interpolation of precipitation under topographic influence at different time scales 1 in this paper new methodologies for interpolating rainfall data in individual time intervals ranging from a day to a year using gaussian copulas and unsymmetrical v copulas with a variety of treatments of altitude as an exogenous variable are described for shorter time aggregations zeros were treated as censored variables for each selected time step the marginal distributions of precipitation amounts were modeled using nonparametric density estimators while the spatial dependence structures were estimated using a maximum likelihood methodology the methodology was compared to other common geostatistical interpolators such as ordinary kriging and external drift kriging several measures of bias and error structure have been used to assess the efficacy of the methods in a range of comparative split sampling studies the data set chosen for the study comprises daily precipitation time series over 41 years in three regions in germany measured at more than 1200 locations over a large area 126 144 km2 among the many findings in the paper the ones that stand out are i correlation between precipitation and topography increases with the length of time interval and is significantly improved by directional smoothing of topography ii the copula methods are superior to kriging methods in terms of quality of interpolation bias and uncertainty estimation iii the treatment of zeros as censored variables improves interpolation quality for daily and pentad values monthly and annual data in this region present no dry periods iv the copula methods yield full conditional distributions of estimates at a target point in an interval improving substantially on the simple uncertainty estimates derived from kriging and v the gauss copula in particular performs best overall in terms of computational efficiency combined with useful error profiles in the interpolations and of all methods is the most realistic in its error estimates

stochastic reconstruction and interpolation of precipitation fields using combined information of commercial microwave links and rain gauges for the reconstruction and interpolation of precipitation fields we present the application of a stochastic approach called random mixing generated fields are based on a data set consisting of rain gauge observations and path averaged rain rates estimated using commercial microwave link cml derived information precipitation fields are received as linear combination of unconditional spatial random fields where the spatial dependence structure is described by copulas the weights of the linear combination are optimized such that the observations and the spatial structure of the precipitation observations are reproduced the innovation of the approach is that this strategy enables the simulation of ensembles of precipitation fields of any size each ensemble member is in concordance with the observed path averaged cml derived rain rates and additionally reflects the observed rainfall variability along the cml paths the ensemble spread allows additionally an estimation of the uncertainty of the reconstructed precipitation fields the method is demonstrated both for a synthetic data set and a real world data set in south germany while the synthetic example allows an evaluation against a known reference the second example demonstrates the applicability for real world observations generated precipitation fields of both examples reproduce the spatial precipitation pattern in good quality a performance evaluation of random mixing compared to ordinary kriging demonstrates an improvement of the reconstruction of the observed spatial variability random mixing is concluded to be a beneficial new approach for the provision of precipitation fields and ensembles of them in particular when different measurement types are combined

spectral theory for the periodic sine gordon equation a concrete viewpoint a summary of the spectral theory for quasiperiodic sine and sinh gordon equations is given analogies with whole line solitons and scattering theory motivates the discussion the relation between the ingredients in the inverse spectral solution of the periodic sine gordon equation and physical characteristics of sine gordon waves is emphasized the explicit topics covered are summarized in the table of contents in the introduction

nonlinear dynamics in driven damped sine gordon systems abstract many quasi one and two dimensional systems can be modeled by sine gordon equations illustrations are given for driven and damped sine gordon equations of behaviors that are typical of ways that complexity in time and space can be manifested examples include an ac response to a dc driver and spontaneous pattern formation and low dimensional chaos under the influence of ac or ac dc drivers the importance of the coexistence of coherence and chaos for transport phenomena is emphasized

coercive boundary value problems for regular degenerate differential operator equations abstract this study focuses on nonlocal boundary value problems bvp for degenerate elliptic differential operator equations doe that are defined in banach valued function spaces where boundary conditions contain a degenerate function and a principal part of the equation possess varying coefficients several conditions obtained that guarantee the maximal l p regularity and fredholmness these results are also applied to nonlocal bvp for regular degenerate partial differential equations on cylindrical domain to obtain the algebraic conditions that ensure the same properties

copula based geostatistical models for groundwater quality parameters 1 groundwater quality parameters exhibit considerable spatial variability geostatistical methods including the assessment of variograms are usually used to characterize this variability copulas offer an interesting opportunity to describe dependence structures for multivariate distributions bivariate empirical copulas can be used as an alternative to variograms and covariance functions for the description of the spatial variability rank correlations of these copulas express the strength of the dependence independently of the marginal distributions and thus offer an alternative to the variograms empirical copulas for four quality parameters chloride sulfate ph and nitrate obtained from a large scale groundwater quality measurement network in baden wurttemberg germany are calculated they indicate that the spatial dependence structure of the investigated parameters is not gaussian two theoretical copula based models are presented in this paper a gaussian and a non gaussian bootstrap based statistical tests using stochastic simulation of the multivariate distributions are used to investigate the appropriateness of the models according to the test results the gaussian copula is rejected for most of the parameters while the non gaussian alternative is not rejected in most cases

