Approximation orders of shift-invariant subspaces generated by the shifts of one compactly supported function are considered. In that course, explicit approximation maps are constructed. The approach avoids quasi- interpolation and applies to stationary and non-stationary refinements. The general results are specialized to box spline spaces, to obtain new results on their approximation orders.

Topics: DTIC Archive, Ron, Amos, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES,...

This paper determines the nonnegativity of the principal components of an n x n nonnegative matrix P in terms of the marked reduced graph R(A) of A = P - rho(P)I, the minus M matrix which can be associated with P. We then apply this result to consider various types of nonnegative bases for the Perron eigenspace of P which can be extracted from a certain nonnegative matrix which is a polynomial in P. We also obtain a characterization for the eigenprojection on the Perron eigenspace of P to be,...

Topics: DTIC Archive, Neumann, Michael, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES,...

Characterizations of the linear independence and stability properties of the integer translates of a compactly supported univariate refinable function in terms of its mask are established. The results extend analogous ones of Jia and Wang which were derived for dyadic refinements and finite masks.

Topics: DTIC Archive, Ron, Amos, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *SHIFTING,...

A complete characterization is given of closed shift-invariant subspaces of which provide a specified approximation order. When such a space is principal (i.e., generated by a single function), then this characterization is in terms of the Fourier transform of the generator. As a special case, we obtain the classical Strang-Fix conditions, but without requiring the generating function to decay at infinity. The approximation order of a general closed shift-invariant space is shown to be already...

Topics: DTIC Archive, DE Boor, Carl, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *FOURIER...

The paper is concerned with the introduction and study of multiresolution analysis based on the up function, which is an infinitely differentiable function supported on (0,2). Such analysis is, necessarily, nonstationary. It is shown that the approximation orders associated with the corresponding spaces are spectral, thus making the spaces attractive for the approximation of very smooth functions.

Topics: DTIC Archive, Dyn, N, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *FUNCTIONAL...

The Harry Dym equation, which is related to the classical string problem, is derived in three different ways. An implicit cusp solitary wave solution is constructed via a simple direct method. The existing connections between the Harry Dym and the Korteweg-de Vries equations are uniformised and simplified, and transformations between their respective solutions are carried out explicitly. Whenever possible, physical insights are provided.

Topics: DTIC Archive, Hereman, W, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *WAVE EQUATIONS,...

A simple characterization is given of finitely generated subspaces of L2(IR(d)) which are invariant under translation by any (multi)integer, and used to give conditions under which such a space has a particularly nice generating set, namely a basis, and, more than that, a basis with desirable properties, such as stability, orthogonality, or linear independence. The last property makes sense only for 'local' spaces, i.e., shift-invariant spaces generated by finitely many compactly supported...

Topics: DTIC Archive, De Boor, Carl, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *FUNCTIONS,...

The author's conjecture concerning the knot sequence whose associate B-spline sequence has maximum max-norm condition number is disproved. Related condition numbers are explored and the corresponding conjecture concerning the 'worst' knot sequence for them is further supported by numerical results. There is numerical evidence that, in calculations devoted to bounding the p-norm condition number of the (appropriately scaled) B-spline basis, the extreme case occurs for a knot sequence without...

Topics: DTIC Archive, DE Boor, Carl, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *SPLINES,...

This document considers a system of ordinary differential equations of the form (*) q + V sub q (t,q) = f(t) where f and V are periodic in t, V is periodic in the components of q = (q sub 1,..., q sub m), and the mean value of f vanishes. By showing that a corresponding functional is invariant under a natural Z sub n action, a simple variational argument yields at least n + 1 distinct periodic solutions of (*). More general versions of (*) are also treated as is a class of Neumann problems for...

Topics: DTIC Archive, Rabinowitz, Paul H, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *PARTIAL...

The determination of the approximation power of spaces of multivariate splines with the aid of quasi interpolants is reviewed. In the process, streamlined description of the existing quasi interpolants theory is given. The author begin with a brief review of the approximation power of univariate splines since the techniques for its investigation are also those with which people have tried to understand the multivariate setup. (That may in fact be the reason why we know so little about it.) He...

Topics: DTIC Archive, de Boor, Carl, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *MULTIVARIATE...

