Inclusive\bar K^{0*} (892) andK 0*(892) production on silicon by 200 GeVK − andπ −

The production of the neutralK ^? (892) resonances by 200 GeVK ^? andπ ^? has been studied over the kinematic range 0.0<x _f<1.0 andp _t ² <5.0 GeV². Longitudinal and transverse momentum distributions are presented. In addition the decay angular distributions inK ^? fragmentation to \(\bar K^{0*} \) have been investigated.     

On characterizing collections arising from N-gons in the plane

Consider a labeled convex n-gon in the plane and a point x in general position in the interior. We associate with this a collection (x) of 3-element sets, namely those 3-element subsets of the vertices which contain x in their interior. We investigate the problem of characterizing those collections of subsets which can be represented in this matter. We give a complete characterization of this and a related problem.School of Mathematics, University of Minnesota, Minneapolis, MN 55455. This work was supported in part by NSF grant DMS-8700995.Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, England. Work done while Hill Visiting Professor at the University of Minnesota.     

Current distribution on a three-dimensional,bond-diluted,random-resistor network at the percolation threshold

Current and logarithm-current distributions on a three-dimensional random-bond percolation cubic network were studied at the percolation threshold by computer simulations. Predictions of a hierarchical model that combine fractal structure and randomness agree with our numerical simulations. In the thermodynamic limit the logarithm-current distribution exhibits ann(ln(i))i ^1/3 dependence below some characteristic currenti _c. This distribution may scale with lni/lnL, but the data are insufficient to make this a definite conclusion. Due to the small range of lnL considered, a study of the moments does not reveal this behavior and a study of the distribution itself is required.     

Delaunay graphs are almost as good as complete graphs

LetS be any set ofN points in the plane and let DT(S) be the graph of the Delaunay triangulation ofS. For all pointsa andb ofS, letd(a, b) be the Euclidean distance froma tob and let DT(a, b) be the length of the shortest path in DT(S) froma tob. We show that there is a constantc (≤((1+√5)/2) π≈5.08) independent ofS andN such that $$\frac{{DT(a,b)}}{{d(a,b)}}< c.$$      

The computation of characteristic classes of lattice gauge fields

AGL(p,C)-valued lattice gauge fieldu on a simplicial complex determines a principalGL(p,C)-bundle if the plaquette products are sufficiently small with respect to the maximum distortion coefficient of the transporters. A representative cocyclec _q for theq ^th Chern class of can be computed on each 2q-simplex by takingc _q() to be the intersection number of a certain singular 2q-cubeM with a Schubert-type variety _q in the space of allp×p matrices. This reduces to the solution of polynomial equations with coefficients coming fromu and thus avoids numerical integration or cooling-type procedures. An application of this method is suggested for the computation of the topological charge of anSU(3)-valued lattice gauge field on a 4-complex.Partially supported by NSF grant DMS 8607168Partially supported by PSC-CUNY and by NSF grant DMS 8805485     

A reply to “a comment on generalized electromagnetism and Dirac algebra”

Issues raised by W. A. Rodrigues, Jr. are discussed.1. This is not a new result; see,e.g., Rohrlich.⁽³⁾ 2. A typographical error in Eq. (77) is corrected here: The productj A in the right-hand parentheses was erroneously transcribed in Ref. (2) as A.3. I define electromagnetic fieldF = A to be that generated by electric charges and the magnetoelectric fieldG = M to be that generated by magnetic monopoles:F F +₅ G. 4. Rodrigues, on the other hand, takes the position that the importance of the Lagrangian formulation should be downgraded if not discarded altogether: ... it is redundant to look for Lagrangians.⁽¹⁾ 5. In fact, he reformulates it using the language of differential forms.6. It is interesting to observe that this bilinear form has the additional virtue of being appropriate for dealing with the monopolecharge parity question, which was pointed out long ago.⁽¹⁴⁾ 7. In fact, even mathematics looks to Nature for its authority.⁽¹⁶⁾ There is evidence that Rodrigues does not understand this concept.⁽¹⁷⁾     

Time reversal for infinite-dimensional diffusions

Summary In this paper we analize the reversibility of the diffusion property for the solution of certain infinite-dimensional systems of stochastic differential equations. Necessary and sufficient conditions ensuring this reversibility are given. The proofs use the techniques of the stochastic calculus of variations.This work was partly done when the first author was visiting the Centre de Recerca Matemàtica at Barcelona     

On the symmetric square: unstable local transfer

Summary We prove the fundamental lemma for spherical functions with respect to the natural (induction) lifting fromPGL(2) toPGL(3) which appears as the unstable counterpart of the stable symmetric-square lifting fromSL(2) toPGL(3) (see [IV] for an introduction to this project, and [VI] for the final results). Thus spherical functions onPGL(2) andPGL(3) which correspond to each other by satisfying an elementary representation theoretic relation are shown to have matching orbital integrals. The proof of this local statement is based on an application of the global trace formula.Partially supported by NSF grants     

Finite-time implications of relaxation times for stochastically monotone processes

Summary For a continuous-time finite state Markov process with stationary distribution , it is well-known thatP ⁱ (X ^t =j)- ^j isO(e ^-t ) ast, for a certain . For a stochastically monotone process for which the reversed process is also stochastically monotone, one can obtain bounds valid for allt. Precisely, exp(-t). The proof exploits duality for stochastically monotone processes.Research supported by National Science Foundation Grant MCS 84-03239     

Establishing order in planar subdivisions

A planar subdivision is the partition of the plane induced by an embedded planar graph. A representation of such a subdivision isordered if, for each vertexv of the associated graphG, the (say) clockwise sequence of edges in the embedding ofG incident withv appears explicitly.The worst-case complexity of establishing order in a planar subdivision, i.e., converting an unordered representation into an ordered one, is shown to be (n + log (G)), wheren is the size (number of vertices) of the underlying graphG and (G) is (essentially) the number of topologically distinct embeddings ofG in the plane.This work was supported by the National Science and Engineering Research Council of Canada under Grant A3583. A preliminary version of this paper appeared in theProceedings of the Third Annual ACM Symposium on Computational Geometry.