Abstracts for the IMA Preprint Series

Complete Chronological List      Download    Submission Instructions

1   Statistical mechanics, dynamical systems, and turbulence
Abstracts

We present here abstracts of some lecture series in the areas of statistical mechanics, dynamical systems, and turbulence together with reading lists in the hope that they will provide a useful guide to others who wish to learn these subjects.

Download

2   A simple proof of C. Siegel's center theorem
Raphael De laLlave

We give an elementary proof of a particular case of C. Siegel's center theorem, based on a method of M. Herman. Even if the proof has less generality than the standard one, it is simpler and provides sharper bounds.

Download

3   On copositive matrices and strong ellipticity for isotropic elastic materials
H. Simpson and S. Spector

In this paper we establish necessary and sufficient conditions for the strong-ellipticity of the equations governing an isotropic (compressible) nonlinerly elastic material at equilibrium. Our work extends results of Knowles and Sternberg [5] who obtained such conditions for both ordinary and strong ellipticity in the special case when the underlying deformations are plane.

Download

4   Vector fields in the vicinity of a compact invariant manifold
George R. Sell

Let us consider two vector fields

(1)             X' = F(X)
(2)             Y' = F(Y)

defined on a give Euclidean space E where F and G are of class C^N+1. Furthermore, assume that there is a smooth compact manifold M smoothly imbedded in E and that M is invariant for both vector fields. Also that F and G agree on M, i.e. F|M = G|M.
We wish to study the question of C^S-conjugacies between (1) and (2).

Download

5   Non-linear stability of asymptotic suction
Milan Miklavcic

A flow over a plane y = 0 in R³ given by
U(x,y,z) = (1 - e^-y, -1/R, 0)
is called an asymptotic suction velocity profile [12]. R>0 is the Reynolds number. U satisfies the Navier-Stokes equation

          ðv / ðt + (v · ) v = - p₀ + 1/R v
          div v = 0

with p₀ = 0. In the present paper it is proved that the stability of U for small perturbations which initially decay exponentially in the y direction and are periodic in the x and z direction is governed by the eigenvalues of the classical Orr-Sommerfeld equation [1, 8, 12]. For precise statements see Theorems 4, 5, 9, and 15.

Download

6   A simple system with a continuum of stable inhomogeneous steady states
Hans Weinberger

The system

         u_t = {(1 + v)}_xx + (R₁ - au - bv)u
         v_t = (R₂ - bu - av)v
         {(1 + u)}_xx = 0    at    x = 0   and   x = 1
with

         1/2 (a/b + b/a) < R₁/R₂ < a/b

and

         > a(a² - b²) / 2abR₁ - (a² + b²) R₂

was considered by M. Mimura [2] as a model for the population densities of two competing species, one of which increases its migration rate in response to crowding by the other species. It is a special case of the model of N. Shigesada, K. Kawasaki, and E. Teramoto [3].

Download

7   Period 3 bifurcation for the logistic mapping
Bau-Sen Du

In the context of continuous mappings of the interval, one of the most striking features may be Sharkovsky's theorem [6] which, among other thing, shows that the existence of a period 3 point implies the existence of periodic points of every period (see also [2, 5]). Therefore, for a one-parameter family of interval mappings, the determination of period 3 bifurcation points may be interesting. In recent years, the logistic mapping f(x) = 1 - x² has been entensively studied ([1, 4]). By using computer simulation for this family f(x), as the parameter is increased from 0, we can observe the Feigenbaum "cascades" [3]. That is, stable periodic points of double periods accumulate in a geometric and universal way. As the parameter is approximately equal to 1.7498 ([1, p.129]), there seems to be a period 3 bifurcation. In this note, we show that this family f(x) does have a period 3 bifurcation exactly at = 7/4.

Download

8   Optimal Numerical Approximation of a Linear Operator
Hans Weinberger

Many linear problems of numerical analysis can be formulated in the following way: One is given a set of n linear data Nu = and a bound for the norm ||u||_B of an otherwise unknown element of u of a hilbert space B. One wishes to find a best approximation to the element Su, where S is a bounded linear operator from B to another Hilbert space . For example, Su may be the solution of an ordinary or partial differential equation with right-hand side, initial data, or boundary data u.

Download

9   Three component ionic microemulsions
L.R. Angel, D.F. Evans, and B. Ninham

Necessary design features of microemulsions formed from cationic surfactant without any requirement for cosurfactant are illustrated by a study of microemulsions formed from didodecyldimethylammonium bromide in various oils. Ease of purification, preparation and manipulation give this and related systems a considerable advantage over conventional systems in enhancing our understanding of microemulsions and emulsion behavior.

Download

10   Surfactant diffusion; new results and interpretations
D.F. Evans, D. Mitchell, S. Mukherjee, and B. Ninham

Data for surfactant diffusion are reproted for sodium dodecylsulfate at 25° and tetradecyltrimethylammonium bromide at 25°, 90°, and 135°C, as measured by Taylor tube dispersion. These data are analyzed in terms of two limiting forms of theory, one appropriate to "slow" reaction rates, the other to "fast" rates. It is shown that the usual extrapolation to the critical micelle concentration to infer intrinsic diffusion constants is not permissible. The data is explicable if transport occurs by a process wherein ionic micelles disassociate, diffuse as monomers and reassemble into micelles. This is directly contrary to current ideas on diffusion of surfactants.

Download

11   Remark about the final aperiodic regime for maps on the interval
Leif Arkeryd

We consider families of maps on the interval with one maximum, and prove the geometric convergence of the bifurcation parameter for the case of superstable periodic orbits converging towards the final aperiodic regime.

Download

12   Manifolds of global solutions of functional differential equations
Luis T. Magalhães

This paper consider smooth invariant manifolds of global solutions of retarded Functional Differential Equations in Rⁿ. The persistence, under small perturbations, of such manifolds where the flow is given by an Ordinary Differential Equation in Rⁿ is studied. The novelty of the present approach lies on the use of the dynamics of the flow on the manifolds, instead of their attractivity properties.

