Symplectic homology via generating functions

Research at Mathematical Sciences Research Institute supported by an MSRI postdoctoral fellowship. Research at Stanford supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship. Research at Centre Emile Borel, Institut Henri Poincaré, Paris funded by Ministère des Affaires Etrangères, France.     

Flatness Properties of Acts: Some Examples

Research supported by Natural Sciences and Engineering Research Council of Canada Grant A4494 Research supported by Estonian Science Foundation Grant 930     

An elementary and direct proof of the Painlevé property for the Painlevé equations I,II and IV

We present a direct and elementary proof that all the solutions of the Painlevé Equations I, II and IV are meromorphic functions on the whole complex plane. The proof uses some ideas from the existing proofs but applies the ideas in a different setting. Research was supported by Hong Kong Research Grant Council Earmark Grant HKUST6123/00P. Research was supported by Hong Kong Research Grant Council Earmark Grant HKUST6107/02P.     

A minimal cutset of the boolean lattice with almost all members

Two almost explicit constructions are given satisfying the title.This research was done while the authors visited the Institute for Mathematics and its Applications at the University of Minnesota, Minneapolis, MN 55455.Research supported in part by Hungarian National Foundation for Scientific Research, grant no. 1812.Research supported in part by NSF Grant MDS 87-01475.Research supported in part by NSF grant DMS 86-06225 and Airforce Grant OSR-86-0076.     

Homogeneous even kernels on surfaces

Research supported by the Australian Research Council     

Interlacing of zeros of shifted sequences of one-parameter orthogonal polynomials

We study the interlacing property of zeros of Laguerre polynomials of adjacent degree, where the free parameters differ by an integer, and of the same degree, where the free parameter is shifted continuously. Similar interlacing results are proven for the positive zeros of Gegenbauer polynomials. Research by Kathy Driver is supported by the National Research Foundation of South Africa under grant number 2053730. Research by Kerstin Jordaan is partially supported by the National Research Foundation of South Africa under grant number 2054423.     

Lipschitz continuity of the absolute value in preduals of semifinite factors

We prove a weak-type estimate for the absolute value mapping in the preduals of semifinite factors which extends an earlier result of Kosaki for the trace class.Research supported by the Australian Research Council (ARC) and the Netherlands Organization for Scientific Research (NWO)     

InducedC *-algebras and a symmetric imprimitivity theorem

Research partially supported by the Australian Research Grants Scheme     

On the zeros and poles of Padé approximants toe z

Summary In this paper, we study the location of the zeros and poles of general Padé approximats toe ^z. The location of these zeros and poles is useful in the analysis of stability for related numerical methods for solving systems of ordinary differential equations.Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-74-2688, and by the University of South Fla. Research Council.Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-74-2729, and by the Atomic Energy Commission under Grant AT(11-1)-2075.     

Every planar graph has an acyclic 7-coloring

A proper coloring of the vertices of a graph is said to be acyclic provided that no cycle is two colored. We prove that every planar graph has an acyclic seven coloring. Research supported in part by the Research Corporation through a Cottrell College Science Research Grant.     

On the sharpness of theorems concerning zero-free regions for certain sequences of polynomials

Summary In this paper, we establish the sharpness of a theorem concerning zero-free parabolic regions for certain sequences of polynomials satisfying a three-term recurrence relation. Similarly, we establish the sharpness of a zero-free sectorial region for certain sequences of Padé approximants toe ^z .Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-74-2688Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-74-2729, and by the Energy Research and Development Administration (ERDA) under Grant E(11-1)-2075     

The shape of a figure-eight under the curve shortening flow

Research supported in part by an NSF Postdoctoral Research Fellowship     

A set of staircase linear programming test problems

A set of staircase linear programming test problems are made available for computational experiments.Research supported by the U.S. Department of Energy under contract DE-AC02-76CH00016.Research supported by the Belgian National Research Program in Energy, contract E/I/3.     

A characterization of some arithmetical multiplicative functions

Research supported by the Hungarian National Research Foundation No.907.     

The rotation number and the herpolhode angle in Euler’s top

We describe the relation between the rotation number and the herpolhode angle in the rotation of the force-free rigid body.Received: September 23, 2002Research partially supported by NSERC.Research partially supported by European Community funding for the Research and Training Network MASIE (HPRN-CT-2000-00113).     

The dimension of cycle-free orders

The existence of a four-dimensional cycle-free order is proved. This answers a question of Ma and Spinrad. Two similar problems are also discussed.Research partially supported by Office of Naval Research grant N00014-90-J-1206Research partially supported by the National Science Foundation under grant DMS     

Some Semilattices of Semigroups Each Having One Idempotent

Research supported by the Italian Ministry of Universities and Scientific Research     

Onπ-quasinormal subgroups in finite groups

Research supported by Hungarian National Foundation for Scientific Research grant no. 1813.     

Lebesgue function type sums of Hermite interpolations

Research supported by Hungarian National Foundation for Scientific Research Grant No. 1910.     

Efficient generation of zero dimensional ideals in polynomial rings

Senior Research Fellow of the Council of Scientific and Industrial Research, India.