the high accurate block grid method for solving laplace s boundary value problem with singularities a high accurate difference analytical method is introduced for the solution of the mixed boundary value problem for laplace s equation on graduated polygons the polygon can have broken sections and be multiply connected the uniform estimate of the error of the approximate solution is of order o h6 whereas it is of order o h 6 r j p lambda j for the errors of p order derivatives p 1 2 in a finite neighborhood of reentry vertices here h is the mesh step rj is the distance from the current point to the vertex in question lambda j 1 a alpha j and a 1 or 2 depending on the types of boundary conditions further alpha j pi is the value of the interior angle at the considered vertex numerical experiments are illustrated in section ref sec8 to support the analysis made

influence of soil structure and root water uptake strategy on unsaturated flow in heterogeneous media 1 we analyze the combined effects of the spatial variability of soil hydraulic properties and the water uptake by plant roots on unsaturated water flow for this analysis we use a simplified macroscopic root water uptake model which is usually applied only for homogeneous or layered soil and therefore we also determine whether it is applicable for multidimensional heterogeneous media analytical solutions for mean and variance of pressure head first order second moment approximations in layered media and numerical solutions of two dimensional 2 d autocorrelated multi gaussian and non multi gaussian parameter fields are analyzed for steady state and transient flow conditions for non gaussian topological features that have little influence on the mean and the variance of the pressure field if root water uptake is ignored we test whether the influence is significant if root water uptake is accounted for the results reveal that in field structures with large patches of coarse material local regions with pressure head values at the wilting point develop these are surrounded by wet material without a compensation mechanism for local stress the global transpiration demand is not met if local wilting occurs various compensation mechanisms are tested that depend respectively on the saturation the relative conductivity or a strategy where the deficit in the global uptake rate is equally distributed to unstressed locations the strategies lead to a global actual transpiration rate at the potential value and attenuate the formation of locally wilted areas wilted regions can however still occur and may be an artifact of the simplified model concept as root soil interactions are neglected therefore simplified macroscopic models for root water uptake should be used with caution in heterogeneous media

multivariate copula analysis toolbox mvcat describing dependence and underlying uncertainty using a bayesian framework we present a newly developed multivariate copula analysis toolbox mvcat which includes a wide range of copula families with different levels of complexity mvcat employs a bayesian framework with a residual based gaussian likelihood function for inferring copula parameters and estimating the underlying uncertainties the contribution of this paper is threefold a providing a bayesian framework to approximate the predictive uncertainties of fitted copulas b introducing a hybrid evolution markov chain monte carlo mcmc approach designed for numerical estimation of the posterior distribution of copula parameters and c enabling the community to explore a wide range of copulas and evaluate them relative to the fitting uncertainties we show that the commonly used local optimization methods for copula parameter estimation often get trapped in local minima the proposed method however addresses this limitation and improves describing the dependence structure mvcat also enables evaluation of uncertainties relative to the length of record which is fundamental to a wide range of applications such as multivariate frequency analysis

computational procedure for sturm liouville problems the approaches of datzeff c r acad bulg sci 12 1959 113 285 and wittrick and williams quart j mech appl math xxiv 1971 263 int j mech sci 16 1974 209 have been incorporated to develop a procedure for the automatic computation of the eigen values and the eigen functions of one dimensional linear sturm liouville boundary value eigenproblems both singular and nonsingular the continuous coefficients of a regular sturm liouville problem have been approximated by a finite number of step functions in each step the resulting boundary value problem has been integrated exactly and the solutions have then been matched to construct the continuously differentiable solution of the original problem and the corresponding eigencondition step sizes have been chosen automatically so that the local error has been held in a predetermined interval representative test examples have been computed to illustrate the accuracy reliability and efficiency of the algorithm proposed

improved spatial prediction a combinatorial approach 1 this paper presents a combinatorial approach for improving spatial predictions first copulas are used to interpolate a spatially distributed point rainfall field to a uniform spatial grid it is observed that results vary substantially depending on the parameters chosen for interpolation leading to the hypothesis that it may be advantageous to estimate copula parameters locally or to combine local and global copula predictions it is found that by modifying the method of forecast combinations prediction errors in the spatial interpolation of rainfall can be reduced although this method of combining predictions is applied in the context of rainfall interpolation using local and global copula predictions it can be used on other spatial variables and interpolation methods

