super yangian y osp 1 2 and the universal r matrix of its quantum double we present the drinfel d realisation of the super yangian y osp 1 2 including the explicit expression for the coproduct we show in particular that it is necessary to introduce supplementary serre relations the construction of its quantum double is carried out this allows us to give the universal r matrix of dy osp 1 2

behavior of sensitivities in the one dimensional advection dispersion equation implications for parameter estimation and sampling design the spatial and temporal variability of sensitivities has a significant impact on parameter estimation and sampling design for studies of solute transport in porous media physical insight into the behavior of sensitivities is offered through an analysis of analytically derived sensitivities for the one dimensional form of the advection dispersion equation when parameters are estimated in regression models of one dimensional transport the spatial and temporal variability in sensitivities influences variance and covariance of parameter estimates several principles account for the observed influence of sensitivities on parameter uncertainty 1 information about a physical parameter may be most accurately gained at points in space and time with a high sensitivity to the parameter 2 as the distance of observation points from the upstream boundary increases maximum sensitivity to velocity during passage of the solute front increases and the consequent estimate of velocity tends to have lower variance 3 the frequency of sampling must be in phase with the s shape of the dispersion sensitivity curve to yield the most information on dispersion 4 the sensitivity to the dispersion coefficient is usually at least an order of magnitude less than the sensitivity to velocity 5 the assumed probability distribution of random error in observations of solute concentration determines the form of the sensitivities 6 if variance in random error in observations is large trends in sensitivities of observation points may be obscured by noise and thus have limited value in predicting variance in parameter estimates among designs 7 designs that minimize the variance of one parameter may not necessarily minimize the variance of other parameters 8 the time and space interval over which an observation point is sensitive to a given parameter depends on the actual values of the parameters in the underlying physical system

a comparison of four inverse approaches to groundwater flow and transport parameter identification four different methods of parameterizing spatially varying log transmissivities in an inverse approach are compared with respect to prediction accuracy of simulated flow and transport transport parameter estimation is included by two stage feedback optimization in stage one the log transmissivities are estimated by fitting both head and concentration data given initial values of the source concentration and the dispersivities in stage two the source concentration and the dispersivities are estimated by fitting the concentration data with the updated transport parameters final estimates of the log transmissivities are obtained by repeating the optimization of stage one the formulated objective functions are minimized using levenberg marquardt s algorithm the models are applied to synthetic two dimensional transport problems in steady state flow regimes the true log transmissivity fields are generated by the turning bands method thereby incorporating spatial variability the test cases differ in the input variances of the generated fields and with respect to the amount and accuracy of observed transmissivity data

existence uniqueness and invariant measures for stochastic semilinear equations on hilbert spaces a class of stochastic evolution equations with additive noise and weakly continuous drift is considered first regularity properties of the corresponding ornstein uhlenbeck transition semigrouprt are obtained we show thatrt is a compactc0 semigroup in all sobolev spaceswn p which are built on its invariant measure then we show the existence uniqueness compactness and smoothing properties of the transition semigroup for semilinear equations inlp spaces and spacesw1 p as a consequence we prove the uniquencess of martingale solutions to the stochastic equation and the existence of a unique invariant measure equivalent to it is shown also that the density of this measure with respect to is inlp for allp 1

a statistical methodology for estimating transport parameters theory and applications to one dimensional advectivec dispersive systems a simulation nonlinear multiple regression methodology for estimating parameters that characterize the transport of contaminants is developed and demonstrated finite difference contaminant transport simulation is combined with a nonlinear weighted least squares multiple regression procedure the technique provides optimal parameter estimates and gives statistics for assessing the reliability of these estimates under certain general assumptions about the distributions of the random measurement errors monte carlo analysis is used to estimate parameter reliability for a hypothetical homogeneous soil column for which concentration data contain large random measurement errors the value of data collected spatially versus data collected temporally was investigated for estimation of velocity dispersion coefficient effective porosity first order decay rate and zero order production the use of spatial data gave estimates that were 2 3 times more reliable than estimates based on temporal data for all parameters except velocity comparison of estimated linear and nonlinear confidence intervals based upon monte carlo analysis showed that the linear approximation is poor for dispersion coefficient and zero order production coefficient when data are collected over time in addition examples demonstrate transport parameter estimation for two real one dimensional systems first the longitudinal dispersivity and effective porosity of an unsaturated soil are estimated using laboratory column data we compare the reliability of estimates based upon data from individual laboratory experiments versus estimates based upon pooled data from several experiments second the simulation nonlinear regression procedure is extended to include an additional governing equation that describes delayed storage during contaminant transport the model is applied to analyze the trends variability and interrelationship of parameters in a mourtain stream in northern california

