quasilinear parabolic systems of several components in this paper we investigate the blowup criteria of the quasilinear parabolic system u imath t c imath u imath alpha imath delta u imath prod jmath 1 n u jmath p imath jmath imath 1 2 cdots n with homogeneous dirichlet boundary conditions on a bounded domain r n where c i 0 i 0 p i 0 1 i n are constants denote by i the identity matrix and p p i which is assumed to be irreducible that i p is a singular m matrix is shown to be the critical case in which 1 plays a fundamental role where 1 is the first dirichlet eigenvalue of the laplacian on as a result we give a general answer to the question of galaktionov and levine on the porous medium systems

sequential change point detection methods for nonstationary time series we present two new spectral based methods for detection of changes in autocorrelation structure in a continuous valued time series in an online process monitoring setting our methods are based on the idea that changes in the autocorrelation structure are reflected by changes in the fourier or wavelet based spectrum and can be detected by comparing estimated spectra of adjacent blocks of the series to be effective for slowly changing spectral structure the methods are extended to allow information from more than one past block to be used in determining whether a change has occurred in such a way as to minimize computational burden through simulation we evaluate the performance of our methods and find that they can provide reliable and timely detection of changes in covariance structure in an online monitoring framework we illustrate the methods using electroencephalogram traces brain waves and run time computer performance metrics

semilinear reaction diffusion systems of several components abstract the homogeneous dirichlet boundary value problem u it u i j 1 n u j p ij i 1 2 n in a bounded domain r n is considered where p ij 0 1 i j n are constants denote by i the identity matrix and p pij which is assumed to be irreducible we find out that whether or not i p is a so called m matrix plays a fundamental role in the blow up theorems

wavelet variance based estimation for composite stochastic processes this article presents a new estimation method for the parameters of a time series model we consider here composite gaussian processes that are the sum of independent gaussian processes which in turn explain an important aspect of the time series as is the case in engineering and natural sciences the proposed estimation method offers an alternative to classical estimation based on the likelihood that is straightforward to implement and often the only feasible estimation method with complex models the estimator furnishes results as the optimization of a criterion based on a standardized distance between the sample wavelet variances wv estimates and the model based wv indeed the wv provides a decomposition of the variance process through different scales so that they contain the information about different features of the stochastic model we derive the asymptotic properties of the proposed estimator for inference and perform a simulation study to compare our estimator to the mle and the lse with

quasilinear parabolic systems with nonlinear boundary conditions ui x 0 ui0 x 0 x 0 i 1 n where 0 r is a bounded domain with smooth boundary 0 is the unit outward normal vector and the constants mi 0 i 0 mij 0 i j 1 n ui0 x i 1 n are positive c functions and satisfy the compatibility conditions 1 the present address academy of mathematics and systems sciences academia sinica beijing 100080 people s republic of china doi 10 1006 jdeq 2000 3784 available online at http www idealibrary com on

the role of critical exponents in blow up theorems the sequel abstract in 27 fujita showed that for positive solutions the initial value problem in r n for u t u u p with p 1 exhibited the following behavior if p p c 1 2 n then the initial value problem does not have any nontrivial non negative solution existing on r n 0 a global solution whereas if p p c there exist global small data positive solutions as well as solutions which are non global we call such a result a blow up theorem of fujita type in 50 levine discussed the various theorems of this type that had appeared in the literature prior to 1990 in this paper we revisit the literature since 1990

diffusivity versus absorption through the boundary for all 0 1 then we do expect to find that any solution becomes unbounded in finite time see 13 15 63 it is our goal to prove an analogous result for m f 1 for a 1 one can find that if v is a positive solution of

extended divergence measure fields and the euler equations for gas dynamics a class of extended vector fields called extended divergence measure fields is analyzed these fields include vector fields in l p and vector valued radon measures whose divergences are radon measures such extended vector fields naturally arise in the study of the behavior of entropy solutions of the euler equations for gas dynamics and other nonlinear systems of conservation laws a new notion of normal traces over lipschitz deformable surfaces is developed under which a generalized gauss green theorem is established even for these extended fields an explicit formula is obtained to calculate the normal traces over any lipschitz deformable surface suitable for applications by using the neighborhood information of the fields near the surface and the level set function of the lipschitz deformation surfaces as an application we prove the uniqueness and stability of riemann solutions that may contain vacuum in the class of entropy solutions of the euler equations for gas dynamics

least gradient problem with respect to a non strictly convex norm abstract we study the planar least gradient problem with respect to an anisotropic norm for continuous boundary data we prove existence of minimizers for strictly convex domains furthermore we inspect the issue of uniqueness and regularity of minimizers only in terms of the modes of convexity of the norm and the domain the results are independent from the regularity of the norm