Download

13   Tori in resonance
Kenneth Meyer

This paper gives three examples of ordinary differential equations which depend on one or more parameters and which admit invariant tori for some values of the parameters. These examples illustrate how invariant tori evolve as the parameters are changed; in particular how they disappear, bifurcate and lose smoothness. The equations presented are choosen to be as simple as possible in order to clearly show the interesting phenomenon without unnecessary details. However, the theory of normal forms and unfoldings was used to select typical examples, but no attempt will be made to define precisely the universe of discourse where these examples are generic. The unfolding of invariant tori would consist of a mutitude of cases not all of which are that interesting.

Download

14   Surface models with nonlocal potentials: Upper bounds
C. Eugene Wayne

The behavior of fluctuations in a class of surface models with exponentially decaying nonlocal potentials is studied. Combining a Mayer expansion with a duality transformation we demonstrate the equivalence of these models to a class of two dimensional spin systems with nonlocal interactions. The expansions give sufficient control over the potentials to allow the fluctuations to be bounded from above by the means of complex translations in the spin representation of the model.

Download

15   On stability and uniqueness of fluid flow through a rigid porous medium
K.A. Pericak-Spector

We study a set of equations describing the flow of an incompressible viscous fluid through a rigid porous medium. Existence, uniqueness and stability results are established for the case of a region impregnated with fluid, and uniqueness for an unsaturated region.

Download

16   Smooth linearization near a fixed point
George R. Sell

In this paper we extend a theorem of Sternberg and Bileckii. We study a vector field, or a diffeomorphism, in the vicinity of a hyperbolic fixed point. We show that if the eigenvalues of the linear part (at the fixed point) satisfy 2N-algebraic conditions (where N > 1), then there is a C^N-linearization in the vicinity of this fixed point. If the fixed point is stable, then the C^N-linearization theorem follows when only (N + 1)-algebraic conditions are satisfied. Examples are given which show that the first of these results is sharp. An application to celestial mechanics is included.

Download

17   A nonlinear stability analysis of a model equation for alloy solidification
David Wollkind

Controlled plane front solidification of alloys and other binary substances under an imposed temperature gradient is used in practice to grow single crystals, refine materials (e.g., zone refining), and obtain uniform or non-uniform composition within the material grown [1]. The most important industrial applications of this type of solidification are for growth of crystals for metal oxide semiconductors (MOS's) [1]. Growth of oxide crystals for jewels is another, much older commercial application of single crystal growth [1]. Another important application is in growth of oxides for laser systems and other optical devices [1]. Further industrial applications arise in ingot casting and in the steel and glass industries [2]. For all of these solidification situations involving binary materials, quantitative predictions of interfacial cellular morphology, including information on cell size and intracellular solute distribution, prove to be extremely valuable and are of a particular aid to industrial researchers.

Download

18   Local conjugacy on the Julia set for some holomorphic perturbations of
Pierre Collet

We consider holomorphic perturbations f of f₀, f₀(z) = z², which are small in a neighborhood of the unit circle (the Julia set of f₀). We show that if the C¹ conjugacy invariants of f and f₀ are identical, then f and f₀ are conjugate on their part of the Julia set which remains near the unit circle.

Download

19   On the modified Bessel functions of the first kind (1st paper); and On barrelling for a material in finite elasticity (2nd paper)
Henry C. Simpson, Scott J. Spector

A. On the modified Bessel functions of the first kind: We consider the functions v (t) t I (t) / I _{+ 1} (t) where I are the modified Bessel functions of the first kind of order 0. We prove that v is strictly monotone and strictly convex on R⁺. These results have application in finite elasticity.
B. On barrelling for a material in finite elasticity: In this paper we investigate the question of stability for a solid circular cylinder, composed of a particular homogeneous isotropic (compressible) nonlinearly elastic material, that is subjected to compressive end forces in the direction of its axis (so as to give fixed axial displacements at the ends).

Download

20   Linearization and global dynamics
George R. Sell

In this paper we show how the spectral theory of linear skew-product flows may be used to study the following three questions in the qualitative theory of dynamical systems: (1) when is an -limit set or an attractor a manifold?
(2) Under which conditions will a dynamical system undergo a Hopf-Landau bifurcation from a k-dimensional torus to a (k + 1)-dimensional torus?
(3) When is a vector field i the vicinity of a compact invariant manifold smoothly conjugate to the linearized vector field and how smooth is the conjugacy?

Download

21   Global Lyapunov exponents, Kaplan-Yorke formulas and the dimension of the attractors for 2D Navier-Stokes equations
P. Constantin and C. Foias

We study the fractal and Hausforff dimensions of the universal attractor for the Navier-Stokes equations in two space dimensions. The finite dimensionality of the attractors for the Navier-Stokes equation was first implicitly proven in [16] and explicitely in [10]. The subject has been investigated recently by several authors.

Download

22   Stability for semilinear parabolic equations with noninvertible linear operator
Milan Miklavcic

Suppose that
         x'(t) + Ax(t) = f(t, x(t)),     t ≥ 0
is a semilinear parabolic equation, e^-At is bounded and f satisfies the usual continuity condition. If for some 0 < ≤ 1,  0 < < 1,   p > 1,   > 1
         ||t Ae^-At|| ≤ C,   t ≥ 1
         ||f(t, x)|| ≤ C(||A x|| ^p + (1 + t)^-),   t ≥ 0
whenever ||A x|| + ||x|| is small enough, then for small initial data there exist stable global solutions. Moreover, if the space is reflexive then their limit states exist. Some theorems that are useful for obtaining the above bounds and some examples are also presented.