nonlinear fourier analysis for the infinite interval korteweg de vries equation ii numerical tests of the direct scattering transform abstract a recursive algorithm for computing the direct scattering transform dst of a discrete space or time series whose dynamics is described approximately by the infinite line korteweg de vries kdv equation is tested for numerical accuracy by considering several example problems for which the exact dst spectrum is known the effects of truncation roundoff discretization and noise errors are specifically addressed procedures for estimating errors in a general experimental context are developed and the nonlinear filtering of noise is discussed

a note on the bitsadze samarskii type nonlocal boundary value problem in a banach space abstract the bitsadze samarskii type nonlocal boundary value problem u t a u t f t 0 t 1 u 0 u 1 u 0 1 in an arbitrary banach space e with the positive operator a is considered the well posedness of this boundary value problem in the spaces of smooth functions is established the new exact schauder s estimates of solutions of the boundary value problems for elliptic equations are obtained

difference method of fourth order accuracy for the laplace equation with multilevel nonlocal conditions abstract we consider the multipoint nonlocal boundary value problem for the two dimensional laplace equation in a rectangular domain the solution of this problem is defined as a 9 point finite difference solution with the fourth order gluing operator of the local dirichlet boundary value problem by constructing a special method to find a function as the boundary value on the side of the rectangle where the nonlocal condition is given numerical experiments are illustrated to support the analysis made

radial basis function method for a multidimensional linear elliptic equation with nonlocal boundary conditions the development of numerical methods for the solution of partial differential equations pdes with nonlocal boundary conditions is important since such type of problems arise as mathematical models of various real world processes we use radial basis function rbf collocation technique for the solution of a multidimensional linear elliptic equation with classical dirichlet boundary condition and nonlocal integral conditions rbf based meshless methods are easily implemented and efficient especially for multidimensional problems formulated on complexly shaped domains in this paper properties of the method are investigated by studying two and three dimensional test examples with manufactured solutions we analyze the influence of the rbf shape parameter and the distribution of the nodes on the accuracy of the method as well as the influence of nonlocal conditions on the conditioning of the collocation matrix

multivariate type g matern stochastic partial differential equation random fields for many applications with multivariate data random field models capturing departures from gaussianity within realizations are appropriate for this reason we formulate a new class of multivariate non gaussian models based on systems of stochastic partial differential equations with additive type g noise whose marginal covariance functions are of matern type we consider four increasingly flexible constructions of the noise where the first two are similar to existing copula based models in contrast with these the last two constructions can model non gaussian spatial data without replicates computationally efficient methods for likelihood based parameter estimation and probabilistic prediction are proposed and the flexibility of the models suggested is illustrated by numerical examples and two statistical applications less

nonlinear fourier analysis for the infinite interval korteweg de vries equation i an algorithm for the direct scattering transform the nonlinear fourier analysis of wave motion governed approximately by the korteweg de vries kdv equation on the infinite line is the central point of discussion we assume that the wave amplitude is recorded in the form of a discrete space or time series which is determined either by experimental measurement or by computer simulation of the physical system of interest we develop numerical data analysis procedures based upon the scattering transform solution to the kdv equation as given by gardner et al 1 we are motivated by the observation that historically the fourier transform has been ubiquitously used to spectrally analyze linear wave data here we develop methods for employing the scattering transform as a tool to similarly analyze nonlinear wave data specifically we develop numerical methods to evaluate the direct scattering transform dst of a space or time series the approach thus provides a basis for analyzing and interpreting nonlinear wave behavior in the wavenumber or frequency domain the dst spectrum separates naturally into soliton and radiation components and may be simply interpreted in terms of the large time asymptotic state of the infinite line kdv equation

reaction diffusion equations with nonlocal boundary and nonlocal initial conditions in this paper we investigate the existence multiplicity and asymptotic behavior of solutions for a reaction diffusion equation under nonlocal boundary and nonlocal initial conditions a distinctive feature of this type of boundary and initial conditions is that the parabolic equation may possess multiple solutions even if the reaction function is smooth including linear functions of special concern is the asymptotic behavior of these multiple solutions in relation to the solutions of the corresponding steady state problem which may also possess multiple solutions in some special cases both the time dependent and the steady state problems possess an infinite number of solutions and each of the time dependent solutions converges to one of the steady state solutions