special cases of the planar least gradient problem abstract we study two special cases of the planar least gradient problem in the first one the boundary conditions are imposed on a part of a strictly convex domain in the second case we impose the dirichlet data on the boundary of a rectangle an example of convex but not strictly convex domain we show the existence of solutions and study their properties for particular cases of boundary data

the dirichlet problem for the total variation flow suppose that is an open bounded domain with a lipschitz boundary the purpose of this chapter is to study the dirichlet problem left begin gathered frac partial u partial t div left frac du left du right right in q left 0 infty right times omega hfill u left t x right phi left x right on s left 0 infty right times partial omega hfill u left 0 x right u 0 left x right in x in omega hfill end gathered right 5 1 where u0 l1 and l1 this evolution equation is related to the gradient descent method used to solve the problem begin gathered minimize int omega left du right int omega f udx int partial omega left u phi right d mathcal h n 1 hfill u in bv left omega right hfill end gathered 2 where f l1 l existence for this variational problem was proved in 118 theorem 1 4

asymptotic decorrelation of wavelet packet transform for certain long memory processes the asymptotic decorrelation of the discrete wavelet transform for long memory processes such as the fractionally differenced fd process the autoregressive fractionally integrated moving average arfima process and the gegenbauer autoregressive moving average garma process as well as the statistical inference techniques based on this property have received much attention nowadays in this paper we investigate the asymptotic decorrelation property of the discrete wavelet packet transform dwpt for two classes of discrete time long memory processes containing the arfima and the garma processes especially we prove theoretically that the covariance across between packet dwpt coefficients decays hyperbolically or exponentially fast as the width of the underlying daubechies scaling and wavelet filters to generate the dwpt gets large meanwhile we show that the covariance between within packet dwpt coefficients converges hyperbolically fast to its corresponding counterpart when the underlying scaling and wavelet filters to generate the dwpt are the shannon s ideal low and high pass filters

critical fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux we establish the critical fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux and then determine the blow up rates and the blow up sets for the nonglobal solutions

empirical aspects of the whittle based maximum likelihood method in jointly estimating seasonal and non seasonal fractional integration parameters abstract this paper addresses the efficiency of the maximum likelihood ml method in jointly estimating the fractional integration parameters d s and d respectively associated with seasonal and non seasonal long memory components in discrete stochastic processes the influence of the size of non seasonal parameter over seasonal parameter estimation and vice versa was analyzed in the space d d s 0 1 0 1 by using mean squared error statistics m s e d s and m s e d this study was based on monte carlo simulation experiments using the ml estimator with whittle s approximation in the frequency domain numerical results revealed that efficiency in jointly estimating each integration parameter is affected in different ways by their sizes as d s and d increase simultaneously to 1 m s e d s and m s e d become larger however effects on m s e d s are much stronger than the effects on m s e d moreover as each parameter tends individually to 1 m s e d becomes larger but m s e d s is barely influenced

wavelet based estimation for seasonal long memory processes we introduce the multiscale analysis of seasonal persistent processes that is time series models with a singularity in their spectral density function at one or more frequencies in 0 1 2 the discrete wavelet packet transform dwpt and a nondecimated version of it known as the maximal overlap dwpt modwpt are introduced as alternative methods to fourier based techniques for analyzing time series that exhibit seasonal long memory the approximate log linear relationship between the wavelet packet variance and frequency is used to produce a least squares estimator of the fractional difference parameter approximate maximum likelihood estimation is performed by replacing the variance covariance matrix with a diagonalized matrix based on the dwpt simulations are performed to compare the wavelet based techniques with the spectral estimate based techniques for both least squares and maximum likelihood procedures an application of this methodology to atmospheric and economic time series is used for demon

critical curves for fast diffusive non newtonian equations coupled via nonlinear boundary flux this paper deals with the critical curve for a nonlinear boundary value problem of a fast diffusive non newtonian system we first obtain the critical global existence curve by constructing the self similar supersolution and subsolution and then the critical fujita curve is conjectured with the aid of some new results

continuity of minimizers to weighted least gradient problems abstract we revisit the question of existence and regularity of minimizers to the weighted least gradient problem with dirichlet boundary condition inf a x d u u b v u g where g c and a c 2 is a weight function that is bounded away from zero under suitable geometric conditions on the domain r n we construct continuous solutions of the above problem for any dimension n 2 by extending the sternberg williams ziemer technique sternberg et al 1992 to this setting of inhomogeneous variations we show that the level sets of the constructed minimizer are minimal surfaces in the conformal metric a 2 n 1 i n this result complements the approach in jerrard et al 2018 since it provides a continuous solution even in high dimensions where the possibility exists for level sets to develop singularities the proof relies on an application of a strict maximum principle for sets with area minimizing boundary established by leon simon in simon 1987