Given a linear space S (over some field), we attempt to determine the dimension of spaces of a certain form with a L a (finite) sequence of linear endomorphisms of S, i.e., a sequence in L(S).

Topics: DTIC Archive, DE Boor, Carl, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *KERNEL...

It was proved in an earlier work that corner cutting of any kind converges to a Lipschitz-continuous curve, but the question of how one might guarantee that the limiting curve be smoother than that was not considered there. Recently, Gregory and Qu GQ took up this question and established sufficient conditions for a certain systematic and local corner cutting scheme to give a limiting curve in C. Since GQ use the same parametrization of the successive broken lines that made the argument in B so...

Topics: DTIC Archive, De Boor, Carl, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *CUTTING,...

Minitab is a user-friendly statistical computer package widely used in industry and academia. The Kaplan-Meier ple and the Tarone-Ware class of tests are often used in biostatistics and reliability theory to compare two survival distributions. The Tarone-Ware class of tests is generated by allowing the power of the sample size to run from zero (inclusive) up to and including one. The value 0 corresponds to the Mantel-Haenszel test, .5 to the Tarone-Ware and 1 to the Tarone-Ware version of...

Topics: DTIC Archive, Soms, Andrew P, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *COMPUTER...

This document establishes the existence of a homoclinic solution of a Hamiltonian system assuming that the potential V is T periodic in t, grows more rapidly than quadratically as the value of 9 approaches limit of infinity and satisfies some other technical conditions. The homoclinic solution is obtained as the limit of subharmonic solutions of (*). The subharmonic solutions are found using a minimax argument.

Topics: DTIC Archive, Rabinowitz, Paul H, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *ORBITS,...

Topics: DTIC Archive, Crandall, M G, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *MATHEMATICAL...

The generalization of univariate interpolation to the multivariate context is made difficult by the fact that one has to decide just which of the many of its nice properties to preserve,as it is impossible to preserve them all. Particularly annoying is the fact that the dimensions of standard multivariate polynomial spaces, such as pi sub k, make up only a small subset of double Z, hence we cannot hope to interpolate uniquely at an arbitrary pointset contained as proper subclass within from an...

Topics: DTIC Archive, De Boor, Carl, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES,...

Topics: DTIC Archive, Ron, Amos, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES,...

We study in this paper certain types of bases for shift-invariant subspaces. Our primary objective is to connect among three important families of basis sets: shift-invariant sets. Weyl-Heisenberg sets, and affine (wavelet) sets. The present paper is the first in a series of three, and is concerned with the basic theory of shift-invariant bases for the shift-invariant spaces. The two papers, (RS1) and (RS2), will focus on the applications of the theory developed here to Weyl-Heisenberg and...

Topics: DTIC Archive, Ron, Amos, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *SHIFTING,...

The construction of a polynomial interpolant to data given at finite pointsets (or, most generally, to data specified by finitely many linear functionals) is considered, with special emphasis on the linear system to be solved. Gauss elimination by segments(i.e., by groups of columns rather than by columns) is proposed as a reasonable means for obtaining a description of all solutions and for seeking out solutions with 'good' properties. A particular scheme, due to Amos Ron and the author, for...

Topics: DTIC Archive, De Boor, C, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *MULTIVARIATE...

Methods for representing multi-dimensional objects, such as functions of several variables and, more generally, (hyper-)surfaces is the main objective. One goal of such representation, whether approximate or exact, is the efficient evaluation of the object: Multivariate Polynomial Interpolation as well as Scattered Data Approximation both fall into this category. Another goal is a representation that allows one to identify and access easily and simultaneously relevant aspects of the object. The...

Topics: DTIC Archive, DE Boor, Carl, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *MULTIVARIATE...

The existence and partial regularity of the Nash point equilibria for a pair of multiple integrals are studied. The conditions as well as the results are similar to those for local minima obtained by Acerbi, Fusco and Giaquinta, Guisti. Keywords: Ky Fan inequality; Quasiconvexity; Lower semicontinuity; Hausdorff measure.

Topics: DTIC Archive, Chang, Kung-Ching, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *CALCULUS...

The existence of various kinds of connecting orbits is established for a certain Hamiltonian system as well as its time dependent analogue. For the autonomous case, our main assumption is that V has a global maximum, e.g. at X = O and we find a various kinds of orbits terminating at O. For the time dependent case V has a local but not global maximum at X = O and we find a homoclinic orbit emanating from and terminating at O. Keywords: Periodic solution.

