Compactness of isospectral conformal metrics onS 3

Research supported by NSF grants DMS-88-16321 and DMS-87-02871.     

Morera and mean-value type theorems in the hyperbolic disk

Some Morera and mean-value type theorems are proved in the hyperbolic disk. Partially supported by NSF grants DMS-9000619 and CDR-8803012. Partially supported by NSF grants DMS-8703072 and DMS-9000619, and DGI-CYT grant PB 89-0311.     

Gradient estimates,Harnack inequalities and estimates for heat kernels of the sum of squares of vector fields

Research partially supported by NSF grant no. DMS-87-04209 and DMS-90-04062     

On the scaling limit of a singular integral operator

The scaling limit and Schauder bounds are derived for a singular integral operator arising from a difference equation approach to monodromy problems. Research supported in part by National Science Foundation grants DMS-02-45371 and DMS-04-05519.     

Proof of a conjecture on multisets of hook numbers

A conjecture of Regev and Vishik on the equality of two multisets of hook numbers is proved. Supported in part by N.S.F. Grant No. DMS-94-01197. Supported in part by N.S.F. Grant No. DMS-95-00646.     

The structure of singly-periodic minimal surfaces

The research described in this paper was supported by research grant DE-FG02-86ER250125 of the Applied Mathematical Science subprogram of Office of Energy Research, U.S. Department of Energy, and National Science Foundation grants DMS-8611574 and DMS-8802858     

A Markov-modulated M/G/1 queue II: Busy period and time for buffer overflow

We consider an M/G/1 queue where the arrival and service processes are modulated by a two state Markov chain. We assume that the arrival rate, service time density and the rates at which the Markov chain switches its state, are functions of the total unfinished work (buffer content) in the queue. We compute asymptotic approximations to performance measures such as the mean residual busy period, mean length of a busy period, and the mean time to reach capacity.This research was supported in part by NSF Grants DMS-84-06110, DMS-85-01535 and DMS-86-20267, and grants from the U.S. Israel Binational Science Foundation and the Israel Academy of Sciences.     

Robust convex quadratically constrained programs

In this paper we study robust convex quadratically constrained programs, a subset of the class of robust convex programs introduced by Ben-Tal and Nemirovski [4]. In contrast to [4], where it is shown that such robust problems can be formulated as semidefinite programs, our focus in this paper is to identify uncertainty sets that allow this class of problems to be formulated as second-order cone programs (SOCP). We propose three classes of uncertainty sets for which the robust problem can be reformulated as an explicit SOCP and present examples where these classes of uncertainty sets are natural. Research partially supported by DOE grant GE-FG01-92ER-25126, NSF grants DMS-94-14438, CDA-97-26385, DMS-01-04282 and ONR grant N000140310514.Research partially supported by NSF grants CCR-00-09972, DMS-01-04282 and ONR grant N000140310514.     

On the eigenvalues of matrices with given upper triangular part

We give necessary and sufficient conditions for a set of numbers to be the eigenvalues of a completion of a matrix prescribed in its upper triangular part.Partially supported by the NSF Grant DMS-8701615-02Partially supported by the NSF Grant DMS-8802836 and United States-Israel Binational Science Foundation Grant 88-00304/I.     

Affine systems inL 2 (ℝ d ) II: Dual systems

The fiberization of affine systems via dual Gramian techniques, which was developed in previous papers of the authors, is applied here for the study of affine frames that have an affine dual system. Gramian techniques are also used to verify whether a dual pair of affine frames is also a pair of bi-orthogonal Riesz bases. A general method for a painless derivation of a dual pair of affine frames from an arbitrary MRA is obtained via the mixed extension principle. This work was partially sponsored by the National Science Foundation under Grants DMS-9102857, DMS-9224748, and DMS-9626319, by the United States Army Research Office under Contracts DAAL03-G-90-0090, DAAH04-95-1-0089, and by the Strategic Wavelet Program Grant from the National University of Singapore.     

On a stopping process for oscillatory integrals

In this paper we introduce a stopping process to analyze oscillatory integral operators with degenerate phases. The resulting bounds give smoothing properties for averages along variable families of curves inR ⁿ with two-sided torsion. Supported in part by the National Science Foundation under Grants DMS-92-04196 and DMS-91-04455.A01.     

