on almost global existence for nonrelativistic wave equations in 3d almost global solutions are constructed to three dimensional quadratically nonlinear wave equations the proof relies on generalized energy estimates and a new decay estimate the method applies to equations that are only classically invariant such as the nonlinear system of hyperelasticity 1996 john wiley sons inc

spectral zero crossings localization properties and applications we present an analysis of the rate of sign changes in the discrete fourier spectrum of a sequence the sign changes of either the real or imaginary parts of the spectrum are considered and the rate of sign changes is termed as the spectral zero crossing rate szcr we show that szcr carries information pertaining to the locations of transients within the temporal observation window we show duality with temporal zero crossing rate analysis by expressing the spectrum of a signal as a sum of sinusoids with random phases this extension leads to spectral domain iterative filtering approaches to stabilize the spectral zero crossing rate and to improve upon the location estimates the localization properties are compared with group delay based localization metrics in a stylized signal setting well known in speech processing literature we show applications to epoch estimation in voiced speech signals using the szcr on the integrated linear prediction residue the performance of the szcr based epoch localization technique is competitive with the state of the art epoch estimation techniques that are based on average pitch period

delayed singularity formation in 2d compressible flow the initial value problem for the compressible euler equations in two space dimensions is studied of interest is the lifespan of classical solutions with initial data that is a small perturbation from a constant state the approach taken is to regard the compressible solution as a nonlinear superposition of an underlying incompressible flow and an irrotational compressible flow this viewpoint yields an improvement for the lifespan over that given by standard existence theory the estimate for the lifespan is further improved when the initial data possesses certain symmetry in the case of rotational symmetry a result of s alinhac is reconsidered the approach is also applied to the study of the incompressible limit the analysis combines energy and decay estimates based on vector fields related to the natural invariance of the equations 0 introduction the compressible euler equations comprise a nonlinear symmetric hyperbolic system of pde s that model ideal fluid flow the charac teristic wave speeds of this system are given by the fluid velocity and the local sound speed the two wave families associated to these speeds may be con sidered separately hydrodynamical waves are described by the incompressible euler equations while acoustical waves are approximated by the linear wave equation or more precisely by the compressible euler equations with irrotational fluid velocity this paper attempts to use the nonlinear superposition of these two flows to study the long time behavior of small amplitude disturbances in two dimensional compressible fluid flow consider the initial value problem for the compressible euler equations in two or three space dimensions with smooth initial data which is a small perturbation of amplitude e from a constant state the life span is defined as the largest time interval on which there exists a classical solution to the initial value problem from the theory of symmetric hyperbolic systems 6 8 the life span is at least 0 e results on formation of singularities show that the life span of a classical solution is no better than 0 e2 in 2d 16 and o exp l 2 in 3d 17 in this paper we extend the length of the life span under various assumptions on the initial data in two space dimensions the simplest case is the one in which the initial fluid velocity is irrotational that is its curl is zero the compressible euler equations then behave much the same as scalar nonlinear wave equations this can readily be guessed by writing the velocity as the gradient of a potential although we will not use this approach here we shall see in theorem 2 that the life span of 2d irrotational

computation of isotopisms of algebras over finite fields by means of graph invariants in this paper we define a pair of faithful functors that map isomorphic and isotopic finite dimensional algebras over finite fields to isomorphic graphs these functors reduce the cost of computation that is usually required to determine whether two algebras are isomorphic in order to illustrate their efficiency we determine explicitly the classification of two and three dimensional partial quasigroup rings

on frequency estimation summary t this paper discusses a least squares procedure and the use of the periodogram for isolating a discrete harmonic of a time series it is shown that the usual asymptotics on estimation of frequency amplitude and phase of such a harmonic have to be used with great caution from a moderate sample perspective computational issues are discussed and some illustrations are provided bolt brillinger 1979 make use of these asymptotic results we consider a time series model of the form x a cos wt f e where e is a stationary noise sequence and one is interested in estimating the amplitude frequency and phase of the harmonic component the asymptotic theory of the least squares estimates of these parameters has a long history whittle 1951 1953 obtained some of the earliest results more recent results are by hasan 1982 hannan 1973 and walker 1971 who formalize and extend whittle s results in these works it is shown that the asymptotic variance of the frequency estimate is of order n 3 and that the asymptotic variances of the other two components are of the more usual order n these results extend when there are several harmonic components the rate for the estimate of w seems almost unbelievably good and our work was motivated by a desire to see how reliable the asymptotic theory is in brief we find that the product of the amplitude and the sample size n must be quite large in order for the asymptotic theory to be meaningful if this product is not large the frequency estimate is much more variable than indicated by the asymptotic theory and the amplitude estimate is severely biased in applications in which the amplitude is small giving rise to a small peak in the periodogram these results suggest that naive application of the asymptotic theory to gauge resolution can be quite misleading section 2 of this paper is devoted to a review and examination of the asymptotic theory we are also concerned with computational issues arising from the least squares problem this problem is nonlinear in the parameters so that some sort of iterative search must be employed typically search methods start from an initial guess and then proceed by a sequence of modified newton raphson steps for this nonlinear least squares problem it turns out that there are many local minima with a separation in frequency about n l which makes the stationary point to which the iterative scheme converges extremely sensitive to the starting values and this problem gets worse as the sample size increases furthermore it follows from the results of 2 that the estimate of the amplitude is very biased unless the frequency is resolved with order o n so that failure to converge to the global minimum may give a very poor estimate of amplitude the problem becomes