on estimation of the wavelet variance summary the wavelet variance decomposes the variance of a time series into components associated with different scales we consider two estimators of the wavelet variance the first based upon the discrete wavelet transform and the second called the maximal overlap estimator based upon a filtering interpretation of wavelets we determine the large sample distribution for both estimators and show that the maximal overlap estimator is more efficient for a class of processes of interest in the physical sciences we discuss methods for determining an approximate confidence interval for the wavelet variance we demonstrate through monte carlo experiments that the large sample distribution for the maximal overlap estimator is a reasonable approximation even for the moderate sample size of 128 observations we apply our proposed methodology to a series of observations related to vertical shear in the ocean

critical exponents for porous medium systems coupled via nonlinear boundary flux abstract this paper is concerned with the porous medium equations for coupling via nonlinear boundary flux we obtain the critical global existence curve and the critical fujita curve for the problem considered by constructing the self similar supersolutions and subsolutions

wavelets and functional magnetic resonance imaging of the human brain the discrete wavelet transform dwt is widely used for multiresolution analysis and decorrelation or whitening of nonstationary time series and spatial processes wavelets are naturally appropriate for analysis of biological data such as functional magnetic resonance images of the human brain which often demonstrate scale invariant or fractal properties we provide a brief formal introduction to key properties of the dwt and review the growing literature on its application to fmri we focus on three applications in particular i wavelet coefficient resampling or wavestrapping of 1 d time series 2 to 3 d spatial maps and 4 d spatiotemporal processes ii wavelet based estimators for signal and noise parameters of time series regression models assuming the errors are fractional gaussian noise fgn and iii wavelet shrinkage in frequentist and bayesian frameworks to support multiresolution hypothesis testing on spatially extended statistic maps we conclude that the wavelet domain is a rich source of new concepts and techniques to enhance the power of statistical analysis of human fmri data

modeling persistence in hydrological time series using fractional differencing the class of autoregressive integrated moving average arima time series models may be generalized by permitting the degree of differencing d to take fractional values models including fractional differencing are capable of representing persistent series d 0 or short memory series d 0 the class of fractionally differenced arima processes provides a more flexible way than has hitherto been available of simultaneously modeling the long term and short term behavior of a time series in this paper some fundamental properties of fractionally differenced arima processes are presented methods of simulating these processes are described estimation of the parameters of fractionally differenced arima models is discussed and an approximate maximum likelihood method is proposed the methodology is illustrated by fitting fractionally differenced models to time series of streamflows and annual temperatures

a nonlinear diffusion system coupled via nonlinear boundary flux abstract in this paper we deal with the global existence and nonexistence of solutions to a nonlinear diffusion system coupled via nonlinear boundary flux by constructing various kinds of sub and super solutions and using the basic properties of m matrix we give the necessary and sufficient conditions for global existence of nonnegative solutions the critical curve of fujita type is conjectured with the aid of some new results which extend the recent results of wang et al nonlinear anal 71 2009 2134 2140 and li et al j math anal appl 340 2008 876 883 to more general equations

on boundary detachment phenomena for the total variation flow with dynamic boundary conditions abstract we combine the total variation flow suitable for crystal modeling and image analysis with the dynamic boundary conditions we analyze the behavior of facets at the parts of the boundary where these conditions are imposed we devote particular attention to the radially symmetric data we observe that the boundary layer detachment actually can happen at concave parts of the boundary

note on critical exponents for a system of heat equations coupled in the boundary conditions this note establishes the blow up estimates near the blow up time for a system of heat equations coupled in the boundary conditions under certain assumptions the exact rate of blow up is established we also prove that the only solution with vanishing initial values whenpq 1 is the trivial one

critical exponents for a fast diffusive polytropic filtration equation with nonlinear boundary flux abstract in this paper we deal with a fast diffusive polytropic filtration equation u t x u m x p 2 u m x 1 p 1 1 m in r 0 subject to a nonlinear boundary flux u m x p 2 u m x 0 t u q 0 t t 0 we first get the behavior of the solution at infinity and establish the critical global existence exponent and critical fujita exponent for the fast diffusive polytropic filtration equation furthermore give the blow up set and upper bound of the blow up rate for the nonglobal solutions

