposure and safety. This relationship is reflected by the safety performance functions (SPFs) calibrated for various classes of roads and intersections. One of the main uses of SPFs is to identify locations with potential for accident reduction. While this application is certainly important, the use of SPFs provides no information related to the nature of the accident occurrence. Without being able to relate accident frequency and severity to roadway geometrics, traffic control devices, roadside features, roadway condition, driver behavior, or vehicle type, it is not possible to develop effective countermeasures. A methodology was developed to provide guidance in diagnostics of safety problems, recognition of accident patterns, and development of appropriate countermeasures. Considering that traffic accidents can be viewed as random Bernoulli trials, it is possible to detect deviation from the statistical process by computing observed cumulative probability for each of the accident characteristics. Detection of an accident pattern at an intersection suggests the presence of an element in the roadway environment that triggered a deviation from a random statistical process in the direction of reduced safety. Identification of such an element always provides a critical clue to accident causality.

Gorenstein liaison of divisors on standard determinantal schemes and on rational normal scrolls

Let C⊂ P n be an arithmetically Cohen–Macaulay subscheme. In terms of Gorenstein liaison it is natural to ask whether C is in the Gorenstein liaison class of a complete intersection. In this paper, we study the Gorenstein liaison classes of arithmetically Cohen–Macaulay divisors on standard determinantal schemes and on rational normal scrolls. As main results, we obtain that if C is an arithmetically Cohen–Macaulay divisor on a “general” arithmetically Cohen–Macaulay surface in P 4 or on a rational normal scroll surface S⊂ P n , then C is glicci (i.e. it belongs to the Gorenstein liaison class of a complete intersection).

Intersecting conical intersection seams in tetra-atomic molecules: the S1–S0 internal conversion in HNCO

Symmetry-allowed intersections of two states of different symmetry, different-symmetry intersections, are the class of conical intersection most commonly studied in small molecules. A same-symmetry seam of conical interaction, originating from the same two states, may intersect this different-symmetry seam. These intersections of intersections are themselves continuously connected, forming a multidimensional subspace in the symmetry-allowed seam. A confluence of seams requires changes in the conical topography which can affect nuclear dynamics significantly. The indirect photodissociation of HNCO to H + NCO results from an internal conversion attributable to the portion of the S0-S1 seam with HNCO in a trans configuration. A previously introduced perturbative analysis is used to show that a manifold of confluences of conical intersections exists in this region. These confluences can influence the internal conversion dynamics and should be incorporated into a detailed description of this process. This represents the first time a dynamically relevant manifold of confluences has been demonstrated in a tetra-atomic molecule.

Conference discussion of the nuclear few-body problem: questions and issues

We analyse the consequences of the Virasoro conjecture of Eguchi, Hori and Xiong for Gromov-Witten invariants, in the case of zero degree maps to the manifolds P1and P2 (or more generally, smooth projective curves and smooth simply connected projective surfaces). We obtain predictions involving intersections of psi and lambda classes on Mg,n. In particular, we show that the Virasoro conjecture for P2 implies the numerical part of Faber's conjecture on the tautological Chow ring of Mg.

Monomial Ideals and the Gorenstein Liaison Class of a Complete Intersection

In an earlier work, the authors described a mechanism for lifting monomial ideals to reduced unions of linear varieties. When the monomial ideal is Cohen–Macaulay (including Artinian), the corresponding union of linear varieties is arithmetically Cohen–Macaulay. The first main result of this paper is that if the monomial ideal is Artinian then the corresponding union is in the Gorenstein linkage class of a complete intersection (glicci). This technique has some interesting consequences. For instance, given any (d + 1)-times differentiable O-sequence H, there is a nondegenerate arithmetically Cohen–Macaulay reduced union of linear varieties with Hilbert function H which is glicci. In other words, any Hilbert function that occurs for arithmetically Cohen–Macaulay schemes in fact occurs among the glicci schemes. This is not true for licci schemes. Modifying our technique, the second main result is that any Cohen–Macaulay Borel-fixed monomial ideal is glicci. As a consequence, all arithmetically Cohen–Macaulay subschemes of projective space are glicci up to flat deformation.

Recursions for characteristic numbers of genus one plane curves

Characteristic numbers of families of maps of nodal curves to P2 are defined as intersection of natural divisor classes. (This definition agrees with the usual definition for families of plane curves.) Simple recursions for characteristic numbers of genus one plane curves of all degrees are computed.

The supersymmetric Camassa–Holm equation and geodesic flow on the superconformal group

We study a family of fermionic extensions of the Camassa–Holm equation. Within this family we identify three interesting classes: (a) equations, which are inherently Hamiltonian, describing geodesic flow with respect to an H1 metric on the group of superconformal transformations in two dimensions, (b) equations which are Hamiltonian with respect to a different Hamiltonian structure and (c) supersymmetric equations. Classes (a) and (b) have no intersection, but the intersection of classes (a) and (c) gives a system with interesting integrability properties. We demonstrate the Painlevé property for some simple but nontrivial reductions of this system, and also discuss peakon-type solutions.

Licci ideals and the non-almost complete intersection locus

We extend results of Huneke and Ulrich on the structure of ideals in the linkage class of a complete intersection, for the class of ideals which are linked to a complete intersection in an even number of steps. In particular for such ideals the non-almost complete intersection locus has codimension at most ten.

Heteroclinic primary intersections and codimension one Melnikov method for volume-preserving maps.