streamflow prediction in ungauged catchments using copula based dissimilarity measures 1 there are many procedures in the available literature to perform prediction in ungauged basins commonly the euclidean metric is used as a proxy of the hydrologic dissimilarity here we propose a procedure to find a metric on the basis of dissimilarity measures that are estimated from pairwise empirical copula densities of runoff a metric is then defined in an transformed space of basin descriptors whose parameterization is obtained with a variance reducing technique a hydrologic model was run in an ungauged basin with sets of global parameters obtained from the k nearest neighboring donor basins using various metrics to take into account the uncertainty of its parameterization hydrologic model parameters were regionalized with a multiscale parameter regionalization technique whose transfer function parameters were found via calibration the streamflow in an ungauged basin was found as an ensemble streamflow prediction to account for the uncertainties of the transfer function parameters as well as those to define the metric this technique was applied in 38 german basins ranging in size from 70 to 4000 km2 for each basin a number of catchment descriptors and several climatic indices were quantified e g mean slope aspect shape factor mean elevation and mean monthly temperature in january among others daily streamflow time series correspond to the period from 1961 to 2000 simulated daily discharge was validated with a jackknife cross validation technique nash sutcliffe efficiencies obtained in this way ranged between 0 76 and 0 86 these results suggested that the proposed technique would produce reasonable results in ungauged basins

finite difference methods for solution of nonlocal boundary value problems the article is devoted to the construction and investigation of various types of difference schemes relevant to nonlocal boundary value problems stated for multidimensional elliptic equations suitable tools for performing the investigation are developed including difference analogue of green s formula and inequalities corresponding to nonlocal boundary conditions

a spatial markov model for the evolution of the joint distribution of groundwater age arrival time and velocity in heterogeneous media the evolution of the joint distribution of groundwater age velocity and arrival times based on a markov model for the velocities of fluid particles in heterogeneous porous media has been quantified an explicit evolution equation for the joint distribution of age arrival time and particle velocity is derived which is equivalent to a continuous time random walk for age velocity and arrival time the approach is fully parameterized by the correlation model and the distribution of groundwater flow velocities the transition probability for subsequent particle velocities along streamlines is implemented by a copula which is an efficient method to generate a correlated velocity series with prescribed marginal distribution we discuss different solution methods based on finite differences and random walk particle tracking the latter is based on continuous time random walks whose transition times are obtained kinematically from the flow velocities specifically we discuss a renormalization scheme to accelerate the particle tracking simulations based on the definition of aggregate particle transitions while at the same time renormalizing velocity correlation the impact of velocity correlation and velocity distribution on the evolution of age at different distances from the inlet plane is also studied at distances of the order of the correlation length persistent particle velocities give the same behavior as stochastic streamtube models for velocity distributions which give rise to transition times with finite variance the age distributions evolve toward an inverse gaussian for heavy tailed weighting times they evolve toward stable distribution as the distance from the inlet increases

geostatistical interpolation using copulas 1 in many applications of geostatistical methods the dependence structure of the investigated parameter is described solely with the variogram or covariance functions which are susceptible to measurement anomalies and implies the assumption of gaussian dependence moreover the kriging variance respects only observation density data geometry and the variogram model to address these problems we borrow the idea from copulas to depict the dependence structure without the influence of the marginal distribution the methodology and basic hypotheses for application of copulas as geostatistical methods are discussed and the gaussian copula as well as a non gaussian copula are used in this paper copula parameters are estimated using a division of the observations into multipoint subsets and a subsequent maximization of the corresponding likelihood function the interpolation is carried out with two different copulas where the expected and median values are calculated from the copulas conditioned with the nearby observations the full conditional copulas provide the estimation distributions for the unobserved locations and can be used to define confidence intervals which depend on both the observation geometry and values observations of a large scale groundwater quality measurement network in baden wurttemberg are used to demonstrate the methodology five groundwater quality parameters chloride nitrate ph sulfate and dissolved oxygen are investigated all five parameters show non gaussian dependence the copula based interpolation results of the five parameters are compared to the results of conventional ordinary and indicator kriging different statistical measures including mean squared error relative differences and probability scores are used to compare cross validation and split sampling results of the interpolation methods the non gaussian copulas give better results than the geostatistical interpolations validation of the confidence intervals shows that they are more realistic than the estimation variances obtained by ordinary kriging

nonlinear normal modes for the toda chain abstract the toda chain is a nonlinear mass spring chain which can in principle be integrated analytically by the action angle theory of classical mechanics we show that the transformation from physical variables to action variables can be implemented very simply on a computer we study the correspondence between action variables and the motions of the chain and find the role of the action variables to be very similar to the role of normal mode amplitudes in the harmonic chain this similarity leads to a partly rigorous partly heuristic normal mode analysis for the toda chain new results are obtained when this normal mode analysis is applied to certain perturbations of the toda chain such as the fermi pasta ulam chain or the toda chain with a mass impurity