discrimination among one dimensional models of solute transport in porous media implications for sampling design a methodology is developed for discrimination among models of transient solute transport in porous media the method utilizes nonlinear regression on observations of solute concentration discrimination requires comparisons of model predictions to observations systematic error in residuals stability in parameter estimates from regression on different observation sets and other measures of model fit among hypothesized models of transport the set of observations of solute concentration to which models are fitted strongly influences the assessment of these discrimination criteria the most desirable observation set for discrimination amplifies the weaknesses of those models that appear to describe existing conditions but are in fact unsuitable for prediction the inadequacies of various observation sets are illustrated in four examples of discrimination between one dimensional models of solute transport our purpose in these examples is to understand the physical deterministic basis of sampling design for model discrimination in addition to physical attributes such as transport processes boundary conditions and flow geometry the assumed distribution of random error in the regression model is also treated as a model attribute to be tested by the designed experiment a common problem in field studies occurs when the set of available observations does not include sufficient information with which to discriminate among hypothesized models hence supporting the need to design a second round of sampling specifically for discrimination a proposed objective function in the sampling design problem favors design points at locations and times when two hypothesized transport models display the greatest differences in predicted concentration two hypothetical examples demonstrate the effectiveness of the objective function and the application of the discrimination criteria

on the ornstein uhlenbeck operator in spaces of continuous functions we study the realization of the ornstein uhlenbeck operator a in the space of the uniformly continuous and bounded functions in rn we prove that it generates a semigroup which is neither strongly continuous nor analytic but enjoys nice smoothing properties such properties are used to prove a schauder type theorem for the elliptic equation u au f

local wick polynomials and time ordered products of quantum fields in curved spacetime in order to have well defined rules for the perturbative calculation of quantities of interest in an interacting quantum field theory in curved spacetime it is necessary to construct wick polynomials and their time ordered products for the noninteracting theory a construction of these quantities has recently been given by brunetti fredenhagen and kohler and by brunetti and fredenhagen but they did not impose any locality or covariance condition in their constructions as a consequence their construction of time ordered products contained ambiguities involving arbitrary functions of spacetime point rather than arbitrary parameters in this paper we construct an extended wick polynomial algebra large enough to contain the wick polynomials and their time ordered products by generalizing a construction of dutsch and fredenhagen to curved spacetime we then define the notion of a local covariant quantum field and seek a definition of local wick polynomials and their time ordered products as local covariant quantum fields we introduce a new notion of the scaling behavior of a local covariant quantum field and impose scaling requirements on our local wick polynomials and their time ordered products as well as certain additional requirements such as commutation relations with the free field and appropriate continuity properties under variations of the spacetime metric for a given polynomial order in powers of the field we prove that these conditions uniquely determine the local wick polynomials and their time ordered products up to a finite number of parameters these parameters correspond to the usual renormalization ambiguities occurring in minkowski spacetime together with additional parameters corresponding to the coupling of the field to curvature we also prove existence of local wick polynomials however the issue of existence of local time ordered products is deferred to a future investigation

inverse groundwater modeling for hydraulic conductivity estimation using bayesian model averaging and variance window 1 this study proposes a bayesian model averaging bma method to address parameter estimation uncertainty arising from nonuniqueness in parameterization methods bma is able to incorporate multiple parameterization methods for prediction through the law of total probability and to obtain an ensemble average of hydraulic conductivity estimates two major issues in applying bma to hydraulic conductivity estimation are discussed the first problem is using occam s window in usual bma applications to measure approximated posterior model probabilities occam s window only accepts models in a very narrow range tending to single out the best method and discard other good methods we propose a variance window to replace occam s window to cope with this problem the second problem is the kashyap information criterion kic in the approximated posterior model probabilities which tends to prefer highly uncertain parameterization methods by considering the fisher information matrix with sufficient amounts of observation data the bayesian information criterion bic is a good approximation and is able to avoid controversial results from using kic this study adopts multiple generalized parameterization gp methods such as the bma models to estimate spatially correlated hydraulic conductivity numerical examples illustrate the issues of using kic and occam s window and show the advantages of using bic and the variance window in bma application finally we apply bma to the hydraulic conductivity estimation of the 1500 foot sand in east baton rouge parish louisiana