Download

23   Perturbations of geodesic flows on surfaces of constant negative curvature and their mixing properties
P. Collet, H. Epstein, and G. Gallavotti

We consider one parameter analytic Hamiltonian perturbations of the geodesic flows on surfaces of constant negative curvature. We find two different necessary and sufficient conditions for the canonical equivalence of the perturbed flows and the non perturbed ones. One condition says that the "Hamilton-Jacobi" (introduced in this work) for the conjugation problem should admit a solution as a formal power series (not necessarily convergent) in the perturbation parameter. The alternative condition is based on the identification of a complete set of invariants for the canonical conjugation problem. The relation with the similar problems arising in the KAM theory of the perturbations of quasi periodic Hamiltonian motions is briefly discussed. As a byproduct of our analysis we obtain some results on the Livscic, Guillemin, Kazhdan equation and on the Fourier series for the SL(2, R) group. We also prove that the analytic functions on the phase space for the eodesic flow of unit speed have a mixing property (with respect to the geodesic flow and to the invariant volume measure) which is exponential with a universal exponent, independent on the particular function, equal to the curvature of the surface divided by 2. This result is contrasted with the slow mixing rates that the same functions show under the horocyclic flow: in this case we find that the decay rate is the inverse of the time ("up to logarithms").

Download

24   On the thermodynamics of interstitial working
J.E. Dunn and J. Serrin

In order to model fluid capillarity effects, the Dutch physicist Korteweg formulated in 1901 a constitutive equation for the Cauchy stress that included density gradients. Specifically, Koretweg proposed for study a compressible fluid model in which the "elastic" or "equilibrium" portion of the Cauchy stress tensor T is given by
         T = $hat T$ ( , , grad , grad² )
            = (-p + + |grad |²) 1 + grad grad
               + grad² ,

where = (x, t) is the density of the fluid at the place x at time t, where grad and grad² are, respectively, the first and second (spatial) gradients of with respect to x (with = tr (grad² ) = the Laplacian of ), and where p, , , , and are material functions of and the temperature . To model viscous effects in the dynamic response of his fluids, Korteweg added to the right hand side of (1.1) the classic form of Cauchy and Poisson, i.e., (tr D) 1 + 2 D, where D is the usual stretching tensor of hydrodynamics, and where and are the usual viscosity coefficients and may depend on and .

Download

25   On the absence of bifurcation for elastic bars in uniaxial tension
Scott J. Spector

We prove that an elastic bar undergoing uniaxial tension will not neck before the axial load on the bar attains a (local) maximum. Further, if the bar is in a hard loading device we show that necking is delayed until after maximum load is achieved. The key ingredient in the latter result is a generalized Korn inequality.

Download

26   Maps of an interval
W. A. Coppel
(There are three expository lectures in this preprint)

26-1  Motivation and elementary properties

26-2  Peiodic orbits, topological dynamics, chaos

26-3  Quadratic maps, qualitative and quantitative universality

27   Phase transitions in the Ising model with traverse field
James Kirkwood

The Ising model perturbed by a small transverse field is shown to have a phase transition by two methods. With the first method, using a Peierls' contour argument, we are only able to show that spontaneous magnetization occurs with the transverse field goint to 0 as ^-1/3. With the second method, which used reflection positivity, long range order is shown to occur for a small transverse field independent of temperature.

Download

28   The asymptotics of solutions of singularly perturbed functional differential equations: distributed and concentrated delays are different
Luis Magalhães

This paper illustrated the differences between systems with distributed delays and systems having only concentrated delays in what concerns the asymptotic rates of solutions of singularly perturbed linear retarded functional differential equations. An example of a system with distributed delays shows that the introduction of a ``slow" variable coupled with the ``fast" variable may decrease the asymptotic rates of solutions observed when the perturbation parameter is close to zero. Such a situation cannot happen for ordinary differential equations, or even for differential-difference equations.

Download

29   Homoclinic orbits for flow in R³
Charles Tresser

We propose a rough classification for volume contracting flows in R³ with chaotic behavior. In the simplest cases, one looks at the nature of a homoclinic loop for the flow. Most configurations have been studied at length in the literature; here we examine briefly the ``forgotten" case.

Download

30   About some theorems by L.P. Sil'nikov
Charles Tresser

Some theorems by L.P. Sil'nikov, which describe the dynamics in the neighborhood of homoclinic orbits, bi-asymptotic to a saddle focus, and initially proved for real analytic vector fields are collected here. Recent results in dynamical systems theory allow us to precise some of the conclusions and to generalize these theorems to the C^1,1 class. Certain heteroclinic loops involving a saddle focus are also considered.

Download

31   On the renormalized coupling constant and the susceptibility in ₄⁴ field theory and the Ising model in four dimensions
Michael Aizenmann

We discuss the Euclidean ₄⁴ field theory, and the critical behavior in ferromagnetic systems in four dimensions. It is rigorously shown that there are at most logarithmic corrections to the mean field law in the behavior of the magnetic susceptibility = ₄⁴ S₂ (0, x). Furthermore, if any such corrections are present in a continuum limit which is used to construct a ₄⁴ field theory the limiting theory would be non-interacting. Our analysis extends to ferromagnetic systems of variables which belong to the Simon-Griffiths class.

Download

32   The KAM theory of systems with short range interactions I
C. Eugene Wayne

The Kolmogorov, Arnol'd, Moser (KAM) theory [15, 1, 16] proves that ``small" perturbations of integrable Hamiltonian systems possess ``large" sets of initial conditions for which the trajectories remain quasiperiodic. In this paper we discuss how the ``strength" of the allowed perturbation varies with the number of degrees of freedom, N, in the system.

Download

33   Temporal and spatial chaos in a Van der Waals fluid due to periodic thermal fluctuations
M. Slemrod and J.E. Marsden

This paper applies the Mel'nikov technique to prove the existence of deterministic chaos in two problems for a Van der Waals fluid. The first problem shows that temporal chaos results as a result of small time periodic fluctuations about a subcritical temperature when the fluid is initially quenched in the unstable spinoidal region. The second problem shows that spatial chaos arises from small spatially periodic flunctions in an infinite tube of fluid if the ambient pressure is appropriately chosen.

Download

34   Percolation in continuous systems
James R. Kirkwood and C. Eugene Wayne

A rigorous proof of the existence of a percolation phase transition in a system of noninteracting discs in the plane is presented. In addition, bounds on the critical density and critical area fraction are derived. The lower bound makes use of Halperin's idea of a self-avoiding walk of discs. The upper bound is proved by relating the continuum model to the site percolation problem on a triangular lattice, whose critical probability is exactly known.