modeling complex geological structures with elementary training images and transform invariant distances 1 we present a new framework for multiple point simulation involving small and simple training images the use of transform invariant distances by applying random transformations expands the range of structures available in the simple patterns of the training image the training image is no longer regarded as a global conceptual geological model but rather a basic structural element of the subsurface complex geological structures are obtained whose spatial structure can be parameterized by adjusting the statistics of the random transformations on the basis of field data or geological context in most cases such parameterization is possible by adjusting two numbers only this method allows us to build models that 1 reproduce shapes corresponding to a desired prior geological concept and 2 are in phase with different types of field observations such as orientation hydrofacies or geophysical measurements the main advantage is that the training images are so simple that they can be easily built even in 3 d we apply the method on a synthetic example involving seismic data where the transformation parameters are data driven we also show examples where realistic 2 and 3 d structures are built from simplistic training images with transformation parameters inferred using a small number of orientation data

on the numerical integration of the schrodinger equation in the finite difference schemes abstract formulae for the integration of the schrodinger equation for bound states based on the scheme of central differences are generated from the taylor expansion with the help of formal pade approximants these methods are studied in matrix form and a limiting formula the best for a given discretization is obtained

the solitons of zabusky and kruskal revisited perspective in terms of the periodic spectral transform abstract we consider the numerical soliton experiments of zabusky and kruskal 1 and address their results in light of the spectral structure of the periodic korteweg devries kdv equation we derive and exploit a simple relationship between the infinite line transfer matrix and the monodromy matrix of periodic theory this establishes the connection at all stages of our analysis between the infinite line soliton and the soliton limit of periodic theory we develop analytical and numerical procedures for determining the spectral structure of a periodic wave train and discuss how the methods may be viewed as a generalization of ordinary periodic fourier analysis finally we introduce the concept of a reference level which is defined to be the level upon which the solitons propagate these results together with judicious numerical experiments allow us to reassess the work of zabusky and kruskal from the standpoint of periodic theory for the kdv equation we find their system to be soliton dominated and our estimates of the soliton amplitudes and phase speeds agree well with those given in their classic paper we also find that even in the presence of periodic boundary conditions the solitons behave like infinite line solitons in that they undergo phase shifts upon collision with each other our estimate of the fpu recurrence time which includes the effect of phase shifting is within one percent of their observed value

entropy copula method for single site monthly streamflow simulation 1 an entropy copula method is proposed for single site monthly streamflow simulation in this method the joint distribution of adjacent monthly streamflows is constructed using the copula method whereas the marginal distribution of streamflow for each month is derived using the entropy method then the conditional distribution is derived from which monthly streamflow is generated moment statistics of monthly streamflow such as mean standard deviation and skewness can be modeled by the entropy based marginal distribution while the dependence structure between streamflows of adjacent months can be modeled by the copula based joint distribution the proposed entropy copula method can be extended by incorporating an aggregate variable for modeling the interannual dependence application to the simulation of monthly streamflow from the colorado river illustrates the effectiveness of the proposed method

operator splitting methods for generalized korteweg de vries equations we apply the method of operator splitting on the generalized korteweg de vries kdv equation ut f u x uxxx 0 by solving the nonlinear conservation law ut f u x 0 and the linear dispersive equation ut uxxx 0 sequentially we prove that if the approximation obtained by operator splitting converges then the limit function is a weak solution of the generalized kdv equation convergence properties are analyzed numerically by studying the effect of combining different numerical methods for each of the simplified problems

on a mapping approach to investigating the bootstrap accuracy a simple mapping approach is proposed to study the bootstrap accuracy in a rather general setting it is demonstrated that the bootstrap accuracy can be obtained through this method for a broad class of statistics to which the commonly used edgeworth expansion approach may not be successfully applied we then consider some examples to illustrate how this approach may be used to find the bootstrap accuracy and show the advantage of the bootstrap approximation over the gaussian approximation for the multivariate kolmogorov smirnov statistic we show the error of bootstrap approximation is as small as that of the gaussian approximation for the multivariate kernel type density estimate we obtain an order of the bootstrap error which is smaller than the order of the error of the gaussian approximation given in rio 1994 we also consider an application of the bootstrap accuracy for empirical process to that for the copula process

