weak solutions of a class of quasilinear hyperbolic integro differential equations describing viscoelastic materials global weak solutions of scalar second order quasilinear hyperbolic integro differential equations with singular kernels are constructed perturbations of rest states are shown to propagate with finite speed smoothing effects of the solution operator are exhibited and conditions for the asymptotic stability of rest states are given the equations arise in viscoelasticity

convergence of the viscosity method for isentropic gas dynamics a convergence theorem for the method of artificial viscosity applied to the isentropic equations of gas dynamics is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

an effective algorithm for string correction using generalized edit distance ii computational complexity of the algorithm and some applications this paper deals with the problem of estimating an unknown transmitted string xs belonging to a finite dictionary h from its observable noisy version y in the first part of this paper 18 we have developed an algorithm referred to as algorithm i to find the string x h which minimizes the generalized levenshtein distance d xy in this part of the paper we study the computational complexity of algorithm i and illustrate quantitatively the advantage algorithm i has over the standard technique and other algorithms its superiority has been shown for various dictionaries including the one consisting of the 1021 most common english words of length greater than unity 23 a comparison between algorithm i and other algorithms used to correct misspelled words of a regular language is also made here some applications of algorithm i are also discussed

algorithms for approximate graph matching abstract labeled graphs are graphs in which each node and edge has a label the distance between two labeled graphs is considered to be the weighted sum of the costs of edit operations insert delete and relabel the nodes and edges to transform one graph to the other the paper considers two variants of the approximate graph matching problem agm given a pattern graph p and a data graph d 1 1 what is the distance between p and d 2 2 what is the minimum distance between p and d when subgraphs can be freely removed from d we first show that no efficient algorithm can solve either variant of the agm unless p np then we present several heuristic algorithms leading to approximate solutions the heuristics are based on probabilistic hill climbing and maximum flow techniques our experimental results involving the comparison of real and simulated data demonstrate the good performance of the algorithms presented

an effective algorithm for string correction using generalized edit distances i description of the algorithm and its optimality abstract this paper deals with the problem of estimating a transmitted string xs from the corresponding received string y which is a noisy version of xs we assume that y contains any number of substitution insertion and deletion errors and that no two consecutive symbols of xs were deleted in transmission we have shown that for channels which cause independent errors and whose error probabilities exceed those of noisy strings studied in the literature 12 at least 99 5 of the erroneous strings will not contain two consecutive deletion errors the best estimate x of xs is defined as that element of h which minimizes the generalized levenshtein distance d x y between x and y using dynamic programming principles an algorithm is presented which yields x without computing individually the distances between every word of h and y though this algorithm requires more memory it can be shown that it is in general computationally less complex than all other existing algorithms which perform the same task

string alignment with substitution insertion deletion squashing and expansion operations abstract let x and y be any two strings of finite length the problem of transforming x to y using the edit operations of substitution deletion and insertion has been extensively studied in the literature the problem can be solved in quadratic time if the edit operations are extended to include the operation of transposition of adjacent characters and is np complete if the characters can be edited repeatedly in this paper we consider the problem of transforming x to y when the set of edit operations is extended to include the squashing and expansion operations whereas in the squashing operation two or more contiguous characters of x can be transformed into a single character of y in the expansion operation a single character in x may be expanded into two or more contiguous characters of y these operations are typically found in the recognition of cursive script a quadratic time solution to the problem has been presented this solution is optimal for the infinite alphabet case the strategy to compute the sequence of edit operations is also presented

on rank one convex and polyconvex conformal energy functions with slow growth we make some remarks about rank one convex and polyconvex functions on the set of all real n n matrices that vanish on the subset k n consisting of all conformal matrices and grow like a power function at infinity we prove that every non negative rank one convex function that vanishes on k n and grows below a power of degree n 2 must vanish identically in odd dimensions n 3 we prove that every non negative polyconvex function that vanishes on k n must vanish identically if it grows below a power of degree n while in even dimensions such polyconvex functions can exist that also grow like a power of half dimension degree

pattern recognition of strings with substitutions insertions deletions and generalized transpositions abstract we study the problem of recognizing a string y which is the noisy version of some unknown string x chosen from a finite dictionary h the traditional case which has been extensively studied in the literature is the one in which y contains substitution insertion and deletion sid errors although some work has been done to extend the traditional set of edit operations to include the straightforward transposition of adjacent eharacters see j assoc comput mach 22 177 183 1975 the problem is unsolved when the transposed characters are themselves subsequently substituted as is typical in cursive and typewritten script in molecular biology and in noisy chain coded boundaries in this paper we present the first reported solution to the analytic problem of editing one string x to another y using these four edit operations a scheme for obtaining the optimal edit operations has also been given both these solutions are optimal for the infinite alphabet case using these algorithms we present a syntactic pattern recognition scheme which corrects noisy text containing all these types of errors the paper includes experimental results involving sub dictionaries of the most common english words which demonstrate the superiority of our system over existing methods

a viscous approximation for a 2 d steady semiconductor or transonic gas dynamic flow existence theorem for potential flow in this paper we solve a boundary value problem in a two dimensional domain 1 for a system of equations of fluid poisson type that is a viscous approximation to a potential equation for the velocity coupled with an ordinary differential equation along the streamlines for the density and a poisson equation for the electric field a particular case of this system is a viscous approximation of transonic flow models the general case is a model for semiconductors we show existence of a density p velocity potential cp and electric potential in the bounded domain r that are c fi c fi and w2 p 2 functions respectively such that p cp 3 the speed ivlpl and the electric field e v are uniformly bounded in the viscous parameter this is a necessary step in the existing programs in order to show existence of a solution for the transonic flow problem 0 19 john wiley sons inc 1 presentation of the model

on a periodic boundary value problem with a finite number of gaps in its spectrum co 4 9 n a 3 a t t wy 3 are called instability intervals all but the first interval in 3 are finite and may shrink to a point under special conditions erdelyi 3 discovered situations where all but a finite number of finite instability intervals vanish when q t is a suitable elliptic function lax 9 showed that a function q t which satisfies the nth order korteweg de vries equation requires 1 to have no more than n non vanishing finite instability intervals conversely if all finite instability intervals vanish then q t in 1 is necessarily a constant this fact was proved by borg 11 hochstadt 71 and ungar 121 when all but n finite instability intervals vanish q t satisfies a differential equation of the form

periodic solutions of the kdv equation in this paper we construct a large family of special solutions of the kdv equation which are periodic in x and almost periodic in t these solutions lie on n dimensional tori very likely they are dense among all solutions the special solutions are characterized variationally they minimize fn u subject to the constraints fj u aj j 1 n 1 here fj denote the remarkable sequence of conserved functionals discovered by kruskal and zabusky the above minimum problem was originally suggested by them in exploring the manifold of solutions of this minimum problem we make essential use of gardner s discovery that these functionals are in involution with respect to a suitable poisson bracket gardner greene kruskal and miura have shown that the eigenvalues of the schrodinger operator are conserved functionals if the potential is a function of t and satisfies the kdv equation in section 6 a new set of conserved quantities is constructed which serve as a link between the eigenvalues of the schrodinger operator and the fj another result in section 6 is a slight sharpening of an earlier result of the author and j moser for the special solutions constructed above all but 2n 1 eigenvalues of the schrodinger operator are double the simplest class of special solutions n 1 are cnoidal waves in an appendix m hyman describes the results of computing numerically the next simplest case n 2 these calculations show that the shape of these solutions recurs exactly after a finite time in a shifted position the theory verifies this fact

null lagrangians weak continuity and variational problems of arbitrary order abstract we consider the problem of minimizing integral functionals of the form i u f x k u x dx where r p u r and k u denotes the set of all partial derivatives of u with orders k the method is based on a characterization of null lagrangians l ku depending only on derivatives of order k applications to elasticity and other theories of mechanics are given

isometric immersions of surfaces with two classes of metrics and negative gauss curvature the isometric immersion of two dimensional riemannian manifolds or surfaces with negative gauss curvature into the three dimensional euclidean space is studied in this paper the global weak solutions to the gauss codazzi equations with large data in l infty are obtained through the vanishing viscosity method and the compensated compactness framework the l infty uniform estimate and h 1 compactness are established through a transformation of state variables and construction of proper invariant regions for two types of given metrics including the catenoid type and the helicoid type the global weak solutions in l infty to the gauss codazzi equations yield the c1 1 isometric immersions of surfaces with the given metrics

a formal theory for optimal and information theoretic syntactic pattern recognition abstract in this paper we present a foundational basis for optimal and information theoretic syntactic pattern recognition we do this by developing a rigorous model m for channels which permit arbitrarily distributed substitution deletion and insertion syntactic errors more explicitly if a is any finite alphabet and a the set of words over a we specify a stochastically consistent scheme by which a string u a can be transformed into any y a by means of arbitrarily distributed substitution deletion and insertion operations the scheme is shown to be functionally complete and stochastically consistent apart from the synthesis aspects we also deal with the analysis of such a model and derive a technique by which pr y u the probability of receiving y given that u was transmitted can be computed in cubic time using dynamic programming one of the salient features of this scheme is that it demonstrates how dynamic programming can be applied to evaluate quantities involving complex combinatorial expressions and which also maintain rigid probability consistency constraints experimental results which involve dictionaries with strings of lengths between 7 and 14 with an overall average noise of 39 75 demonstrate the superiority of our system over existing methods apart from its straightforward applications in string generation and recognition we believe that the model also has extensive potential applications in speech uni dimensional signal processing and computational molecular biology

restrictions on microstructure we consider the following question given a set of matrices with no rank one connections does it support a nontrivial young measure limit of gradients our main results are these a a young measure can be supported on four incompatible matrices b in two space dimensions a young measure cannot be supported on finitely many incompatible elastic wells c in three or more space dimensions a young measure can be supported on three incompatible elastic wells and d if supports a nontrivial young measure with mean value 0 then the linear span of must contain a matrix of rank one

constrained string editing abstract let x and y be any two strings of finite length we consider the problem of transforming x to y using the edit operations of deletion insertion and substitution the optimal transformation is the one which has the minimum edit distance associated with it the problem of computing this distance and the optimal transformation using no edit constraints has been studied in the literature in this paper we consider the problem of transforming x to y using any arbitrary edit constraint involving the number and type of edit operations to be performed an algorithm is presented to compute the minimum distance associated with editing x to y subject to the specified constraint the algorithm requires o x y min x y time and space the technique to compute the optimal transformation is also presented