Dines—Fourier—Motzkin quantifier elimination and an application of corresponding transfer principles over ordered fields

A constructive procedure using Dines—Fourier—Motzkin elimination is given for eliminating quantifiers in a linear first order formula over ordered fields. An ensuing transfer principle is illustrated by showing that a locally one-to-one affine map is globally one-to-one and onto all over ordered fields.This research is based on work supported in part by the National Science Foundation under Grant DMS-86-03232, by the Department of Energy grant DE-FG03-87ER25028 and by the United States-Israel Binational Science Foundation Grant 85-00295.     

A version of Rolle's theorem and applications

This paper deals with global injectivity of vector fields defined on euclidean spaces. Our main result establishes a version of Rolle's Theorem under generalized Palais-Smale conditions. As a consequence of this, we prove global injectivity for a class of vector fields defined on n-dimensional spaces.Research partially supported by CNPq/Brazil under grant # 307014/89-4Research partially supported by CNPq/Brazil under grant # 301251/78-9     

A MUSIC-type algorithm for detecting internal corrosion from electrostatic boundary measurements

We establish an asymptotic representation formula for the steady state current perturbations caused by internal corrosive boundary parts of small surface measure. Based on this formula we design a non-iterative method of MUSIC (multiple signal classification) type for localizing the corrosive parts from voltage-to-current observations. We perform numerical experiments to test the viability of the algorithm and the results clearly demonstrate that the algorithm works well even in the presence of relatively high noise ratios. H. Ammari is partially supported by the Brain Pool Korea Program at Seoul National University, H. Kang is partially supported by KOSEF grant R01-2006-000-10002-0, E. Kim is supported by BK21 Math. Division at Seoul National University, and M.S. Vogelius is partially supported by NSF grant DMS-0604999.     

Growth functions,rewriting systems,and the Euler characteristic

We present a formula that expresses the number of admissible words for an arbitrary system of prohibitions in terms of the generating series. We also indicate applications of this formula to the calculation of the topological entropy of symbolic systems and to the calculation of growth functions of groups and algebras. Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 653–668, November, 1995. This research was partially supported by the Russian Foundation for Basic Research under grant No. 94-01-00820 and by the International Science Foundation grant MV1000.     

Milnor numbers for surface singularities

An additive formula for the Milnor number of an isolated complex hypersurface singularity is shown. We apply this formula for studying surface singularities. Durfee's conjecture is proved for any absolutely isolated surface and a generalization of Yomdin singularities is given. This work was supported in part by a Spanish FPI'91 grant and by the Spanish project PB94-0291.     

Standard position for objects in hyperbolic space

It is shown that, by applying hyperbolic isometries, one may arrangen points in hyperbolic (n–1)-space in a certain standard position. Similar results are developed for complex hyperbolic space, as well as hyperbolic spaces defined over nearly arbitrary fields. The algebraic basis of the paper is the determination of the structure of a double coset space which occurs in representation theory.Partially supported by NSA grant # MDA-904-96-0018.Partially supported by NSA grant # MDA904-95-1-1089.     

Local contribution to the Lefschetz fixed point formula

Summary For a class of self-correspondencesC calledweakly hyperbolic, we give a computable formula for the contribution of a fixed point component to the Lefschetz number ofC. The formula applies to Lefschetz numbers of cohomology with coefficients in a constructible complex of sheaves (such as intersection homology).Oblatum 9-XI-1990 & 29-IV-1992In memory of J.L. VerdierPartially supported by NSF grant # DMS8802638 and DMS9001941Partially supported by NSF grant # DMS8803083 and DMS9106522     

First applications of a formula for the error of finite sinc interpolation

In former articles we have given a formula for the error committed when interpolating a several times differentiable function by the sinc interpolant on a fixed finite interval. In the present work we demonstrate the relevance of the formula through several applications: correction of the interpolant through the insertion of derivatives to increase its order of convergence, improvement of the barycentric formula, rational sinc interpolants (with and without replacement of the (usually unknown) derivatives with finite differences), convergence acceleration through extrapolation and improvement of one-sided interpolants. Work partly supported by the Swiss National Science Foundation under grant Nr 200021-116122.     

An asymptotic formula for the voltage potential in the case of a near-surface conductivity inclusion

We rigorously derive an asymptotic expansion of the steady-state voltage potentials in the presence of a conductivity inclusion of small volume that is close to a planar surface. This new formula is motivated by the practically important inverse problem of imaging a conductivity inclusion near a planar interface. Partly supported by ACI Jeunes Chercheurs (0693) from the Ministry of Education and Scientific Research, France. Partially supported by grant R02-2003-000-10012-0 from the Korea Science and Engineering Foundation. Received: December 2, 2003; revised: January 18, 2004     

On formulas of Ramanujan and Evans

We give short elementary proofs of a formula of Ramanujan as interpreted by Bradley, and a companion formula originally proved by W. Chu. We also give an elementary proof of a generalization of an identity originally proved using modular functions and used to study a generating function for the number of partitions with specified crank. Research partially supported by NSF grant DMS 99-70865. 2000 Mathematics Subject Classification Primary—39A70, 11P83; Secondary—33C20     

A likelihood ratio formula for random fields with application to physical geodesy

A formula for the likelihood ratio applicable to estimation and inference problems arising in random field data models in physical geodesy is derived based on multiparameter white noise theory.Research supported in part under grant no. 78-3550, Applied Mathematics Division, AFOSR, United States Air Force.     