parameter estimation by ensemble kalman filters with transformed data approach and application to hydraulic tomography 1 ensemble kalman filters enkfs are a successful tool for estimating state variables in atmospheric and oceanic sciences recent research has prepared the enkf for parameter estimation in groundwater applications enkfs are optimal in the sense of bayesian updating only if all involved variables are multivariate gaussian subsurface flow and transport state variables however generally do not show gaussian dependence on hydraulic log conductivity and among each other even if log conductivity is multi gaussian to improve enkfs in this context we apply nonlinear monotonic transformations to the observed states rendering them gaussian gaussian anamorphosis ga similar ideas have recently been presented by beal et al 2010 in the context of state estimation our work transfers and adapts this methodology to parameter estimation additionally we address the treatment of measurement errors in the transformation and provide several multivariate analysis tools to evaluate the expected usefulness of ga beforehand for illustration we present a first time application of an enkf to parameter estimation from 3 d hydraulic tomography in multi gaussian log conductivity fields results show that 1 ga achieves an implicit pseudolinearization of drawdown data as a function of log conductivity and 2 this makes both parameter identification and prediction of flow and transport more accurate combining enkfs with ga yields a computationally efficient tool for nonlinear inversion of data with improved accuracy this is an attractive benefit given that linearization free methods such as particle filters are computationally extremely demanding

solution of the schrodinger equation by a spectral method abstract a new computational method for determining the eigenvalues and eigenfunctions of the schrodinger equation is described conventional methods for solving this problem rely on diagonalization of a hamiltonian matrix or iterative numerical solutions of a time independent wave equation the new method in contrast is based on the spectral properties of solutions to the time dependent schrodinger equation the method requires the computation of a correlation function r 0 r t from a numerical solution r t fourier analysis of this correlation function reveals a set of resonant peaks that correspond to the stationary states of the system analysis of the location of these peaks reveals the eigenvalues with high accuracy additional fourier transforms of r t with respect to time generate the eigenfunctions the effectiveness of the method is demonstrated for a one dimensional asymmetric double well potential and for the two dimensional henon heiles potential

analytical relationship between gaussian and transformed gaussian spatially distributed fields 1 a transformation of a gaussian random field results in a change of the spatial dependence in simple terms the range and the shape of a variogram are different between an underlying gaussian and a transformed gaussian field there is a relationship between the underlying and the transformed spatial dependence this paper shows how this relationship can be expressed analytically rather than generating multidimensional random fields and conducting spatial statistical analysis we develop an accurate and efficient approach based on a unique mapping of the correlation coefficients of the original multi gaussian fields to the transformed correlation coefficients to evaluate the spatial correlation of transformed non gaussian random fields for any type of geostatistical parameterization such a mapping can also yield accurate estimation of the spatial correlation of the underlying gaussian field given the spatial correlation of the transformed field results indicate that 1 a nonlinear transformation of spatially distributed fields usually changes the spatial dependence structure and 2 the relationship between the dependence structures of the underlying and the transformed field can be expressed analytically and it is sufficient to do this in one dimension we use the developed approach to investigate the change of correlations of connected random fields generated by the absolute value transformation results show 1 the correlation lengths of the underlying gaussian fields are 1 67 and 2 64 times of those of transformed non gaussian fields for gaussian and exponential covariance models respectively 2 the anisotropic ratio does not change and 3 the anticorrelation in hole effect correlation models disappear

computational synergetics and mathematical innovation it is demonstrated how the computer used in a heuristic mode has greatly augmented our understanding of the mathematics of nonlinear dynamical process examples are given of recent work in soliton mathematics mainly but also nonlinear iterative mappings and low order nonlinear ordinary differential equation systems the role of good graphics in enhancing the discovery and retention of new mathematical properties of equations is illustrated several examples are given of the present frontier of research in two space dimensional nonlinear evolutionary problems

numerical solutions of the korteweg di vries equation using the periodic scattering transform m representation abstract we develop a numerical procedure based upon the periodic scattering transform for determining the spatial and temporal evolution of solutions to the korteweg de vries kdv equation with periodic boundary conditions in this approach solutions to kdv are found in terms of the representation i e the wave amplitude is given by a trace formula consisting of a linear superposition of hyperelliptic functions j x t 1 j n which are governed by n nonlinearly coupled ordinary differential equations our approach consists of the numerical integration of these equations using a second order taylor series expansion with variable integration step size it is well known that the j are generalizations of elliptic functions to the hyperelliptic class nevertheless we find that the j x t bear little or no resemblance to elliptic functions except in the small amplitude linear limit or for the case of a single soliton we study in particular the most difficult numerical case which occurs for the n soliton wave train solution of the periodic kdv equation