testing for homogeneity of variance in time series long memory wavelets and the nile river 1 we consider the problem of testing for homogeneity of variance in a time series with long memorystructure wedemonstratethat atest whose nullhypothesis isdesigned tobewhite noisecan in fact be applied on a scale by scale basis to the discrete wavelet transform of long memory processes in particular we show that evaluating a normalized cumulative sum of squares test statistic using critical levels for the null hypothesis of white noise yields approximately the same null hypothesis rejection rates when applied to the discrete wavelet transform of samples from a fractionally differenced process the point at which the test statistic using a nondecimated version of the discrete wavelet transform achieves its maximum value can be used to estimate the time of the unknown variance change we apply our proposed test statistic on five time series derived from the historical record of nile river yearly minimum water levels covering 622 1922 a d each series exhibiting various degrees of serial correlation including long memory in the longest subseries spanning 622 1284 a d the test confirms an inhomogeneity of variance at short time scales and identifies the change point around 720 a d which coincides closely with the construction of a new device around 715 a d for measuring the nile river the test also detects a change in variance for a record of only 36 years index terms 1829 hydrology groundwater hydrology 1869 hydrology stochastic processes 3299 mathematical geophysics general or miscellaneous

pseudolinear estimation of fractionally integrated arma arfima models with automotive application a novel pseudolinear method for the estimation of fractionally integrated arma arfima models that are capable of representing combined long and short term dependency is introduced the method is based on the relationship of the ar ma parameters and the coefficients of the fractional power operator binomial series expansion with the model s inverse function these lead to the formulation of a special form regression problem that can be decomposed into a univariate nonlinear and a multivariate linear regression and may be thus tackled via a special pseudolinear procedure this decomposition in turn leads to the elimination of the need for initial guess parameter values drastic simplification in the detection and handling of potential local extrema problems as well as computational simplicity the method s strong consistency is established whereas its performance characteristics are assessed via monte carlo experiments and comparisons with the maximum likelihood method the pseudolinear method is also used for the arfima modeling and prediction of power consumption in an experimental automobile fully active suspension system the consumption of which is shown to exhibit long term dependency a comparison with arma arima type modeling is also made and the obtained arfima models are shown to achieve improved predictive performance at a drastically reduced parametric complexity

the critical curve for a non newtonian polytropic filtration system coupled via nonlinear boundary flux this paper deals with the critical curve of the non newtonian polytropic filtration equation coupled via nonlinear boundary flux the critical global existence curve is obtained by constructing various self similar supersolutions and subsolutions furthermore we get some new results on the critical fujita curve

critical curves of the non newtonian polytropic filtration equations coupled with nonlinear boundary conditions abstract in this paper we consider the existence and non existence of global solutions of the non newtonian polytropic filtration equations with nonlinear boundary conditions we first obtain the critical global existence curve by constructing various self similar supersolutions and subsolutions and then the critical fujita curve is conjectured with the aid of some new results

minimum bias multiple taper spectral estimation two families of orthonormal tapers are proposed for multitaper spectral analysis minimum bias tapers and sinusoidal tapers spl upsisup k where spl upsisub nsup k spl radic 2 n 1 sin spl pi kn n 1 and n is the number of points the resulting sinusoidal multitaper spectral estimate is s spl circ f 1 2k n 1 spl sigmasub j 1sup k y f j 2n 2 y f j 2n 2 sup 2 where y f is the fourier transform of the stationary time series s f is the spectral density and k is the number of tapers for fixed j the sinusoidal tapers converge to the minimum bias tapers like 1 n since the sinusoidal tapers have analytic expressions no numerical eigenvalue decomposition is necessary both the minimum bias and sinusoidal tapers have no additional parameter for the spectral bandwidth the bandwidth of the jth taper is simply 1 n centered about the frequencies spl plusmn j 2n 2 thus the bandwidth of the multitaper spectral estimate can be adjusted locally by simply adding or deleting tapers the band limited spectral concentration spl intsub wsup w v f sup 2 df of both the minimum bias and sinusoidal tapers is very close to the optimal concentration achieved by the slepian 1978 tapers in contrast the slepian tapers can have the local bias spl intsub 1 2 sup 1 2 f sup 2 v f sup 2 df much larger than of the minimum bias tapers and the sinusoidal tapers

non uniqueness of minimizers in the least gradient problem abstract minimizers in the least gradient problem with discontinuous boundary data need not be unique however all of them have a similar structure of level sets here we give a full characterization of the set of minimizers in terms of any one of them and discuss stability properties of an approximate problem

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed