choice of column scores for testing independence in ordered 2 x k contingency tables the numerous statistical methods for testing no association between a binary response rows and k ordered categories columns group naturally into two classes those that require preassigned numerical column scores and those that do not an example of the former would be a logistic regression analysis and of the latter would be a wilcoxon rank sum test in this paper we demonstrate that the perceived advantage of not preassigning scores is illusory we do this by presenting an example from our consulting experience in which the midrank scores used by the rank tests that do not require preassigned scores are clearly inappropriate our recommendations are to assign reasonable column scores whenever possible and to consider equally spaced scores when the choice is not apparent midranks as scores should always be examined for their appropriateness before a rank test is applied

spectral stability of small amplitude viscous shock waves in several space dimensions a planar viscous shock profile of a hyperbolic parabolic system of conservation laws is a steady solution in a moving coordinate frame the asymptotic stability of viscous profiles and the related vanishing viscosity limit are delicate questions already in the well understood case of one space dimension and even more so in the case of several space dimensions it is a natural idea to study the stability of viscous profiles by analyzing the spectrum of the linearization about the profile the evans function method provides a geometric dynamical systems framework to study the eigenvalue problem in this approach eigenvalues correspond to zeros of an essentially analytic function mathcal e rho lambda rho omega which detects nontrivial intersections of the so called stable and unstable spaces that is spaces of solutions that decay on one or the other side of the shock wave respectively in a series of pioneering papers kevin zumbrun and collaborators have established in various contexts that spectral stability that is the non vanishing of mathcal e rho lambda rho omega and the non vanishing of the lopatinski kreiss majda function imply nonlinear stability of viscous shock profiles in several space dimensions in this paper we show that these conditions hold true for small amplitude extreme shocks under natural assumptions this is done by exploiting the slow fast nature of the small amplitude limit which was used in a previous paper by the authors to prove spectral stability of small amplitude shock waves in one space dimension geometric singular perturbation methods are applied to decompose the stable and unstable spaces into subbundles with good control over their limiting behavior three qualitatively different regimes are distinguished that relate the small strength epsilon of the shock wave to appropriate ranges of values of the spectral parameters various rescalings are used to overcome apparent degeneracies in the problem caused by loss of hyperbolicity or lack of transversality

the gap lemma and geometric criteria for instability of viscous shock profiles an obstacle in the use of evans function theory for stability analysis of traveling waves occurs when the spectrum of the linearized operator about the wave accumulates at the imaginary axis since the evans function has in general been constructed only away from the essential spectrum a notable case in which this difficulty occurs is in the stability analysis of viscous shock profiles here we prove a general theorem the gap lemma concerning the analytic continuation of the evans function associated with the point spectrum of a traveling wave into the essential spectrum of the wave this allows geometric stability theory to be applied in many cases where it could not be applied previously we demonstrate the power of this method by analyzing the stability of certain undercompressive viscous shock waves a necessary geometric condition for stability is determined in terms of the sign of a certain melnikov integral of the associated viscous profile this sign can easily be evaluated numerically we also compute it analytically for solutions of several important classes of systems in particular we show for a wide class of systems that homoclinic solitary waves are linearly unstable confirming these as the first known examples of unstable viscous shock waves we also show that strong heteroclinic undercompressive waves are sometimes unstable similar stability conditions are also derived for lax and overcompressive shocks and for nn

multidimensional viscous shocks ii the small viscosity limit in this paper we prove the existence of curved multidimensional viscous shocks and also justify the small viscosity limit starting with a curved multidimensional inviscid shock solution to a system of hyperbolic conservation laws we show that the shock can be obtained as a small viscosity limit of solutions to an associated parabolic problem viscous shocks the two main hypotheses are a natural evans function assumption on the viscous profile together with a restriction on how much the shock can deviate from flatness the main tools are a conjugation lemma that removes xn dependence from the linearization of the parabolic problem about the viscous profile new degenerate kreiss type symmetrizers used to prove an l2 estimate for the linearized problem and a finite regularity calculus of semiclassical and mixed type classical semiclassical pseudodifferential operators 2003 wiley periodicals inc

almost periodic solutions of delay difference systems in the present paper we study the properties of almost periodic solutions for delay difference systems and establish some theorems on the existence of almost periodic solutions for delay difference systems by means of liapunov functionals the obtained results confirm not only the existence but also the uniqueness as well as the uniform asymptotic stability of the almost periodic solution

permanence and almost periodic solution of a discrete impulsive richards growth equation with variable delays and feedback control dynamics of a discrete almost periodic impulsive richards growth equation is studied we also consider the model with variable delays and feedback control the technique employed to prove our main results is very skillful and interesting in the old years the researchers usually considered the permanence and almost periodic dynamics of the discrete time models without impulsive perturbations in biological populations in this paper we study a discrete impulsive richards growth equation with variable delays and feedback control by using some analysis technics and constructing a suitable lyapunov functional we investigate the permanence and global attractivity of the model based on the results of permanence and global attractivity some sufficient conditions for the existence of a unique globally attractive positive almost periodic solution to the model are established by the relation between the solutions of impulsive system and the corresponding non impulsive difference system and the almost periodic functional hull theory of difference system to some extent our main results complement and generalize some scientific work in recent years finally some examples and numerical simulations are given to illustrate the effectiveness of our main results

global stability of almost periodic solution of multispecies mutualism system with time delays and impulsive effects abstract this paper discusses an almost periodic multispecies lotka volterra mutualism system with time delays and impulsive effects by using the theory of comparison theorem and constructing a suitable lyapunov functional sufficient conditions which guarantee the existence and uniqueness and global asymptotical stability of almost periodic solution of this system are obtained the results of this paper is completed new an suitable example indicates the feasibility of the main results

almost periodic solutions of a discrete almost periodic logistic equation with delay abstract in this paper we consider an almost periodic discrete logistic equation with delay by constructing suitable lyapunov functional and almost periodic functional hull theory a sufficient condition is obtained for the existence of a unique almost periodic solution which is globally attractive an example together with its numerical simulation shows the feasibility of our main result

a comparison of tests of the independence of two covariance stationary time series abstract the approximate slopes of several tests of the independence of two covariance stationary time series are derived and compared it is shown that the approximate slopes of regression tests are at least as great as those based on the residuals of univariate arima models and that there are cases in which the former are arbitrarily great while the latter are arbitrarily small these analytical findings are supported by a monte carlo study that shows that in samples of size 100 and 250 the asymptotic distribution theory under the null hypothesis is adequate for all tests but under alternatives to the null hypothesis the rate of type ii error for the test based on arima model residuals is often more than double that of the regression tests

stability of viscous scalar shock fronts in several dimensions we prove nonlinear stability of planar shock front solutions for viscous scalar conservation laws in two or more space dimensions the proof uses the integrated equation and an effective equation for the motion of the front itself we derive energy estimates that balance terms from the integrated equation with terms from the front motion equation in this paper we prove that viscous shock profiles for scalar conservation laws are stable in two or more space dimensions these multidimensional stability questions are separate from their one dimensional analogues because of the possibility of transverse instabilities such as those that occur in combustion fronts lu and in shock waves with phase changes the proof here is a rigorous version of arguments that are used to derive effective equations such as the kuramoto sivashinsky equation to describe the behavior of fronts the one dimensional stability for scalar conservation laws was proven by ii in and oleinik io using the integrated equation see below and a max imum principle another proof based on weighted norms and spectral theory for the linearized problem was given by sattinger s the multidimensional stability proof below has more in common with the stability proofs for systems of conservation laws in one space dimension begun by kawashima and mat sumura km and goodman go and completed by liu li these proofs use l2 energy estimates for the integrated equation we consider equations of the form ut f u x g u y uxx uyy where f u is a strictly convex function of u

piecewise aggregate representations and lower bound distance functions for multivariate time series abstract dimensionality reduction is one of the most important methods to improve the efficiency of the techniques that are applied to the field of multivariate time series data mining due to multivariate time series with the variable based and time based dimensions the reduction techniques must take both of them into consideration to achieve this goal we use a center sequence to represent a multivariate time series so that the new sequence can be seen as a univariate time series thus two sophisticated piecewise aggregate representations including piecewise aggregate approximation and symbolization applied to univariate time series are used to further represent the extended sequence that is derived from the center one furthermore some distance functions are designed to measure the similarity between two representations through being proven by some related mathematical analysis the proposed functions are lower bound on euclidean distance and dynamic time warping in this way false dismissals can be avoided when they are used to index the time series in addition multivariate time series with different lengths can be transformed into the extended sequences with equal length and their corresponding distance functions can measure the similarity between two unequal length multivariate time series the experimental results demonstrate that the proposed methods can reduce the dimensionality and their corresponding distance functions satisfy the lower bound condition which can speed up the calculation of similarity search and indexing in the multivariate time series datasets

stability of large ekman boundary layers in rotating fluids the aim of this paper is to investigate the stability of ekman boundary layers for rotating fluids when the ekman number and the rossby number go to zero more precisely we prove that spectral stability implies linear and nonlinear stabilities of approximate solutions in particular we replace the smallness condition obtained with energy methods in 5 by a weaker spectral condition which is sharp

testing for independence between two covariance stationary time series summary a one sided asymptotically normal test for independence between two stationary time series is proposed by first prewhitening the two time series and then basing the test on the residual cross correlation function the test statistic is a properly standardised version of the sum of weighted squares of residual cross correlations with weights depending on a kernel function haugh s 1976 test can be viewed as a special case of our approach in the sense that it corresponds to the use of the truncated kernel many kernels deliver better power than haugh s test a simulation study shows that the new test has good power against short and long cross correlations

existence and stability of multidimensional shock fronts in the vanishing viscosity limit in this paper we present a new approach to the study of linear and nonlinear stability of inviscid multidimensional shock waves under small viscosity perturbation yielding optimal estimates and eventually an extension to the viscous case of the celebrated theorem of majda on existence and stability of multidimensional shock waves more precisely given a curved lax shock solution u0 to a hyperbolic system of conservation laws we construct nearby viscous shock solutions ue to a parabolic viscous perturbation of the hyperbolic system which converge to u0 as viscosity e 0 and satisfy an appropriate conormal version of majda s stability estimate

using permutations to detect dependence between time series abstract in this paper we propose an independence test between two time series which is based on permutations the proposed test can be carried out by means of different common statistics such as pearson s chi square or the likelihood ratio we also point out why an exact test is necessary simulated and real data return exchange rates between several currencies reveal the capacity of this test to detect linear and nonlinear dependences

stability of systems of viscous conservation laws we consider systems of conservation laws and give conditions for nonlinear stability of viscous shock profiles the analysis applies to classical shocks of arbitrary strength 1998 john wiley sons inc

boundary layers for viscous perturbations of noncharacteristic quasilinear hyperbolic problems abstract in this paper we study viscous perturbations of quasilinear hyperbolic systems in several dimensions as the viscosity goes to zero the boundary is noncharacteristic for the hyperbolic system we in particular describe the boundary layer which arises near the boundary and give a sufficient condition for the convergence of the solution to the solution of some mixed hyperbolic problem with some nonlinear maximal dissipative boundary conditions a counterexample is given when this condition is not satisfied and the solution blows up as the viscosity goes to 0

viscous limits for piecewise smooth solutions to systems of conservation laws in this paper we study the zero dissipation problem for a general system of conservation laws with positive viscosity it is shown that if the solution of the problem with zero viscosity is piecewise smooth with a finite number of noninteracting shocks satisfying the entropy condition then there exist solutions to the corresponding system with viscosity that converge to the solutions of the system without viscosity away from shock discontinuities at a rate of order e as the viscosity coefficient e goes to zero the proof uses a matched asymptotic analysis and an energy estimate related to the stability theory for viscous shock profiles

viscous boundary value problems for symmetric systems with variable multiplicities abstract extending investigations of metivier and zumbrun in the hyperbolic case we treat stability of viscous shock and boundary layers for viscous perturbations of multidimensional hyperbolic systems with characteristics of variable multiplicity specifically the construction of symmetrizers in the low frequency regime where variable multiplicity plays a role at the same time we extend the boundary layer theory to real or partially parabolic viscosities neumann or mixed type parabolic boundary conditions and systems with nonconservative form in addition proving a more fundamental version of the zumbrun serre rousset theorem valid for variable multiplicities characterizing the limiting hyperbolic system and boundary conditions as a nonsingular limit of a reduced viscous system the new effects of viscosity are seen to be surprisingly subtle in particular viscous coupling of crossing hyperbolic modes may induce a destabilizing effect we illustrate the theory with applications to magnetohydrodynamics

gas liquid two phase flow structure in the multi scale weighted complexity entropy causality plane abstract the multi scale weighted complexity entropy causality plane ms wcecp is proposed for characterizing the physical structure of complex system firstly we use the method to investigate typical nonlinear time series compared with the multi scale complexity entropy causality plane ms cecp the ms wcecp can not only uncover the dynamic information loss of complex system with the increase of scale but also can characterize the complexity of nonlinear dynamic system in particular the algorithm of ms wcecp performs strong anti noise ability then we calculate the ms wcecp for the conductance fluctuating signals measured from vertical upward gas liquid two phase flow experiments in a small diameter pipe the results demonstrate that the ms wcecp is a useful approach for exploring the stability and complexity in gas liquid two phase flows

spectral stability of small shock waves this paper is the first in a series of articles that study the eigenvalue problem for small amplitude shock waves in systems of conservation laws with viscosity or relaxation the papers show in various contexts that in the zero amplitude limit appropriately scaled versions of the associated evans bundles converge to suspensions of evans bundles for fixed shock waves in related reduced systems with lower dimensional state space in this article the new geometric framework establishing this connection is introduced in the simplest context that of shock waves associated with a simple genuinely nonlinear mode in systems with identity viscosity in one space dimension

the experimental signals analysis for bubbly oil in water flow using multi scale weighted permutation entropy abstract we firstly combine multi scale method ms and weighted permutation entropy wpe to analyze chaotic noisy and fractal time series and find that mswpe can distinguish different nonlinear time series and exhibit a better robustness in the presence of higher levels of noise a task that multi scale permutation entropy mspe fails to work we then apply mswpe to analyze the signals from vertical upward oil in water two phase flow experiments our results suggest that the change rate of mswpe enables to characterize the transition of flow patterns and multi scale weighted permutation entropy allows indicating the discrepancy of complexity of oil in water two phase flow

multidimensional viscous shocks i degenerate symmetrizers and long time stability received by the editors september 18 2002 2000 mathematics subject classification primary 35l60 secondary 35b35 35b45 35k55 35l65 76l05

stability of one dimensional boundary layers by using green s functions the aim of this paper is to investigate the stability of one dimensional boundary layers of parabolic systems as the viscosity goes to 0 in the noncharacteristic case and more precisely to prove that spectral stability implies linear and nonlinear stability of approximate solutions in particular we replace the smallness condition obtained by the energy method 10 13 by a weaker spectral condition 2001 john wiley sons inc

nonclassical multidimensional viscous and inviscid shocks extending our earlier work on lax type shocks of systems of conservation laws we establish existence and stability of curved multidimensional shock fronts in the vanishing viscosity limit for general lax or undercompressive type shock waves of nonconservative hyperbolic systems with parabolic regularization the hyperbolic equations may be of variable multiplicity and the parabolic regularization may be of real or partially parabolic type we prove an existence result for inviscid nonconservative shocks that extends to multidimensional shocks a one dimensional result of x lin proved by quite different methods in addition we construct families of smooth viscous shocks converging to a given inviscid shock as viscosity goes to zero thereby justifying the small viscosity limit for multidimensional nonconservative shocks in our previous work on shocks we made use of conservative form especially in parts of the low frequency analysis thus most of the new analysis of this paper is concentrated in this area by adopting the more general nonconservative viewpoint we are able to shed new light on both the viscous and inviscid theory for example we can now provide a clearer geometric motivation for the low frequency analysis in the viscous case also we show that one may in the treatment of inviscid stability of nonclassical and or nonconservative shocks remove an apparently restrictive technical assumption made by mokrane and coulombel in their work on respectively shocktype nonconservative boundary problems and conservative undercompressive shocks another advantage of the nonconservative perspective is that lax and undercompressive shocks can be treated by exactly the same analysis

zero dissipation limit of solutions with shocks for systems of hyperbolic conservation laws we consider the convergence of solutions of conservation laws with viscosity to solutions having shocks of hyperbolic conservation laws without viscosity as the viscosity tends to zero our analysis reveals a rich structure of nonlinear wave interactions due to the presence of shocks and initial layers these interactions generate four different wave patterns initial layers shock layers diffusion waves and coupling waves we study the propagation and interactions of the four wave patterns by a detailed pointwise analysis

periodicity versus chaos in one dimensional dynamics we survey recent results in one dimensional dynamics and as an application we derive rigorous basic dynamical facts for two standard models in population dynamics the ricker and the hassell families we also informally discuss the concept of chaos in the context of one dimensional discrete time models first we use the model case of the quadratic family for an informal exposition we then review precise generic results before turning to the population models our focus is on typical asymptotic behavior seen for most initial conditions and for large sets of maps parameter sets corresponding to different types of attractors are described in particular it is shown that maps with strong chaotic properties appear with positive frequency in parameter space in our population models natural measures asymptotic distributions and their stability properties are considered