A Markov-modulated M/G/1 queue I: Stationary distribution

We consider an M/G/1 queueing system in which the arrival rate and service time density are functions of a two-state stochastic process. We describe the system by the total unfinished work present and allow the arrival and service rate processes to depend on the current value of the unfinished work. We employ singular perturbation methods to compute asymptotic approximations to the stationary distribution of unfinished work and in particular, compute the stationary probability of an empty queue.This research was supported in part by NSF Grants DMS-84-06110, DMS-85-01535 and DMS-86-20267, and grants from the U.S. Israel Binational Science Foundation and the Israel Academy of Sciences.     

Knot polynomials and Vassiliev's invariants

Summary A fundamental relationship is established between Jones' knot invariants and Vassiliev's knot invariants. Since Vassiliev's knot invariants have a firm grounding in classical topology, one obtains as a result a first step in understanding the Jones polynomial by topological methods.Oblatum 20-V-1991 & 10-VI-1992Research supported in part by NSF Grant DMS-88-055627.Research supported in part by NSF Grant DMS-90-04017.     

Embedded minimal surfaces with an infinite number of ends

The research described in this paper was supported by research grant DE-FG02-86ER250125 of the Applied Mathematical Science subprogram of the Office of Energy Research, U.S. Department of Energy, and National Science Foundation grants DMS-8503350 and DMS-8611574     

Error bounds for minimal energy bivariate polynomial splines

Summary. We derive error bounds for bivariate spline interpolants which are calculated by minimizing certain natural energy norms. Received March 28, 2000 / Revised version received June 23, 2000 / Published online March 8, 2002 RID="*" ID="*" Supported by the National Science Foundation under grant DMS-9870187 RID="**" ID="**" Supported by the National Science Foundation under grant DMS-9803340 and by the Army Research Office under grant DAAD-19-99-1-0160     

On solution-containing ellipsoids in linear programming

Ellipsoids that contain all optimal dual slack solutions and those that contain all optimal primal solutions and that are independent of the algorithm used are derived. Based upon these ellipsoids, two criteria each for detecting optimal basic and nonbasic variables prior to optimality in interior-point methods are obtained. Using these results, we then derive a sufficient condition for a linear program to be feasible.This research was supported in part by NSF Grant DMS-85-12277, DMS-91-06195, CDR-84-21402 and ONR Contract N00014-87-K-0214.     

The strong halfspace theorem for minimal surfaces

The research in this paper was supported by research grants DE-FG02-86ER250125 of the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy and National Science Foundation, Division of Mathematical Sciences research grants DMS-8503350 and DMS-8611574     

Motion of level sets by mean curvature III

We continue our investigation [6,7] (see also [4], etc.) of the generalized motion of sets via mean curvature by the level set method. We study more carefully the fine properties of the mean curvature PDE, to obtain Hausdorff measure estimates of level sets and smoothness whenever the level sets are graphs. L. C. E. was supported in part by NSF Grant DMS-86-01532. J. S. was supported in part by NSF Grant DMS-88-02858 and DOE Grant DE-FG02-86ER25015.     

A two-level additive Schwarz preconditioner for the stationary Stokes equations

We consider the stationary Stokes equations on a polygonal domain whose boundary has more than one component, i.e., flow with obstacles. A two-level additive Schwarz preconditioner is developed for the divergence-free nonconforming P1 finite element. The condition number of the preconditioned system is shown to be bounded independent of mesh sizes and the number of subdomains in the case of generous overlap.This work was supported in part by the National Science Foundation under Grant Nos. DMS-92-09332 and DMS-94-96275.     

Lattice embeddings below a nonlow2 recursively enumerable degree

We introduce techniques that allow us to embed below an arbitary nonlow₂ recursively enumerable degree any lattice currently known to be embeddable into the recursively enumerable degrees. Research partially supported by NSF Grants DMS-9204308, DMS-93-44740, a US-NZ binational grant NSF 90-20558, the U.S. ARO through ACSyAM at the Mathematical Sciences Institute of Cornell Univrsity Contract DAAL03-91-C-0027 and the IGC of Victoria University.