gaussian and non gaussian inverse modeling of groundwater flow using copulas and random mixing this paper presents a new copula based methodology for gaussian and non gaussian inverse modeling of groundwater flow the presented approach is embedded in a monte carlo framework and it is based on the concept of mixing spatial random fields where a spatial copula serves as spatial dependence function the target conditional spatial distribution of hydraulic transmissivities is obtained as a linear combination of unconditional spatial fields the corresponding weights of this linear combination are chosen such that the combined field has the prescribed spatial variability and honors all the observations of hydraulic transmissivities the constraints related to hydraulic head observations are nonlinear in order to fulfill these constraints a connected domain in the weight space inside which all linear constraints are fulfilled is identified this domain is defined analytically and includes an infinite number of conditional fields i e conditioned on the observed hydraulic transmissivities and the nonlinear constraints can be fulfilled via minimization of the deviation of the modeled and the observed hydraulic heads this procedure enables the simulation of a great number of solutions for the inverse problem allowing a reasonable quantification of the associated uncertainties the methodology can be used for fields with gaussian copula dependence and fields with specific non gaussian copula dependence further arbitrary marginal distributions can be considered

efficient pairwise composite likelihood estimation for spatial clustered data spatial clustered data refer to high dimensional correlated measurements collected from units or subjects that are spatially clustered such data arise frequently from studies in social and health sciences we propose a unified modeling framework termed as geocopula to characterize both large scale variation and small scale variation for various data types including continuous data binary data and count data as special cases to overcome challenges in the estimation and inference for the model parameters we propose an efficient composite likelihood approach in that the estimation efficiency is resulted from a construction of over identified joint composite estimating equations consequently the statistical theory for the proposed estimation is developed by extending the classical theory of the generalized method of moments a clear advantage of the proposed estimation method is the computation feasibility we conduct several simulation studies to assess the performance of the proposed models and estimation methods for both gaussian and binary spatial clustered data results show a clear improvement on estimation efficiency over the conventional composite likelihood method an illustrative data example is included to motivate and demonstrate the proposed method

a note on the well posedness of the nonlocal boundary value problem for elliptic difference equations the nonlocal boundary value problem for elliptic difference equations in an arbitrary banach space is considered the well posedness of this problem is investigated the stability almost coercive stability and coercive stability estimates for the solutions of difference schemes of the second order of accuracy for the approximate solutions of the nonlocal boundary value problem for elliptic equation are obtained the theoretical statements for the solution of these difference schemes are supported by the results of numerical experiments

factor copula models for replicated spatial data abstractwe propose a new copula model that can be used with replicated spatial data unlike the multivariate normal copula the proposed copula is based on the assumption that a common factor exists and affects the joint dependence of all measurements of the process moreover the proposed copula can model tail dependence and tail asymmetry the model is parameterized in terms of a covariance function that may be chosen from the many models proposed in the literature such as the matern model for some choice of common factors the joint copula density is given in closed form and therefore likelihood estimation is very fast in the general case one dimensional numerical integration is needed to calculate the likelihood but estimation is still reasonably fast even with large datasets we use simulation studies to show the wide range of dependence structures that can be generated by the proposed model with different choices of common factors we apply the proposed model to spatial temperature data and com

bayesian assessment of the expected data impact on prediction confidence in optimal sampling design 1 incorporating hydro geo logical data such as head and tracer data into stochastic models of subsurface flow and transport helps to reduce prediction uncertainty because of financial limitations for investigation campaigns information needs toward modeling or prediction goals should be satisfied efficiently and rationally optimal design techniques find the best one among a set of investigation strategies they optimize the expected impact of data on prediction confidence or related objectives prior to data collection we introduce a new optimal design method called predia gnosis preposterior data impact assessor predia derives the relevant probability distributions and measures of data utility within a fully bayesian generalized flexible and accurate framework it extends the bootstrap filter bf and related frameworks to optimal design by marginalizing utility measures over the yet unknown data values predia is a strictly formal information processing scheme free of linearizations it works with arbitrary simulation tools provides full flexibility concerning measurement types linear nonlinear direct indirect allows for any desired task driven formulations and can account for various sources of uncertainty e g heterogeneity geostatistical assumptions boundary conditions measurement values model structure uncertainty a large class of model errors via bayesian geostatistics and model averaging existing methods fail to simultaneously provide these crucial advantages which our method buys at relatively higher computational costs we demonstrate the applicability and advantages of predia over conventional linearized methods in a synthetic example of subsurface transport in the example we show that informative data is often invisible for linearized methods that confuse zero correlation with statistical independence hence predia will often lead to substantially better sampling designs finally we extend our example to specifically highlight the consideration of conceptual model uncertainty