We study families of volume preserving diffeomorphisms in R(3) that have a pair of hyperbolic fixed points with intersecting codimension one stable and unstable manifolds. Our goal is to elucidate the topology of the intersections and how it changes with the parameters of the system. We show that the "primary intersection" of the stable and unstable manifolds is generically a neat submanifold of a "fundamental domain." We compute the intersections perturbatively using a codimension one Melnikov function. Numerical experiments show various bifurcations in the homotopy class of the primary intersections. (c) 2000 American Institute of Physics.

Representing the UMLS as an object-oriented database: modeling issues and advantages.

The Unified Medical Language System (UMLS) combines many well-established authoritative medical informatics terminologies in one knowledge representation system. Such a resource is very valuable to the health care community and industry. However, the UMLS is very large and complex and poses serious comprehension problems for users and maintenance personnel. The authors present a representation to support the user's comprehension and navigation of the UMLS. An object-oriented database (OODB) representation is used to represent the two major components of the UMLS-the Metathesaurus and the Semantic Network-as a unified system. The semantic types of the Semantic Network are modeled as semantic type classes. Intersection classes are defined to model concepts of multiple semantic types, which are removed from the semantic type classes. The authors provide examples of how the intersection classes help expose omissions of concepts, highlight errors of semantic type classification, and uncover ambiguities of concepts in the UMLS. The resulting UMLS OODB schema is deeper and more refined than the Semantic Network, since intersection classes are introduced. The Metathesaurus is classified into more mutually exclusive, uniform sets of concepts. The schema improves the user's comprehension and navigation of the Metathesaurus. The UMLS OODB schema supports the user's comprehension and navigation of the Metathesaurus. It also helps expose and resolve modeling problems in the UMLS.

Optimized Tensor-Product Approximation Spaces

This paper is concerned with the construction of optimized grids and approximation spaces for elliptic differential and integral equations. The main result is the analysis of the approximation of the embedding of the intersection of classes of functions with bounded mixed derivatives in standard Sobolev spaces. Based on the framework of tensor-product biorthogonal wavelet bases and stable subspace splittings, the problem is reduced to diagonal mappings between Hilbert sequence spaces. We construct operator adapted finite element subspaces with a lower dimension than the standard full-grid spaces. These new approximation spaces preserve the approximation order of the standard full-grid spaces, provided that certain additional regularity assumptions are fulfilled. The form of the approximation spaces is governed by the ratios of the smoothness exponents of the considered classes of functions. We show in which cases the so-called curse of dimensionality can be broken. The theory covers elliptic boundary value problems as well as boundary integral equations.

Cycles of small codimension on a simple - or -dimensional Abelian variety

Let be a simple - or -dimensional Abelian variety over the field of complex numbers, where is a prime number. Assume that one of the following conditions holds:1) is a totally real field of degree 1, 2 or 4 over ; 2) is a simple -dimensional Abelian variety of CM-type such that is a normal extension;3) is a simple -dimensional Abelian variety such that is an imaginary quadratic extension of .Then for every positive integer the -space is spanned by cohomology classes of intersections of divisors.

Milnor numbers and classes of local complete intersections

Milnor numbers and classes of local complete intersections

Substituent effects and the noncrossing rule: The importance of reduced symmetry subspaces. I. The quenching of OH(A 2Σ+) by H2

The effects of substituent substitution on the locus of a seam of conical intersection and the importance of conical intersections in the associated low symmetry subspaces are considered. For molecules with more than three atoms and with some symmetry the seam of conical intersection may well include an accidental symmetry-allowed portion involving two states of different symmetry. However, in regions of reduced point group symmetry, conical intersections involving two states of the same symmetry may exist. This later class of conical intersections is rarely considered although it could significantly alter the predicted outcome of a nonadiabatic process. The efficient quenching of OH(A 2Σ+)by H2, a consequence of OH–H2 conical intersections, is particularly compelling in this regard. Previous analyses have considered only the C2v2A1–2B2 accidental symmetry-allowed portion of the seam of conical intersection. It is demonstrated that when intersections of states of the same symmetry are considered conical intersections with Cs symmetry are found that are likely to play an important role in the quenching process.

Intersection of Conjugacy Classes of Chevalley Groups with Gauss Cells

Let G̃ be a proper Chevalley group or a finite twisted Chevalley group. We give some description of the intersections of noncentral conjugacy classes of G̃ with certain Gauss cells, which we call Coxeter cells. This generalizes previous results of the authors (Comm. Algebra, 1994, 22, 5935–5950; 1995, 23, 3085–3098; 1996, 24, 4447–4475). It is also the basis of yet another generalization of the same result involving weight functions on conjugacy classes.

Supergravity solutions for localized intersections of branes

We construct an explicit supergravity solution for a configuration of localized D4-brane ending on a D6-brane, restricted to the near horizon region of the latter. We generate this solution by dimensionally reducing the supergravity solution for a flat M5-brane in $R^{1,7} \times C^2/Z_N$ with the M5-brane partially embedded in $C^2/Z_N$. We describe the general class of localized intersections and overlaps whose supergravity solutions are constructible in this way.

Propriétés de l'intersection des classes de Gevrey et de certaines autres classes

It is well-known that, in the case of Gevrey classes as in the case of C k classes, a loss of regularity cannot be avoided in the division by a generic polynomial. We show here that the intersection of Gevrey classes inherits the same good properties as the C ∞ class. Indeed, we prove here a Whitney extension theorem, a Lojasiewicz theorem on regular situation, some theorems of division and preparation and a Whitney spectral theorem. In fact, this work deals with more general non-quasianalytic classes.