explicit relation between the wiener index and the edge wiener index of the catacondensed hexagonal systems the wiener index w g and the edge wiener index we g of a graph g are defined as the sum of all distances between pairs of vertices in a graph g and the sum of all distances between pairs of edges in g respectively the wiener index due to its correlation with a large number of physico chemical properties of organic molecules and its interesting and non trivial mathematical properties has been extensively studied in both theoretical and chemical literature the edge wiener index of g is nothing but the wiener index of the line graph of g the concept of line graph has been found various applications in chemical research in this paper we show that if g is a catacondensed hexagonal system with h hexagons and has t linear segments s 1 s 2 s t of lengths l s i l i 1 i t then w e g 25 16 w g 1 16 120 h 2 94 h 29 1 4 i 1 t l i 1 2 our main result reduces the problems on the edge wiener index to those on the wiener index in the catacondensed hexagonal systems which makes the former ones easier

higher order crossings spectral analysis of an almost periodic random sequence in noise the precise effect of noise on hoc higher order crossing sequences is examined settling some issues not dealt with previously it is shown that it is possible to construct hoc sequences that converge to true discrete frequencies in a mixed spectrum even for very low signal to noise ratios the availability of the correlation function is then assumed when the expected hocs from repeated differences are known the correlation function is automatically known as well however other quantities not just the expected hoc can serve the same purpose for example under the gaussian assumption the correlation function can be obtained from that of the binary process derived by clipping the original process at any level

a method for determining periods in time series abstract the periods corresponding to peaks in the autoregressive and window spectral density estimators are shown to be consistent and asymptotically normal estimators of peak periods in the true spectral density under assumptions of known autoregressive order and under slight modifications of the assumptions often made to show the asymptotic normality of window estimators respectively the asymptotic variances are obtained and the use of the theory is illustrated by obtaining an asymptotic confidence interval for a peak period using a set of hormone data

asymptotic analysis of a fast algorithm for efficient multiple frequency estimation based on an asymptotic analysis of the contraction mapping cm method of li and kedem 1993 a bandwidth shrinkage rule is proposed for fast and accurate estimation of the frequencies of multiple sinusoids from noisy measurements the cm frequency estimates are defined as the fixed points of a contractive mapping formed by the lag one autocorrelation coefficient calculated from the output of a parametric filter applied to the observed time series with bandwidth parameters judiciously chosen according to the asymptotic analysis the algorithm is shown to be able to accommodate possibly poor initial values of precision o n sup 1 3 and converge to a final estimate whose accuracy is arbitrarily close to o n sup 3 2 the optimal error rate for frequency estimation under the gaussian assumption the total computational complexity of the algorithm is shown to be o n log n which is comparable to that of n point fast fourier transform fft a novelty in the asymptotic analysis is that it accommodates closely spaced frequencies by allowing not only the filter bandwidth but also the frequency separation to be functions of the sample size n this enables an assessment of the accuracy of the frequency estimates for given bandwidths and initial values in situations where some or all of the frequencies are close to each other

iterative filtering for multiple frequency estimation it is well known that prony s least squares estimator gives inconsistent estimates for multiple frequency estimation in a recent attempt to diminish this problem dragosevic and stankovic 1989 couple the least squares method of autoregressive ar estimation with an iterative filtering scheme discussed by kay 1988 using an all pole filter but the inconsistency still persists this paper attacks the chronic inconsistency with a general approach of parametric filtering that unifies and extends the previous work it is shown that the inconsistency can be eliminated with an appropriately parametrized filter the clue for the correct parametrization comes from a formula for the bias of the least squares ar estimator the fact of the matter is that as long as a filter satisfies the parametrization requirement consistent estimates can be obtained from the least squares ar estimator on the basis of the filtered data in particular the all pole filter considered by dragosevic and stankovic can be easily reparametrized so that it too satisfies the parametrization requirement and thus leads to a consistent estimator experimental results show that the modified method has a higher resolution than the discrete fourier transform and that its overall performance is quite remarkable

another aspect of graph invariants depending on the path metric and an application in nanoscience the aim of this paper is to find a new expression for distance based graph invariants of connected graphs having a decomposition into convex subgraphs we apply this method to schultz and gutman indices of graphs it can be generalized to other distance based graph invariants as an application the wiener index of the one pentagonal nanocone is computed