Topics: DTIC Archive, Rabinowitz, Paul H, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *ORBITS,...

This document investigates the relations between an ideal I of finite codimension in the space pi of multivariate polynomials and various ideals which are generated by lower order perturbations of the generators of I. Special emphasis is given to the question of the codimension of I and its perturbed counterpart and to the local approximation order of their kernels. The discussion, stimulated by certain results in approximation theory, allows us to provide a simple analysis of the polynomial...

Topics: DTIC Archive, De Boor, Carl, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *MULTIVARIATE...

Stationary eigenmodes are derived for wave propagation in a medium with quadratic and cubic nonlinearities. Aperiodic algebraic solitary waves are the eigenmodes with a continuous spectrum while periodic solitary waves are those with a spectrum comprising an infinite number of harmonics. Stationary eigenmodes comprising the fundamental and the second harmonic only have also been derived. The stability of the aperiodic solitary waves have been studied numerically and a stabilization technique...

Topics: DTIC Archive, Banerjee, P P, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES,...

The existence of multiple periodic solutions of second order Hamiltonian systems are studied which are both forced periodically in time and depend periodically on the dependent variables. Consider the Hamiltonian system: q(double dot) + V' (q) = 0 where q = (q(1),....,q(n)) and V is periodic in q sub i, 1 or =i or = n. It is known the the equation then possesses at least n + 1 equilibrium solutions. One can give criteria for V so that the equation has non-constant periodic solutions and (b)...

Topics: DTIC Archive, Rabinowitz, Paul H, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES,...

This paper presents a minimax method which gives existence and multiplicity results for time periodic solutions of a class of Hamiltonian systems when a singular potential is present. The singularity satisfies the strong force condition of Gordon. When milder singularities are permitted a notion of generalized T-periodic solution is introduced and we get existence and multiplicity results for such solutions. Keywords: Minimax method; Calculus of variations; Hamiltonian systems; Singular...

Topics: DTIC Archive, Bahri, Abbas, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *MINIMAX...

This paper considers the problem of asymptotic decay as t approaches infinity of solutions of the wave equation u sub tt - delta u = -a(x) beta(u sub t,gradu), (t,x) is an element of R+X Omega (a bounded, open, connected set in R to the Nth power, N or = 1, with smooth boundary), u = O on R+ X del Omega. The nonlinear function beta is assumed to be globally Lipschitz continuous, beta(y) = o(abs. val. y) as abs. val. y approaches infinity, beta(O,y2,..., y(N+1) = O, y1 beta (y1,...,y(N+1) or =...

Topics: DTIC Archive, Slemrod, M, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *WAVE EQUATIONS,...

This document studies the multiplicity of solutions for semilinear elliptic systems as well as Hamiltonian systems, in which the nonlinear terms are periodic in certain variables. The cuplength for cohomology rings of the torus is used. Our results generalize and unify several recent works by Conley-Zehnder, Rabinowitz, Mawhin-Willem, Pucci-Serrin etc. In particular, the resonance problems and indefinite problems are studied. Keywords: Critical point, Neumann problem, Periodic solution.

Topics: DTIC Archive, Chang, Kung-Ching, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES,...

This report provides a brief introduction to the use of MACSYMA, a symbolic manipulation program for mathematics. The first Chapter outlines invoking Macsyma, running tutorials and demos, saving transcripts and programs, editing and plotting facilities. The second Chapter provides 12 examples of Macsyma use. The following topics are touched upon: factorization, integration, matrix multiplications, eigenvalue problem, infinite series, recursion definitions and relations, solving systems of...

Topics: DTIC Archive, Hereman, Willy, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *PROGRAMMING...

The Stokes Phenomenon is known to be a pervasive feature of asymptotics, but its explanation in the literature is obscured by intricate and lengthy technicalities. This article presents a simpler approach to its understanding and treatment as a natural aspect of a well-motivated characterization of functions by approximants of different multivaluedness. Keywords: Waves; Special functions.

Topics: DTIC Archive, Meyer, Richard E, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *SPECIAL...