Values of <Emphasis Type="Italic">L</Emphasis>-functions at integers outside the critical strip

We incorporate the non-critical values of L-functions of cusp forms into a cohomological set-up analogous to the one of Eichler, Manin and Shimura. We use the 1-cocycles we associate in this way to non-critical values to prove an expression for such values which is similar in structure to Manin’s formula for the critical value of the L-function of a weight 2 cusp form. YoungJu Choie is partially supported by KOSEF R01-2003-00011596-0 and by ITRC Research Fund. N. Diamantis is partially supported by EPSRC grant EP/D032350/1.     

A Robin formula for the Fekete-Leja transfinite diameter

We generalize the classical Robin formula to higher dimensions. Work supported in part by NSF grant DMS-0300784.     

Integral invariants of the Hamilton equations

Conditions are found for the existence of integral invariants of Hamiltonian systems. For two-degrees-of-freedom systems these conditions are intimately related to the existence of nontrivial symmetry fields and multivalued integrals. Any integral invariant of a geodesic flow on an analytic surface of genus greater than 1 is shown to be a constant multiple of the Poincaré-Cartan invariant. Poincaré's conjecture that there are no additional integral invariants in the restricted three-body problem is proved. Translated fromMatematicheskie Zametki, Vol. 58, No. 3, pp. 379–393, September, 1995. The work was financially supported by the Russian Foundation for Basic Research (grant No. 242 93-013-16244), International Science Foundation (grant No. MCY 000), and INTAS (grant No. 93-339).     

Estimating errors of numerical approximation for analytic functions

Summary It is shown that very nearly the same estimates for the errors of numerical approximation for analytic functions can be obtained more simply through Cauchy's integral formula that otherwise result from Davis' method using Hilbert space techniques.Research supported in part by the Atomic Energy Commission under contract U.S. AEC AT (11-1) 1469, and in part by the National Science Foundation under grant NSF-GJ-812.     

The asymptotic number of acyclic digraphs. I

We obtain an asymptotic formula forA _n,q , the number of digraphs withn labeled vertices,q edges and no cycles. The derivation consists of two separate parts. In the first we analyze the generating function forA _n,q so as to obtain a central limit theorem for an associated probability distribution. In the second part we show combinatorially thatA _n,q is a smooth function ofq. By combining these results, we obtain the desired asymptotic formula. Research supported by NSF under grant MCS-8300414. Research supported by NSERC under grant A4067. Research supported by NSF under grant MCS-8302282. Research supported by the Australian Department of Science and Technology under the Queen Elizabeth II Fellowship Scheme, while this author was at the University of Newcastle, Australia.     

Difference Equations and Discriminants for Discrete Orthogonal Polynomials

We prove that any set of polynomials orthogonal with respect to a discrete measure supported on equidistant points contained in a half line satisfy a second order difference equation. We also give a discrete analogue of the discriminant and give a general formula for the discrete discriminant of a discrete orthogonal polynomial. As an application we give explicit evaluations of the discrete discriminants of the Meixner and the Hahn polynomials. A difference analogue of the Bethe Ansatz equations is also mentioned.Research partially supported by NSF grant DMS 99-70865     

Central Value Of Automorphic <Emphasis Type="Italic">L</Emphasis>-Functions

We prove a generalization to the totally real field case of the Waldspurger’s formula relating the Fourier coefficient of a half integral weight form and the central value of the L-function of an integral weight form. Our proof is based on a new interpretation of Waldspurger’s formula as a combination of two ingredients – an equality between global distributions, and a dichotomy result for theta correspondence. As applications we generalize the Kohnen–Zagier formula for holomorphic forms and prove the equivalence of the Ramanujan conjecture for half integral weight forms and a case of the Lindel?f hypothesis for integral weight forms. We also study the Kohnen space in the adelic setting. The first author was partially supported by NSF grant DMS-0070762. The second author was partially supported by NSF grant DMS-0355285. Received: July 2005 Accepted: August 2005     

A Feasibility Pump for mixed integer nonlinear programs

We present an algorithm for finding a feasible solution to a convex mixed integer nonlinear program. This algorithm, called Feasibility Pump, alternates between solving nonlinear programs and mixed integer linear programs. We also discuss how the algorithm can be iterated so as to improve the first solution it finds, as well as its integration within an outer approximation scheme. We report computational results. P. Bonami is supported in part by a grant from IBM and by ANR grant BLAN06-1-138894. G. Cornuéjols is supported in part by NSF grant CMMI-0653419, ANR grant BLAN06-1-138894 and ONR grant N00014-03-1-0188. Part of this research was carried out when Andrea Lodi was Herman Goldstine Fellow of the IBM T.J. Watson Research Center whose support is gratefully acknowledged. F. Margot is supported in part by a grant from IBM and by ONR grant N00014-03-1-0188.