singular limit of solutions of the very fast diffusion equation we prove that the distribution solutions of the very fast diffusion equation u t um m u t um m u 0u 0 in rn 0 rn 0 u x 0 u0 x u x 0 u0 x in rnrn where m n 2p n 2 and u0 x e x 2 u0 x e x 2 for any x r1 x r1 where e 0e 0 r1 0r1 0 m0 1 m0 n 2p 1 m0 n 2 we prove that the solution of the above problem will converge uniformly on every compact subset of rn 0 rn 0 to the maximal solution of the equation vt logvvt logv v x 0 u0 x v x 0 u0 x as m 0 m 0 for any smooth bounded domain rn rn m0 1 m0 max 1 n 2 p 1 m0 max 1 n 2 we prove the existence and uniqueness of solutions of the dirichlet problem u t um m u t um m u 0u 0 in 0 0 u u0u u0 in u gu g on 0 0 with either finite or infinite positive boundary value gg we also prove a similar convergence result for the solutions of the above dirichlet problem as m 0m 0

a new result for the porous medium equation derived from the ricci flow given r 2 with a good complete metric we show that the unique solution of the ricci flow approaches a soliton at time infinity solitons are solutions of the ricci flow which move only by diffeomorphism the ricci flow on r 2 is the limiting case of the porous medium equation when m is zero the results in the ricci flow may therefore be interpreted as sufficient conditions on the initial data which guarantee that the corresponding unique solution for the porous medium equation on the entire plane asymptotically behaves like a soliton solution

interaural correlation discrimination from diffuse field reference correlations just noticeable differences in interaural correlation jnds from diffuse sound field reference correlations are obtained in a three interval three alternative forced choice procedure jnds are measured for positive and negative deviations from nine narrowband reference conditions stimuli are 1 equivalent rectangular bandwidth wide noise bursts with center frequencies between 165 and 1500 hz the frequency dependent reference correlation ref is determined by the simulated interaural correlation under ideal diffuse sound field conditions results show that the interaural correlation at threshold for deviation toward the positive correlation range follows the reference curve in a nonlinear fashion for deviation toward the negative correlation range the interaural correlation at threshold is further afar the reference curve and does not markedly resemble its trend the results indicate that the previously found asymmetry for correlation discrimination from uncorrelated broadband stimuli to the pos

phase transitions and generalized motion by mean curvature we study the limiting behavior of solutions to appropriately rescaled versions of the allen cahn equation a simplified model for dynamic phase transitions we rigorously establish the existence in the limit of a phase antiphase interface evolving according to mean curvature motion this assertion is valid for all positive time the motion interpreted in the generalized sense of evans spruck and chen giga goto after the onset of geometric singularities

existence of singular solutions of a degenerate equation in r2 let a 1 a 2 a m 2 2 f c 0 g i c 0 be such that 0 g i t 2 on 0 i 1 m for any open image in new window p 1 we prove the existence and uniqueness of solutions of the equation u t logu u 0 in open image in new window satisfying open image in new window and logu x t log x f t as x logu x t log x a i g i t as x a i 0 uniformly on every compact subset of 0 t for any i 1 m under a mild assumption on u 0 where open image in new window we also obtain similar existence and uniqueness of solutions of the above equation in bounded smooth convex domains of 2 with prescribed singularities at a finite number of points in the domain

on singular diffusion equations with applications to self organized criticality we consider solutions of the singular diffusion equation t um 1ux x m 0 associated with the flux boundary condition limx um 1ux x 0 the evolutions defined by this problem depend on both m and we prove existence and stability of traveling wave solutions parameterized by each traveling wave is stable in its appropriate evolution these traveling waves are in l1 for 1 m 0 but have non integrable tails for m 1 we also show that these traveling waves are the same as those for the scalar conservation law ut f u x uxx for a particular nonlinear convection term f u f u m 1993 john wiley sons inc

a modified method for reconstructing periodic jacobi matrices in this note we discuss the reconstruction of periodic jacobi matrices from spectral data the method combines ideas and techniques from the algorithms given by boley and golub 1 2 and ferguson 3 resulting in a numerically stable algorithm applicable to a larger class of problems the number of initial data items needed for this method equals the number of items in the resulting matrix namely 2n