Download

35   Invariant manifolds for Functional Differential Equations close to ordinary differential equations
Luis T. Magalhães

This paper considers invariant manifolds of global trajectories of retarded Functional Differential Equations in Rⁿ. The persistence, smoothness and stability of such manifolds where the flow is given by an Ordinary Differential Equation (ODE) in Rⁿ is studied for small perturbations of ODEs. The novelty of the present approach lies in the use of the dynamics of the flow on the manifolds, instead of their attractivity properties.

Download

36   The KAM theory of systems with short range interactions, II
C. Eugene Wayne

The proof of the results on the KAM theory of systems with short range interactions, stated in [4] is completed. Estimates on the decay of the interactions generated by the iterative procedure in the KAM theorem are proved, as well as the modification of the theorems of [1-3] needed for our results.

Download

37   Passive quasi-free states of the noninteracting Fermi gas
Jean De Cannière

The passive quasi-free states of the noninteracting Fermi gas with continuous one-particle Hamiltonian H are computed. They turn out to be the well known Fermi-Dirac states, or limits thereof. This still holds true if the spectrum of H has both a continuous and a discrete part, except for the appearance of a class of "ground state-like" states showing a local random excitation of the point spectrum in a neighborhood of the Fermi energy. When H has only pure point spectrum, the requirement that a state be passive and quasi-free is no longer sufficient to characterize the Fermi-Dirac distributions.

Download

38   Maxwell and van der Waals revisited
Elias C. Aifantis

We utilize a modern continuum mechanic framework to reconsider an old problem for fluid interfaces, also addressed by Maxwell and van der Waals. We prove that their results need not be valid necessarily. This conclusion is arrived at as a consequence of questioning the existence of thermodynamic potentials and the validity of usual thermodynamic relations within unstable (spinodal) regions. One central result is that Maxwell's equal area rule needs not be valid and certain statistical models are shown to be internally inconsistent. Prescise conditions for the validity of Maxwell's rule and the variational theory of van der Waals established in terms of the coefficients defining the interfacial stress.

Download

39   On the mechanics of modulated structures
Elias C. Aifantis

The purpose of this lecture is to illustrate the appropriateness and potential of the methods of continuum mechanics in modeling modulated structures. Modulations are viewed, in general, as occurrences which may involve one or more properties of a system and extend from a submicroscopic to a macroscopic scale. They are also viewed as capable of possessing wave lengths and amplitudes which may vary from very small to very large values.

Download

40   The strong topology on symmetric sequence spaces
William H. Ruckle

Let S be a linear space of real sequences written in functional notation s=(s(j))=(s(1), s(2),...). There is a natural duality between S and the space of sequences which are eventually 0 given by the equation
     <s,t> = _j s(j) t(j)   s S,   t .

Download

41   A characterization of Borda's rule via optimization
Charles R. Johnson

It is shown that Borda's social welfare rule coincides with a social welfare function resulting from a well-defined optimization principle applied to a collection of individual binary preferences.

Download

42   The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains
Kazuo Kishimoto and Hans F. Weinberger

43   On work and constraints in mixtures
K.A. Pericak-Spector and W.O. Williams

In recent years workers in mixture theory have become aware of the central role that volume-fraction, the parameter describing the relative proportion of the volume occupied by a constituent, must play in that theory. In particular, the rate of change of volume-fraction, which we here call the chority, must appear in a working term as contributing to the energy, in order to avoid various inconsistencies. This is true both in theories in which volume-fraction appears as a parameter of microstructure and in complete mixture theories.

Download

44   Some remarks on deformations of minimal surfaces
Harold Rosenberg and Eric Toubiana

We consider complete minimal surfaces (c.m.s.'s) in R³ and their deformations. M₁ is an deformation of M₀ if M₁ is a graph over M₀ in an tubular neighborhood of M₁ and M₁ is - C¹ close to M₀. A c.m.s. M₀ is isolated if all minimal surfaces M₁, which are sufficiently small deformations of M₀, are congruent to M₀. Many of the classical minimal surfaces in R³ are known to be isolated [2]; however, no example was known of a nonisolated minimal surface.

Download

45   The duration of transients
S. Pelikan

Imagine a particle moving in a box and making elastic collisions with the sides. Suppose there is a small hole in one side of the box. For many initial conditions the particle will bounce around for a long time and then leave the box. These trajectories are examples of transients. In this paper we investigate the average duration of transients for a certain class of transformations T.

Download

46   Random fluctuations of the duration of harvest
V. Capasso, K.L. Cooke, and M. Witten

In this report, we wish to discuss models of harvesting of a population when the duration of the harvest interval is subject to random fluctuations. This kind of situation arises, for example, if the harvestor or predator can harvest only when weather conditions are favorable. Clearly, the length of the favorable period will be subject to random variations.

Download

47   The L^p-intergrability of Green's functions and fundamental solutions for elliptic and parabolic equations
E. Fabes and D.W. Stroock

Given d ≥ 1 and in (0,1) denote by A_d() the class of smooth, symmetric, d X d matrix-valued functions a (a^ij (x)) on R^d which satisfy

I ≤ a(x) ≤ 1/ I     x in R^d

L_a u = _i,j=1^d  a^ij (x)   ð² u / ðx_i ðx_j (x)

L_a^* v = _i,j=1^d   ð² / ðy_i ðy_j   (a^ij(y) v(y))

sup_x   sup_{a Ad ()}     G_a (x,y) ^q dy <

ðu / ðt (t,x) = L_a u(t,x),
u(0,x) = f(x)       (L_a u = _i,j=1^d  a^ij (x)   ð² / ðx_i ðx_j).

Download

48   Semilinear equations in R^N without conditions at infinity
Haïm Brezis

The purpose of this paper is to point out that some nonlinear elliptic (and parabolic) problems are well-posed in all of R^N without conditions at infinity.