a matrix method for computing szeged and vertex pi indices of join and composition of graphs the szeged index extends the wiener index for cyclic graphs by counting the number of vertices on both sides of each edge and sum these counts klavzar et al s klavzar a rajapakse i gutman the szeged and the wiener index of graphs appl math lett 9 5 1996 45 49 provided an exact formula for computing szeged index of product of graphs in this paper we apply a matrix method to obtain exact formulae for computing the szeged index of join and composition of graphs the join and composition of the vertex pi index of graphs are also computed

some contributions to a frequency location method due to he and kedem the author derives a useful information theoretical technology from the tunable filter that automatically detects the frequency of an unknown signal in white gaussian noise by adjusting its parameter to the correlation coefficient of its output the tunable filter earlier proposed by s he and b kedem see ibid vol 35 no 2 p 360 9 1989 is known as the hk filter the methodology sidesteps the white noise and normality assumptions more importantly it is shown that broad classes of linear filters can be made to implement the detection plan in particular bandpass filters can be expected to lock in even more quickly and accurately than the hk filter this analysis yields a formula for the error contraction at each recursion

calculating the edge wiener and edge szeged indices of graphs the edge szeged and edge wiener indices of graphs are new topological indices presented very recently it is not difficult to apply a modification of the well known cut method to compute the edge szeged and edge wiener indices of hexagonal systems the aim of this paper is to propose a method for computing these indices for general graphs under some additional assumptions

distance based topological indices of the tree like polyphenyl systems topological indices based on the distances between vertices atoms of a molecular graph are widely used for characterizing molecular graphs and their fragments establishing relationships between structures and properties of molecules predicting biological activity of chemical compounds and making other chemical applications polyphenyls are a kind of macrocyclic aromatic hydrocarbons and their derivatives are very important organic chemicals which can be used in organic synthesis drug synthesis heat exchanger etc in this paper we investigate the relationships between the wiener index and other distance based topological indices in the tree like polyphenyl systems and obtain some exactly formulae on the relationships

global existence for three dimensional incompressible isotropic elastodynamics via the incompressible limit the existence of global in time classical solutions to the cauchy problem for incompressible nonlinear isotropic elastodynamics for small initial displacements is proved solutions are constructed via approximation by slightly compressible materials the energy for the approximate solutions remains uniformly bounded on a time scale that goes to infinity as the material approaches incompressibility a necessary component to the long time existence of the approximating solution is a null or linear degeneracy condition inherent in the isotropic case which limits the quadratic interaction of the shear waves the proof combines energy and decay estimates based on commuting vector fields and a compactness argument 2004 wiley periodicals inc

an exact direct method of sinusoidal parameter estimation derived from finite fourier integral of differential equation in this paper we propose a novel method for estimating the parameters frequency amplitude and phase of real sinusoids to derive the estimator we start from the characteristic differential equation of a sinusoid to remove differentials and obtain an algebraic relation for frequency we introduce finite period weighted integrals of the differential equation which become equivalent to the differential equation when a sufficient number of weight functions are applied as weight functions we show that fourier kernels have excellent properties terms related to integral boundaries are readily eliminated observations are provided by fourier coefficients and the relation becomes independently accurate for multiple sinusoids if they are sufficiently spaced we solve the obtained equations in two ways one is for approaching to the cramer rao lower bound crlb and the other is for enhancing the interference rejection capability also methods are proposed to calculate the weighted integrals from sampled signals with an improved accuracy proposed algorithms are examined under noise and sinusoidal interference error variances are compared with the crlb and other fast fourier transform fft based methods

on the edge szeged index of unicyclic graphs with given diameter abstract given a connected graph g the edge szeged index sze g is defined as s z e g e u v e m u e m v e where mu e and mv e are respectively the number of edges of g lying closer to vertex u than to vertex v and the number of edges of g lying closer to vertex v than to vertex u in this paper some extremal problems on the edge szeged index of unicyclic graphs are considered all the n vertex unicyclic graphs with a given diameter having the minimum edge szeged index are identified using a unified approach we identify the n vertex unicyclic graphs with the minimum second minimum third minimum and fourth minimum edge szeged indices

strong consistency of the contraction mapping method for frequency estimation some statistical properties in regard to the contraction mapping cm method are discussed one of the requirements in this method is that the filter be parameterized to satisfy a certain fundamental property the parameterization clearly depends on the normalized noise spectrum which theoretically has to be known or estimated a priori if this information is available one can first whiten the noise with a linear filter and then apply the cm method to the filtered data in this way the parameterization only needs to be done under the white noise assumption and filters like the ar 2 can be used by the cm method in applications however prewhitening may not always be necessary

asymptotic theory for a fast frequency detector a fast technique for efficient online signal detection and tracking is extended by analyzing the asymptotic distribution of the detector a version of the technique is seen to have potentially greater precision than other fast estimators the upper bound being o 1 n sup 2 3 coupled with another device there is potential for achieving the convergence precision of the maximum likelihood estimate which by conventional methods entails considerably computational expense