on the nonlinear schro dinger limit of the korteweg de vries equation abstract using the multiscale approach of zakharov and kuznetsov it is shown that the nonlinear schrodinger periodic scattering data is related to the korteweg de vries periodic scattering data via an average over the korteweg de vries carrier oscillation this allows a complete elucidation of the physical meaning of the nonlinear schrodinger scattering data conservation laws theta function solutions and reality constraint

multivariate hydrological frequency analysis using copulas 1 this article presents the modeling of multivariate extreme values using copulas our approach allows us to model the dependence structure independently of the marginal distributions which is not possible with standard classical methods the methodology has been applied on two different problems in hydrology the first application is concerned with the combined risk in the framework of frequency analysis four copulas have been tested on peak flows from the watershed of peribonka in quebec canada the second application relates to the joint modeling of peak flows and volumes three copulas have been applied to the watershed of the rimouski river in quebec canada this approach using copulas is promising since it allows us to take into account a wide range of correlation which can happen in hydrology

solitons cnoidal waves and nonlinear interactions in shallow water ocean surface waves abstract we analyze shallow water surface wave data from the adriatic sea using a nonlinear generalization of fourier analysis based upon the periodic inverse scattering transform in the function representation for the korteweg de vries kdv equation while linear fourier analysis superposes sine waves the nonlinear fourier approach superposes cnoidal waves the travelling wave solution to kdv plus their mutual nonlinear interactions a new procedure is presented for the nonlinear low pass and band pass filtering of measured wave trains we apply the approach to a measured time series and discuss the dynamics of solitons and the physics of the nonlinear interactions in terms of global spatio temporal phase shifts amongst the cnoidal waves

on the numerical integration of the schrodinger equation numerical tests abstract the various numerical methods obtained in a preceding work in the finite difference scheme are compared among themselves and against the exact solutions of some simple exactly soluble potentials the tests strongly favour the limiting method the discretized plane wave method a discussion of the results in the continuous spectrum is also presented

application of the multiquadric method for numerical solution of elliptic partial differential equations abstract we have used the multiquadric mq approximation scheme for the solution of elliptic partial differential equations with dirichlet and or neumann boundary conditions the scheme has the advantage of using the data points in arbitrary locations with an arbitrary ordering two dimensional laplace poisson and biharmonic equations describing the various physical processes have been taken as the test examples the agreement is found to be very good between the computed and exact solutions the method also provides an excellent approximation with a curved boundary

on the solution of a nonlocal problem in a rectangular domain we consider the bitsadze samarskii nonlocal boundary value problem for the two dimensional poisson equation the solution of this problem is defined as a solution of the local dirichlet boundary value problem by constructing a special method to find a function as the boundary value on the side of the rectangle where the nonlocal condition was given further the five point approximation of the laplace operator is used for the realization of the proposed method numerical experiments are illustrated in the last section to support the analysis made

computation of the direct scattering transform for the nonlinear schroedinger equation abstract the cubic nonlinear schroedinger equation nls describes the space time evolution of narrow banded wave trains in one space and one time 1 1 dimensions the richness of nonlinear wave motions described by nls is exemplified by the fully nonlinear envelope soliton and breather solutions which are fully understood only in terms of the general solution of the equation as described by the inverse scattering transform 1st the method may be viewed as a nonlinear generalization of the linear fourier transform herein we develop a numerical algorithm for determining the scattering transform spectrum of a nonlinear wave train described by the nls equation the analysis of space or time series data obtained from computer simulations of nonlinear narrow band wave trains or from experimental measurements is thus a central point of discussion in particular we develop a numerical algorithm for computing the direct scattering transform dst which may be interpreted as the nonlinear fourier spectrum of the complex envelope function of a wave train the fact that the nonlinear fourier modes are constants of the motion for all time provides a physical basis for the analysis of data while the nonlinear fourier method is specifically applied to the nls equation the approach is easily generalized to include the class of spectral problems due to ablowitz kaup newell and segur akns this class includes several other nonlinear wave equations of physical interest in 1 1 including the kortewegde vries kdv modified kdv sine gordon and sinh gordon equations

on bitsadze samarskii type nonlocal boundary value problems for elliptic differential and difference equations well posedness the well posedness of the bitsadze samarskii type nonlocal boundary value problem in holder spaces with a weight is established the coercivity inequalities for the solution of the nonlocal boundary value problem for elliptic equations are obtained the stable second order of accuracy difference scheme for the approximate solution of the problem is presented the well posedness of this difference scheme in difference analogue of holder spaces is established for applications the almost coercivity and the coercivity estimates for solutions of difference schemes for elliptic equations are obtained