Download

49   Lax-Friedrichs and the viscosity-capillarity criterion
M. Slemrod

It has been shown by Lax some time ago that for hyperbolic conversation laws solutions obtained as limits of the Lax-Friedrichs finite difference scheme will actually satisfy an "entropy" admissibility criterion. The goal of this paper is to attempt to extend Lax's idea to a form which is amenable to mixed problems as well, e.g. the dynamics of a van der Waals fluid. Specifically, we compare shocks obtained by the Lax-Friedrichs scheme with those permitted by the viscosity-capillarity criterion of [2, 3]. We show that for isothermal motion it is expected that shocks produced by Lax-Friedrichs will satisfy the viscosity-capillarity criterion.

Download

50   Spanning tree extensions of the Hadamard-Fischer inequalities
Charles R. Johnson and Wayne W. Barrett

All possible graph theoretic generalizations of a certain sort for the Hadamard-Fischer determinantal inequalities are determined. These involve ratios of products of principal minors which dominate the determinant. Furthermore, the cases of equality in these inequalities are characterized, and equality is possible for every set of values which can occur for the relevant minors. This relates recent work of the authors on positive definite completions and determinantal identities. When applied to the same collections of principal minors, earlier generalizations give poorer, more difficult to compute bounds than the present inequalities. Thus, this work extends, and in certain sense completes, a series of generalizations of Hadamard-Fischer begun in the 1960's.

Download

51   Revelation and implementation under differential information
Andrew Postlewaite and David Schmeidler

Our goal in this pape is to merge several central ideas in economic theory; strategic behavior (incentive compatibility), differential (or incomplete) information, and the Arrow-Debreu model of general equilibrium. By strategic behavior we refer to the literature which models economic institutions as games in strategic form and uses Nash equilibrium as the solution concept. This literature, motivated by informational decentralization questions, deals not with a single economic environment and a single game, but rather considers a class of environments and a strategic outcome function (game form) which is applied uniformly to this class. The concept of differential information is that of Bayesian equilibrium as it has been applied in the literature on implicit contracts, principal-agent problems and bidding and auction models.

Download

52   Complex analytic dynamics on the Riemann sphere
Paul Blanchard

Holomorphic, non-invertible dynamical systems of the Riemann sphere are surprisingly intricate and beautiful. Often the indecomposable, completely invariant sets are fractals (a la Mandelbrot [M1]) because, in fact, they are quasi-self-similar (see Sullivan [S3] and (8.5)). Sometimes they are nowhere differentiable Jordan curves whose Hausdorff dimension is greater than one (Sullivan [S4] and Ruelle [R]). Yet these sets are determined by a single analytic function z_n+1 = R(z_n).

Download

53   Topology and differentiability of labyrinths in the disc and annulus
Gilbert Levitt and Harold Rosenberg

The study of differential equations in the plane which are locally of the form ðy / ðx =F(x,y), gives rise to labyrinths. They are limit sets of bounded solutions to this equation. This is made precise in [Ro], where the singularities considered are thorns and tripods. In part I of this paper, we shall extend the results of [Ro] to differential equations with n-prong singularities, in the disc and annulus. For the disc, the story is not essentially different from the previous case. However, for the annulus, the study is quite different and more complicated. In both cases, we obtain a topological structure theorem for solutions of the equation.

Download

54   Symmetry of constant mean curvature hypersurfaces in hyperbolic space
Gilbert Levitt and Harold Rosenberg

In a recent paper, M. Do Carmo and B. Lawson studied hypersurfaces M of constant mean curvature in hyperbolic space [2]. They use the Alexandrov reflection technique to study M given the asymptotic boundary ðM. For example, one of their theorems says M is a horoshpere when ðM reduces to a point. They also prove a Bernstein type theorem for minimal graphs.
In this paper we shall extend their results to other boundary conditions. We prove an embedded M, of constant mean curvature, with ðM a subset of a codimension one sphere S, either is invariant by reflection in the hyperbolic hyperplane containg S or is a hypersphere. In the former case M is a "bigraph" over H: it meets any geodesic orthogonal to H either not at all or transversaly in two points (one on each side of H) or tangentially on H.

Download

55   Analysis of a dynamic, decentralized exchange economy
Ennio Stacchetti

A dynamic exchange economy model is presented. Similarly to the Walrasian equilibrium problem, each consumer is characterized by a feasible set and by an instantaneous demand function, that depends on the price vector, time, and the commodity holding. The commodity holding of each consumer varies according to his instantaneous demand function at each moment. We show that the market can choose prices that will lead the commodity holding of each consumer to remain in his consumption set while the aggregate commodity holding satisfies the scarcity constraints of the market.

Download

56   On failure of the complementing condition and nonuniqueness in linear elastostatics
Henry Simpson and Scott J. Spector

Consider a homogeneous, isotropic body composed of a compressible linearly elastic material and assume that the body is at equilibrium in a state of plane strain. The traction problem for such a body (in the absence of body forces and surface tractions) consists of finding a displacement U=(u₁,u₂) that satisfies (cf., e.g., Gurtin [4])

 (1)   U + ( + ) div U = 0    in R.

 (2)   [ (U + U^T) + (div U) I] n = 0    on ðR.

Here R R² is a regular region, n the outward unit normal to the boundary, ðR, and , and are the (constant) Lamé moduli.
It is well-known that (1) and (2) have a unique solution, modulo an infinitesimal rigid deformation, provided that ≠ 0, + ≠ 0, and 2 + ≠ 0.
The purpose of this note is to demonstrate that the above mentioned uniqueness result fails when = - . In fact we show that (1) and (2) have an infinite number of linearly independent solutions (in spite of the ellipticity of the equations). The reason for this unusual (for an elliptic system) behavior is that the boundary conditions fail to satisfy the complementing (or Lopatinsky-Shapiro) conditions.

Download

57   Complete integrability in statistical mechanics and the Yang-Baxter equations
Craig Tracy

In this paper we give a differential formulation of the Yang-Baxter equations. This formulation leads to the introduction of the Yang-Baxter ideal I_YB, the basic geometric object in this formulation. These ideas are illustrated in the context of the Baxter model and the general eight-vertex model.