We study the equations of one-dimensional isothermal elastic response as the small viscosity limit of the equations of viscoelasticity, in a context of self-similar viscous limits for Riemann data. The limiting procedure is justified and a solution of the Riemann problem for the equations of elasticity is obtained. The emerging solution is composed of two wave fans, each consisting of rarefactions, shocks and contact discontinuities, separated by constant states. At shocks the self-similar...

Topics: DTIC Archive, Tzavaras, Anthanasios E, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES,...

This document studies subharmonic solutions near an equilibrium point for a Hamiltonian system. On the linear part of the system we impose a condition expressed in terms of its symplectic invariants. The higher order term is assumed to be superquadratic near the equilibrium point, and we show that this condition can be reduced to the center manifold. We transform the Hamiltonian system to a variational problem and we apply a minimax argument to find critical points. Keywords: Hamiltonian...

Topics: DTIC Archive, Felmer, Patricio L, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES,...

A generalization of the class of monotone twistmaps to maps of S sub 1 x R sub n is proposed. The existence of Birkhoff orbits is studied, and a criterion for positive topological entropy is given. These results are then specialized to the case of monotone twist maps. Finally it is shown that there is a large class of symplectic maps to which the foregoing discussion applies. Keywords: Dynamical systems; Theorems.

Topics: DTIC Archive, Angenent, Sigurd B, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES,...

Starting from the Painleve-Backlund equations obtained from Painleve analysis of the Korteweg-de Vries equation, closed form solitary wave solutions are explicitly constructed. It is shown that repetitive application of the Mobius group of fractional linear transformations does not lead to new solutions. Various connections of the Painleve method with Hirota's formalism, the Backlund transformation method, the Lax approach and the Inverse Scattering Technique are discussed in detail.

Topics: DTIC Archive, Hereman, W, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *PARTIAL...

The Buehler (1957) optimal 1-alpha lower confidence limits on the reliability of k of n systems of independent components is derived for the case of zero failures and equal sample sizes. The limiting form of the lower confidence limit is obtained for n-1 of n systems as n goes to infinity. This result is used to show the nonconservativeness of the Maximus method given by Spencer and Easterling (1986). Keywords: Parallel system, Series system.

Topics: DTIC Archive, Soms, Andrew P, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *COMPUTER...

Spaces spanned by finitely or countably many translates of one or several basic functions play an important role in spline theory, radial basis function theory, sampling theory and wavelet theory. Spline theory stresses the case when the basic functions are compactly supported, while sampling theory single out the case when the spectrum (i.e., the support of the Fourier transform) of the basic functions is compact. In the radial basis function theory, neither of these is assumed, and instead,...

Topics: DTIC Archive, De Boor, Carl, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *FOURIER...

Minitab is a user-friendly statistical computer package widely used in industry and academia. The Kaplan-Meier ple and Gehan's test are often used in biostatistics and reliability theory to compare two survival distributions. The main idea of the program is to first break ties between censored and completed observations by adding to the censored observations one-half of the smallest non-zero difference for the ordered combined observations. This does not change the K-M ple or Gehan's test....

Topics: DTIC Archive, Soms, Andrew P, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *COMPUTER...

This paper proves the existence of infinitely many distinct T-periodic solutions of a certain perturbed Hamiltonian system under the conditions that H is of C sub 1, superquadratic, and possesses exponential or polynomial growth at infinity and that f is of sub 1, 2 and T-periodic, via minimax methods. Keywords: Monotone truncations, A priori estimates, Multiple periodic solutions.

Topics: DTIC Archive, Long, Yiming, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, EXPONENTIAL...

The goal was to study the use of (smooth) piecewise polynomial spaces for the approximation of functions in one and, preferably, in several variables and find a better understanding of how well one can approximate from specific spaces, for specific schemes for approximation, including good bases for such spaces, and to make inroads on the problem of extending techniques for curve fitting by smoothly patched curves to surface interpolation. Progress was made on these questions, and on two...

Topics: DTIC Archive, De Boor, Carl, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES,...

This is the first of two papers in which the author develops a theory of parabolic equations for curves on surfaces which can be applied to the so- called curve shortening or flow by mean curvature problem, as well as to a number of models for phase transitions in two dimensions. This document introduces a class of equations for which the initial value problem is solvable for initial data with p-integrable curvature, and we also give estimates for the rate at which the p-norms of the curvature...

Topics: DTIC Archive, Angenent, Sigurd, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *PARTIAL...