mass dependence of quantum energy inequality bounds in a recent paper c j fewster and m j pfenning j math phys 47 082303 2006 quantum energy inequalities were used to place simple geometrical bounds on the energy densities of quantum fields in minkowskian space time regions here we refine this analysis for massive fields obtaining more stringent bounds which decay exponentially in the mass at the technical level this involves the determination of the asymptotic behavior of the lowest eigenvalue of a family of polyharmonic differential equations a result which may be of independent interest we compare our resulting bounds with the known energy density of the ground state on a cylinder space time in addition we generalize some of our technical results to general lp spaces and draw comparisons with a similar result in the literature

further comments on sensitivities parameter estimation and sampling design in one dimensional analysis of solute transport in porous media sensitivities of solute concentration to parameters associated with first order chemical decay boundary conditions initial conditions and multilayer transport are examined in one dimensional analytical models of transient solute transport in porous media a sensitivity is a change in solute concentration resulting from a change in a model parameter sensitivity analysis is important because minimum information required in regression on chemical data for the estimation of model parameters by regression is expressed in terms of sensitivities nonlinear regression models of solute transport were tested on sets of noiseless observations from known models that exceeded the minimum sensitivity information requirements results demonstrate that the regression models consistently converged to the correct parameters when the initial sets of parameter values substantially deviated from the correct parameters on the basis of the sensitivity analysis several statements may be made about design of sampling for parameter estimation for the models examined 1 estimation of parameters associated with solute transport in the individual layers of a multilayer system is possible even when solute concentrations in the individual layers are mixed in an observation well 2 when estimating parameters in a decaying upstream boundary condition observations are best made late in the passage of the front near a time chosen by adding the inverse of an hypothesized value of the source decay parameter to the estimated mean travel time at a given downstream location 3 estimation of a first order chemical decay parameter requires observations to be made late in the passage of the front preferably near a location corresponding to a travel time of times the half life of the solute and 4 estimation of a parameter relating to spatial variability in an initial condition requires observations to be made early in time relative to passage of the solute front

a comparison of two criteria for the design of experiments for discriminating between models box and hill 1967 criticized a criterion for sequential experimental designs suggested by hunter and reiner 1965 for ignoring the effect of the variance of predicted responses conditions are established under which the two criteria are asymptotically equivalent when there are only two rival models for moderate samples both for cases in which the conditions for equivalence hold and for cases in which they do not simulations fail to reveal any difference in behavior between the two criteria the extension of the results to criteria for more than two models is discussed

multiobjective sampling design for parameter estimation and model discrimination in groundwater solute transport sampling design for site characterization studies of solute transport in porous media is formulated as a multiobjective problem optimal design of a sampling network is a sequential process in which the next phase of sampling is designed on the basis of all available physical knowledge of the system three objectives are considered model discrimination parameter estimation and cost minimization for the first two objectives physically based measures of the value of information obtained from a set of observations are specified in model discrimination value of information of an observation point is measured in terms of the difference in solute concentration predicted by hypothesized models of transport points of greatest difference in predictions can contribute the most information to the discriminatory power of a sampling design sensitivity of solute concentration to a change in a parameter contributes information on the relative variance of a parameter estimate inclusion of points in a sampling design with high sensitivities to parameters tends to reduce variance in parameter estimates cost minimization accounts for both the capital cost of well installation and the operating costs of collection and analysis of field samples sensitivities discrimination information and well installation and sampling costs are used to form coefficients in the multiobjective problem in which the decision variables are binary zero one each corresponding to the selection of an observation point in time and space the solution to the multiobjective problem is a noninferior set of designs to gain insight into effective design strategies a one dimensional solute transport problem is hypothesized then an approximation of the noninferior set is found by enumerating 120 designs and evaluating objective functions for each of the designs trade offs between pairs of objectives are demonstrated among the models the value of an objective function for a given design is shown to correspond to the ability of a design to actually meet an objective

micro local approach to the hadamard condition in quantum field theory on curved space time for the two point distribution of a quasi free klein gordon neutral scalar quantum field on an arbitrary four dimensional globally hyperbolic curved space time we prove the equivalence of 1 the global hadamard condition 2 the property that the feynman propagator is a distinguished parametrix in the sense of duistermaat and hormander and 3 a new property referred to as the wave front set spectral condition wfssc because it is reminiscent of the spectral condition in axiomatic quantum field theory on minkowski space results in micro local analysis such as the propagation of singularities theorem and the uniqueness up toc of distinguished parametrices are employed in the proof we include a review of kay and wald s rigorous definition of the global hadamard condition and the theory of distinguished parametrices specializing to the case of the klein gordon operator on a globally hyperbolic space time as an alternative to a recent computation of the wave front set of a globally hadamard two point distribution on a globally hyperbolic curved space time given elsewhere by kohler to correct an incomplete computation in 32 we present a version of this computation that does not use a deformation argument such as that used in fulling narcowich and wald and is independent of the cauchy evolution argument of fulling sweeny and wald both of which are relied upon in kohler s proof this leads to a simple micro local proof of the preservation of hadamard form under cauchy evolution first shown by fulling sweeny and wald relying only on the propagation of singularities theorem in another paper 33 the equivalence theorem is used to prove a conjecture by kay that a locally hadamard quasi free klein gordon state on any globally hyperbolic curved space time must be globally hadamard