Download

58   Boundedness of solutions of Duffing's equation
Tongren Ding

J. Littlewood, L. Markus, and J. Moser proposed independently the boundedness problem for solutions of Duffing's equation: x+g(x)=p(t), where p(t) is continuous and periodic and g(x) is superlinear at infinity. The purpose of this paper is to prove that all solutions of the above-mentioned Duffing's equation are bounded for tR when p(t) is even (or when p(t) is odd and g(x) is odd).

Download

59   Workshop on price adjustment, quantity adjustment, and business cycles
Abstract

The workshop dealt with economic models in which time plays an essential role, and both the description of adjustment to a static equilibrium and the description of equilibrium paths were considered. From a mathematical point of view, discrete dynamical systems and the dynamics of ordinary and partial differential equations played a major role.

Download

60   The Coase theorem - An informational perspective
Rafael Rob

It is common knowledge these days that environmental policy plays a crucial role in a society characterized by a rapidly developing technology. While a world of highly mechanized productions methods offers its inhabitants a larger supply of goods and services, it raises at the same time serious questions about the ecological price that has to be paid for this increased abundance. The public concern expressed through the media, and governmental responses to this concern via budgetary provisions testify to the importance of the issue.

Download

61   Approximate Newton methods and homotopy for stationary operator equations
Joseph W. Jerome

A quadratically convergent algorithm, based upon a Newton-type iteration, is defined to approximate roots of operator equations in Banach spaces. Fréchet derivative operator invertibility is not required; approximate right inverses are used in a neighborhood of the root. This result, which requires an initially small residual, is sufficiently robust to yield existence; it may be viewed as a generalized version of the Kantorovich theorem. A second algorithm, based on continuation via single, Euler-predictor/Newton-corrector iterates, is also presented. It has the merit of controlling the residual until the homotopy terminates, at which point the first algorithm applies. This method is capable of yielding existence of a solution curve as well. An application is given for operators described by compact perturbations of the identity.

Download

62   A note on competitive bidding with asymmetric information
Rafael Robz

An interesting case of competitive bidding with an asymmetrical knowledge about the true value of the auctioned object is examined by R. Wilson [4]. The primary motivation for his study is the insight it provides about the value of information, or, more specifically, about the relative gains of the informed bidder vs. the uninformed bidder. As a by-product one can learn something about the ability of the seller to appropriate or realize the value of the item he offers for sale and about the identiy of the buyer. His analysis tells us, in short, about allocations and imputation under conditions of uncertainty and symmetric market positions - a fundamental question in economic theory. The purpose of this paper is expositional. By means of two alternative approaches, I will derive the equilibrium strategies and outcomes of the bidding game formulated by Wilson. A few flaws in his analysis will be corrected thererby. Additional examples illustrating the results will be offered. To be self-sufficient, let me start out by presenting the real-life situtation we wish to investigate and the model corresponding to it.

Download

63   Equilibrium price distributions
Rafael Rob

Equilibrium price distributions (for a homogeneous product) consistent with individual incentives are investigated. They arise in informationally imperfect markets in which the only primitive datum is the distribution of search costs. It is shown that single, multi- and continuous price distributions are all viable long-run phenomena depending on the nature of search costs. A method for computing equilibrium price distributions is also provided.

Download

64   The linearizing projection, global theories
William H. Ruckle

A linearizing operator or projection is a device which converts nonlinear information into linear form. A well-known example of a linearizing projection is the Shapley value, both in the descrete case (Shapley, 1953) and the continuous case (Aumann and Shapley, 1974). A linearizing projection usually satisfies certain axioms of rationality which insure that it is the "unique, fair" allocation or distribution. Thus it is an admiriable bookkeeping device because bookkeeping must be linear.
In Ruckle (1982) a first attempt was made to treat the Aumann-Shapley theory of values in the setting of functionals defined in an arbitrary Banach space E.
This paper continues the effort begun in Ruckle (1982) by constructing three global theories of linearizing projections (or x₀-value). These theories are called "global" because they refer to spaces of functionals which are defined on the entire Banach space E. In Section 6 we shall describe what we mean by a "local" theory and explain why such theories are needed.

Download

65   Ergodic properties of linear dynamical systems
Russell Johnson, Kenneth Palmer, and George R. Sell

The Multiplicative Ergodic Theorem give information about the dynamical structure of a cocycle , or a linear skew product flow , over a suitable base space M. In typical applications the base space M is either an attractor; a compact invariant set; or the space of coefficients for a diffeomorphism, a differential equation, or a vector field. This theorem asserts that for every invariant probability measure on M there is a measurable decomposition of the vector bundle over M into invariant measurable subbundles, and that every solution with initial conditions in any of these subbundles has strong Lyapunov exponets. These exponents, or growth rates, depend on the measure , and when is ergodic, they are constant (almost everywhere) on M and form a finite set meas(), the measurable (Millionscikov-Oseledec) spectrum.
The main objective in this paper is to study the connection between the measurable spectrum meas() and the dynamical spectrum dyn introduced by Sacker and Sell (1975, 1978, 1980). (Also see Daletskii and Krein (1974), as well as Selgrade (1975). The dynamical spectrum dyn consists of those values R for which the shifted flow fails to have an exponential dichotomy over M. It follows from the Spectral Theorem, Sacker and Sell (1978), that the dynamical spectrum is the finite union of disjoint compact intervals when M is compact and dynamically connected.

Download

66   How a network of processors can schedule its work
Stanley Reiter

The problem addressed in this paper is to design a method by which a network of processors confronted with a flow of tasks may distribute the computing to be done among the processors so as to make effective use of them to perform the required computations. The method, and its variants, presented in this paper gives weight to the objectives of carrying out the prescribed tasks in short time, and to the relative urgencies associated with those tasks. This problem is reminiscent of the problem of scheduling the flow of jobs through a machine shop. The methods presented here are adapted from a method developed for that problem which were described in [1].

Download

67   Linear subdivision is strictly a polynomial phenomenon
R.N. Goldman and D.C. Heath

In this paper we give an elementary proof that polynomial curves are the only differentiable curves which permit subdivision by standard linear techniques. Subdivision methods for rational polynomial curves are also discussed.