The authors present a straightforward method of finding implicit solutions for nonlinear evolution and wave equations The method is illustrated by finding single implicit solitary wave solutions for the Harry Dym, Korteweg-de Vries, modified Korteweg-de Vries and Boussinesq equations. Keywords: Partial differential equations.

Topics: DTIC Archive, Banerjee, Partha P, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *WAVE...

A new approach for the construction of wavelets and prewavelets on IR d from multiresolution is presented. The method uses only properties of shift- invariant spaces and orthogonal projectors from L2(IRd) onto these spaces, and requires neither decay nor stability of the scaling function. Furthermore, this approach allows a simple derivation of previous, as well as new, constructions of wavelets, and leads to a complete resolution of questions concerning the nature of the intersection and the...

Topics: DTIC Archive, DE Boor, Carl, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *MULTIVARIATE...

The polynomial space H in the span of the integer translates of a box spline M admits a well-known characterization as the joint kernel of a set of homogeneous differential operators with constant coefficients. The dual space H has a convenient representation by a polynomial space P, explicity known, which plays an important role in box spline theory as well as in multivariate polynomial interpolation. This paper characterized the dual space P as the joint kernel of simple differential...

Topics: DTIC Archive, De Boor, Carl, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *SPLINES,...

A MACSYMA program is presented which determines whether a given single nonlinear ODE or PDE with real polynomial terms fulfills the necessary conditions for having the Painleve property. The program listing is given, together with a synopsis of the algorithm, a model of the output of the program, a list of tested examples and instructions to use the package. Keywords: Integrability, Symbolic programming, Soliton theory, Dynamical systems.

Topics: DTIC Archive, Hereman, Willy, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *SYMBOLIC...

In this paper we study strictly positive definite functions on the unit sphere of the m-dimensional Euclidean space. Such functions can be used for solving a scattered data interpolation problem on spheres. Since positive definite functions on the sphere were already characterized by Schoenberg some fifty years ago, the issue here is to determine what kind of positive definite functions are actually strictly positive definite. The study of this problem was initiated recently by Xu and Cheney,...

Topics: DTIC Archive, Ron, Amos, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *TOPOLOGY,...

A MACSYMA program is presented which determines whether a given single nonlinear ODE or PDE with (real) polynomial terms fulfills the necessary conditions for having the Painleve property. Together with some mathematical background, the authors give a synopsis of the algorithm for the computer program, its scope and limitations. Various examples of typical output of the program are provided. Keywords: Coefficients, Exponents.

Topics: DTIC Archive, Hereman, Willy, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *COMPUTER...

The study of time periodic solutions of the n-body problem is a classical one. See e.g. (1). The authors' goal in this paper is to present some new variational approaches of a global nature to a class of problems of 3-body type. Keywords: Calculus of variations; Theorems; Computations.

Topics: DTIC Archive, Bahri, Abbas, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *N BODY...

Typical constructions of wavelets depend on the stability of the shifts of an underlying refinable function. Unfortunately, several desirable properties are not available with compactly supported orthogonal wavelets, e.g. symmetry and piecewise polynomial structure. Presently, multiwavelets seem to offer a satisfactory alternative. The study of multiwavelets involves the consideration of the properties of several (simultaneously) refinable functions. In Section 2 of this paper, we characterize...

Topics: DTIC Archive, Hogan, Thomas A., WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES,...

In this paper we generalize several results on uniform approximation orders with radial basis functions in (Buhmann, Dyn and Levin, 1993) and (Dyn and Ron, 1993) to Lp-approximation orders. These results apply, in particular, to approximates from spaces spanned by translates of radial basis functions by scattered centers. Examples to which our results apply include quasi- interpolation and least-squares approximation from radial function spaces.

Topics: DTIC Archive, Buhmann, Martin D, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES,...

Analytical studies of the hole-pressure error for non-Newtonian creeping flows over a transverse slot are pursued with particular interest in the theory of Higashitani, Pritchard, Baird and Lodge (HPBL). To correctly apply the HPBL theory a modified hole-pressure relation (MHPR) is employed. Some important mathematical properties of the MHPR are presented. By studying the MHPR in streamline coordinate formulation we find a fortuitous error cancellation phenomenon in the derivation of HPBL...

Topics: DTIC Archive, Yao, M, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *CREEP,...