construction of band matrices from spectral data abstract a stable numerical algorithm is presented to generate a symmetric p band matrix from the given eigenvalues of the p greatest leading submatrices the algorithm consists of two parts first a matrix with the given spectral data is constructed then this matrix is transformed into a p band matrix leaving invariant the eigenvalues of the p greatest leading submatrices

motion of level sets by mean curvature ii we give a new proof of short time existence for the classical motion by mean curvature of a smooth hypersurface our method consists in studying a fully nonlinear uniformly parabolic equation satisfied by the signed distance function to the surface

inverse eigenvalue problem in structural design a method is presented for the design of a structure with specified low order natural frequencies the method can also be used for design problems in which certain bands devoid of any frequency constraints are specified this can further be used to generate initial feasible designs for optimum design problems with frequency constraints

inverse eigenvalue problems a collection of inverse eigenvalue problems are identified and classified according to their characteristics current developments in both the theoretic and the algorithmic aspects are summarized and reviewed in this paper this exposition also reveals many open questions that deserve further study an extensive bibliography of pertinent literature is attached

behaviour of solutions of a singular diffusion equation near the extinction time abstract we prove that if 2 and 0 u0 l1 r2 lp r2 for some constant p 1 is a radially symmetric function u0 0 and u is the unique solution of the equation u t log u u 0 in r 2 0 t u x 0 u 0 x in r2 which satisfies r 2 u x t d x r 2 u 0 d x 2 t 0 and rur x t u x t uniformly on a b as r x for any 0 t r 2 u 0 d x 2 then there exist unique constants 0 1 2 2 1 such that the rescaled function v y s u y t t t t t with s log t t will converge uniformly on every compact subset of r2 to the solution y of the ode r r r 0 in 0 with r 0 0 0 1 for some constant 0 as s

the numerically stable reconstruction of jacobi matrices from spectral data we present an expose of the elementary theory of jacobi matrices and in particular their reconstruction from the gaussian weights and abscissas many recent works propose use of the diagonal hermitian lanczos process for this purpose we show that this process is numerically unstable we recall rutishauser s elegant and stable algorithm of 1963 based on plane rotations implement it efficiently and discuss our numerical experience we also apply rutishauser s algorithm to reconstruct a persymmetric jacobi matrix from its spectrum in an efficient and stable manner

motion of level sets by mean curvature i we continue our investigation of the level set technique for describing the generalized evolution of hypersurfaces moving according to their mean curvature the principal assertion of this paper is a kind of reconciliation with the geometric measure theoretic approach pioneered by k brakke we prove that almost every level set of the solution to the mean curvature evolution pde is in fact aunit density varifold moving according to its mean curvature in particular a e level set is endowed with a kind of geometric structure the proof utilizes compensated compactness methods to pass to limits in various geometric expressions

inverse spectral analysis for a class of infinite band symmetric matrices abstract this work deals with the direct and inverse spectral analysis for a class of infinite band symmetric matrices this class corresponds to operators arising from difference equations with usual and inner boundary conditions we give a characterization of the spectral functions for the operators and provide necessary and sufficient conditions for a matrix valued function to be a spectral function of the operators additionally we give an algorithm for recovering the matrix from the spectral function the approach to the inverse problem is based on the rational interpolation theory

an inverse eigenvalue problem for the symmetric tridiagonal quadratic pencil with application to damped oscillatory systems a method is presented which constructs an n by n tridiagonal symmetric quadratic pencil which has its 2n eigenvalues and the 2n 2 of its n 1 dimensional leading principal subpencil prescribed it is shown that if the given eigenvalues are distinct there are at most 2 n 2n 3 n 2 different solutions in the degenerate case where some of the given eigenvalues are common there are an infinite number of solutions apart from finding the roots of certain polynomials the problem is solved in a finite number of steps where the problem has only a finite number of solutions they can all be found in a systematic manner the method is demonstrated with a simple example and its use is illustrated with a practical engineering application in vibrations