Download

69   Realization and Nash implementation: Two aspects of mechanism design
Steven R. Williams

In this paper we will show how a message process which "realizes" (or computes) a given social choice rule F can be used to construct a game which implements F in Nash equilibrium. Any efficient encoding of information that occurs in the message process causes a corresponding reduction in the size of the strategy space of the game which we will construct to implement F.
Necessary and (stronger) sufficient conditions on the message process will be given for this construction.

Download

70   Sufficient Conditions for Nash Implementation
Steven R. Williams

Download

71   Equilibria in Banach lattices without ordered preferences
Nicholas C. Yannelis and William R. Zame

Download

72   The reciprocals of solutions of linear ordinary differential equations
William A. Harris, Jr. and Yasutaka Sibuya

Download

73   A dynamical meaning of fractal dimension
Steve Pelikan

Download

74   Continuous-time portfolio management: Minimizing the expected time to reach a goal
David C. Heath and William D. Sudderth

Download

75   Information flows intrinsic to the stability of economic equilibrium
J.S. Jordan

Download

84   Subjective probability and expected utility without additivity
David Schmeidler

86   State categories, closed categories, and the existence semi-continuous entropy functions
F. William Lawvere

87   Functional Remarks on the General Concept of Chaos
F. William Lawvere

101   The derivative of a tensor-valued function of a tensor
Donald E. Carlson and Anne Hoger

113   On the derivatives of the principal invariants of a second-order tensor
D. Carlson and A. Hoger

171   On Hadamard stability in finite elasticity
H.C. Simpson and S.J. Spector

239   Interaction of Shallow-Water Waves and Bottom Topography
B. Boczar-Karaki, J.L. Bona, and D.L. Cohen

286   Finite difference methods for the transient behavior of a semiconductor device
Jim Douglas, Jr. and Yuan Yirang

Download

287   The extrapolation for boundary finite elements
Li Kaitai and Yan Ningning

Download

288   Stochastic growth models
R. Durrett and R. Schonmann

Download

289   Remarks about equilibrium configurations of crystals
David Kinderlehrer

Download

290   Eventual C -regularity and concavity for flows in one-dimensional porous media
D.G. Aronson and J.L. Vazquez

Download

291   Distributed data structures for scientific computation
L.R. Scott, J.M. Boyle, and B. Bagheri

Download

292   Simulation of flow in naturally fractured petroleum reservoirs
Jim Douglas, Jr., Paulo J. Paes Leme, Todd Arbogast, and Tânia Schmitt

Download

293   Optimal regularity for one-dimensional porous medium flow
D.G. Aronson and L.A. Caffarelli

Download

294   Liquid crystals and energy estimates for -valued M maps
Haim Brezis

Download

295   Analysis of the simulation of single phase flow through a naturally fractured reservoir
Todd Arbogast

Download

296   The coupling method of finite elements and boundary elements for radiation problems
He Yinnian and Li Kaitai

Download

297   Nonlinear effects in wave equation with a cubic restoring force
T. Cazenave, A. Haraux, L. Vazquez, and F.B. Weissler

Download

298   Some blow-up results for a nonlinear parabolic equation with a gradient term
M. Chipot and F.B. Weissler

Download

299   Perturbation solutions of simple and double bifurcation problems for Navier-Stokes equations
Li Kaitai

Download

300   The convergence on the multigrid algorithm for Navier-Stokes equations
Chen Zhangxin and Li Kaitai

Download

301   Martingale approach for modeling DNA synthesis
A. Gerardi and G. Nappo

Download

302   Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon
Douglas N. Arnold, L. Ridgway Scott, and Michael Vogelius

Download

303   Error analysis in , for mixed definite element methods for linear and quasi-linear ^M elliptic problems
Ricardo G. Duran

Download

304   An efficient linear scheme to approximate parabolic free boundary problems: Error estimates and implementation
Ricardo Nochetto and Claudio Verdi

Download

305   Nonuniqueness for a hyperbolic system: Cavitation in nonlinear elastodynamics
K.A. Pericak-Spector and Scott J. Spector

Download

306   q-series and orthogonal polynomials associated with Barnes' first Lemma
E.G. Kalnins and Willard Miller, Jr.

Download

307   A uniformly accurate finite element method for Mindlin-Reissner plate
Douglas N. Arnold and Richard S. Falk

Download

308   TVD properties of a class of modified ENO schemes for scalar conservation laws
Chi-Wang Shu

Download

309   A random boundary value problem modeling spatial variability in porous media flow
Edmund Dikow and Ulrich Hornung

Download

310   Compact attractors and singular perturbations
Jack K. Hale

Download

311   The TVD-projection method for solving implicit numeric schemes for scalar conservation laws: A numerical study of a simple case
A. Bourgeat and B. Cockburn

312   Navier-Stokes computation of transonic vortices over a round leading edge delta wing
Bernhard Muller and Arthur Rizzi

Download

313   On the accuracy of vortex methods at large times
J. Thomas Beale

Download

314   Decomposition methods for adherence problems in finite elasticity
P. Le Tallec and A. Lotfi

Download

315   Approximation of waves in composite media
Jim Douglas, Jr. and Juan E. Santos

Download

316   The double porosity model for single phase flow in naturally fractured reservoirs
Todd Arbogast

Download

317   Two-phase immiscible flow in naturally fractured Reservoirs
Todd Arbogast, Jim Douglas, Jr., and Juan E. Santos

Download

318   Numerical simulation of immiscible flow in porous media based on combining the method of characteristics with mixed finite element procedures
Jim Douglas, Jr. and Y. Yirang

Download

319   Sharp maximum norm error estimates for finite element approximations Of the Stokes problem in 2-D
R. Durán, R.H. Nochetto, and J. Wan

Download

320   A phase transition for a system of branching random walks in a random environment
Andreas Greven

Download

321   Brownian models of open queueing networks with homogeneous customer populations
J.M. Harrison and R.J. Williams

Download

322   Solutions et mesures invariantes pour des equations d'evolution Stochastiques du type Navier-Stokes
Ana Bela Cruzeiro