kolmogorov equation associated to a stochastic navier stokes equation abstract a direct solution of the kolmogorov equation associated to a stochastic navier stokes equation is given with restriction to two space dimensions and periodic boundary conditions the existence of a variational solution is proved using a special property of the nonlinear operator

review of parameter identification procedures in groundwater hydrology the inverse problem the purpose of this survey is to review parameter identification procedures in groundwater hydrology and to examine computational techniques which have been developed to solve the inverse problem parameter identification methods are classified under the error criterion used in the formulation of the inverse problem the problem of ill posedness in connection with the inverse problem is addressed typical inverse solution techniques are highlighted the review also includes the evaluation of methods used for computing the sensitivity matrix statistics which can be used to estimate the parameter uncertainty are outlined attempts have been made to compare and contrast representative inverse procedures and direction for future research is suggested

simultaneous confidence and prediction intervals for nonlinear regression models with application to a groundwater flow model methods are presented for computing three types of simultaneous confidence and prediction intervals exact likelihood ratio and linearized on output from nonlinear regression models with normally distributed residuals the confidence intervals can be placed on individual regression parameters or on the true regression function at any number of points in the domain of the independent variables and the prediction intervals can be placed on any number of future observations the confidence intervals are analogous to simultaneous scheffe intervals for linear models and the prediction intervals are analogous to the prediction intervals of hahn 1972 all three types of intervals can be computed efficiently by using the same straightforward lagrangian optimization scheme the prediction intervals can be treated in the same computational framework as the confidence intervals by including the random errors as pseudoparameters in the lagrangian scheme the methods are applied to a hypothetical groundwater model for flow to a well penetrating a leaky aquifer three different data sets are used to demonstrate the effect of sampling strategies on the intervals for all three data sets the linearized confidence intervals are inferior to the exact and likelihood ratio intervals with the latter two being very similar however all three types of prediction intervals yielded similar results the third data set time drawdown data at only a single observation well points out many of the problems that can arise from extreme nonlinear behavior of the regression model

quantum energy inequalities and local covariance i globally hyperbolic spacetimes we begin a systematic study of quantum energy inequalities qeis in relation to local covariance we define notions of locally covariant qeis of both absolute and difference types and show that existing qeis satisfy these conditions local covariance permits us to place constraints on the renormalized stress energy tensor in one spacetime using qeis derived in another in subregions where the two spacetimes are isometric this is of particular utility where one of the two spacetimes exhibits a high degree of symmetry and the qeis are available in simple closed form various general applications are presented including a priori constraints depending only on geometric quantities on the ground state energy density in a static spacetime containing locally minkowskian regions in addition we present a number of concrete calculations in both two and four dimensions that demonstrate the consistency of our bounds with various known ground and thermal state energy densities examples considered include the rindler and misner spacetimes and spacetimes with toroidal spatial sections in this paper we confine the discussion to globally hyperbolic spacetimes subsequent papers will also discuss spacetimes with boundary and other related issues

existence of local covariant time ordered products of quantum fields in curved spacetime we establish the existence of local covariant time ordered products of local wick polynomials for a free scalar field in curved spacetime our time ordered products satisfy all of the hypotheses of our previous uniqueness theorem so our construction essentially completes the analysis of the existence uniqueness and renormalizability of the perturbative expansion for nonlinear quantum field theories in curved spacetime as a byproduct of our analysis we derive a scaling expansion of the time ordered products about the total diagonal that expresses them as a sum of products of polynomials in the curvature times lorentz invariant distributions plus a remainder term of arbitrarily low scaling degree

martingale and stationary solutions for stochastic navier stokes equations we prove the existence of martingale solutions and of stationary solutions of stochastic navier stokes equations under very general hypotheses on the diffusion term the stationary martingale solutions yield the existence of invariant measures when the transition semigroup is well defined the results are obtained by a new method of compactness