Download

323   Solutions et mesures invariantes pour des equations d'evolution Stochastiques du type Navier-Stokes
Ana Bela Cruzeiro

Download

324   Typical cluster size for 2-dim percolation processes (revised)
Bao Gia Nguyen

Download

325   Stable defects of minimizers of constrained variational principles
Robert Hardt, David Kinderlehrer, and Fang-Hua Lin

Download

326   Equilibrium configurations of crystals
Michel Chipot and David Kinderlehrer

Download

327   Malliavin's C functionals of a centered Gaussian system
Kiyosi Itô

Download

328   Derivation of the hydrodynamical equation for one-dimensional Ginzburg-Landau model
Tadahisa Funaki

Download

329   Schauder expansion by some quadratic base function
Masaya Yamaguti

Download

330   Stabilized mixed methods for the Stokes problem
Franco Brezzi and Jim Douglas, Jr.

Download

331   Inertial manifolds for reaction diffusion equations in higher space dimensions
J. Mallet-Paret and G.R. Sell

Download

332   Relaxation methods for liquid crystal problems
San-Yih Lin and Mitchell Luskin

Download

388   The Runge-Kutta Local Projection P¹-Discontinuous-Galerkin Finite Element Method for Scalar Conservation Laws
Bernardo Cockburn and Chi-Wang Shu

460   A quantitative model for lifespan curves
Matthew Witten

531   On the Semilinear Elliptic Equation in
Jong-Shenq Guo

633   Numerical approximation of the solutions of delay differential equations on an infinite interval using piecewise constant arguments
K.L. Cooke and I. Györi

772   Computing centre conditions for certain cubic systems
N.G. Lloyd and J.M. Pearson

860   Quantum holography and neurocomputer architectures
Walter Schempp

987   Numerical methods for the regularization of descriptor systems by output feedback
Angelika Bunse-Gerstner, Volker Mehrmann and Nancy K. Nichols

1043   Protocol verification using discrete-event systems
Karen Rudie and W. Murray Wonham

1044   Nucleation, kinetics and admissibility criteria for propagating phase boundaries
Rohan Abeyaratne and James K. Knowles

1048   On the computation of suboptimal controllers for unstable infinite dimensional systems
Onur Toker and Hitay Özbay

1051   A free boundary problem arising in the modeling of interanl oxidation of binary alloys
Bei Hu and Jianhua Zhang

1055   Multiphase averaging for generalized flows on manifolds
H.S. Dumas, F. Golse, and P. Lochak

1056   Global solutions and quenching to a class of quasilinear parabolic equations
Bei Hu and Hong-Ming Yin

1063   Maximum principle for state-constrained optimal control problems governed by quasilinear elliptic equations
Eduardo Casas and Jiongmin Yong

1064   Optimal control for degenerate parabolic equations with logistic growth
Suzanne M. Lenhart and Jiongmin Yong

1084   Fluids of differential type: Critical review and thermodynamic analysis
J.E. Dunn and K.R. Rajagopal

1231   Entropy maximization
K.B. Athreya

1316   Soliton's rebuilding in one-dimensional Schrödinger model with polynominal nonlinearity
Valery E. Grikurov

Download

1317   On self-similar solutions of the Navier-Stokes equations
J. Necas, M. Ruzicka, and V. Sverák

Download

1318   Remarks on W^2,p-solutions of bilateral obstacle problems
Srdjan Stojanovic

Download

1319   Pseudospectral vs. finite difference methods of initial value-problems with discontinuous coeffcients
Erding Luo and Heinz-Otto Kreiss

Download

1320   Soliton's rebuilding in one-dimensional Schrödinger model with polynominal nonlinearity
Valery E. Grikurov

Download

1321   A multiclass closed queueing network with unconventional heavy traffic behavior
J.M. Harrison and R.J. Williams

Download

1322   Microlocal analysis on Morrey spaces
Michael E. Taylor

Download

1323   Homogenization of biharmonic equations in domains perforated with tiny holes
Chaocheng Huang

Download

1324   An inverse obstacle problem: A uniqueness theorem for spheres
Changmei Liu

Download

1325   Approximation of a laminated microstructure for a rotationally invariant, double well energy density
Mitchell Luskin

Download

1326   Haplotyping algorithms
Eric Sobel, Kenneth Lange, Jeffrey R. O'Connell, and Daniel E. Weeks

Download

1327   Haplotyping algorithms
Eric Sobel, Kenneth Lange, Jeffrey R. O'Connell, and Daniel E. Weeks

Download

1328   Haplotyping algorithms
Eric Sobel, Kenneth Lange, Jeffrey R. O'Connell, and Daniel E. Weeks

Download

1329   Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems
Bernardo Cockburn, Don A. Jones, and Edriss S. Titi

Download

1330   Inverse Schrödinger scattering on the line with partial knowledge of the potential
Tuncay Aktosun

Download

1331   Partition of the potential of the one-dimensional Schrödinger equation
Tuncay Aktosun and Cornelis van der

Download

1332   Convergence of the multigrid method with a wavelet coarse grid operator
Bjorn Engquist and Erding Luo

Download

1333   Ergodic properties of the spin-boson system
V. Jaksic and C.-A. Pillet

Download

1334   Recursive solution for diffuse tomographic systems of arbitrary size
S.K. Patch

Download

1335   Ergodic properties of the spin-boson system
V. Jaksic and C.-A. Pillet

Download

1336   Bitangential structured interpolation theory
Juan C. Cockburn

Download

1337   The blow-up problem for exponential nonlinearities
Satyanad Kichenassamy

Download

1338   How many parameters can one solve for in diffuse tomography?
F.A. Grünbaum and S.K. Patch

Download

1339   Reciprocal relations, bounds and size effects for composites with highly conducting interface
Robert Lipton

Download

1340   A global nonexistence theorem for quasilinear evolution equations with dissipation
Howard A. Levine and James Serrin

Download

1341   The conjugate operator meth