control for safety specifications of systems with imperfect information on a partial order in this paper we consider the control problem for uncertain systems with imperfect information in which an output of interest must be kept outside an undesired region the bad set in the output space the state input output and disturbance spaces are equipped with partial orders the system dynamics are either input output order preserving with output in r2 or given by the parallel composition of input output order preserving dynamics each with scalar output we provide necessary and sufficient conditions under which an initial set of possible system states is safe that is the corresponding outputs are steerable away from the bad set with open loop controls a closed loop control strategy is explicitly constructed which guarantees that the current set of possible system states as obtained from an estimator generates outputs that never enter the bad set the complexity of algorithms that check safety of an initial set of states and implement the control map is quadratic with the dimension of the state space the algorithms are illustrated on two application examples a ship maneuver to avoid an obstacle and safe navigation of an helicopter among buildings

a bound on the number of integrators needed to linearize a control system this paper considers the problem of dynamic feedback linearization for nonlinear control systems for a restricted class of dynamic compensators that correspond to adding chains of integrators to the inputs we give an upper bound on the order of the compensator that needs to be considered in the case of 2 input systems we show that this bound is sharp

analysis of a finite element method for maxwell s equations the use of finite elements to discretize the time dependent maxwell equations on a bounded domain in three dimensional space is analyzed energy norm error estimates are provided when general finite element methods are used to discretize the equations in space in addition it is shown that if some curl conforming elements due to nedelec are used error estimates may also be proved in the l 2 norm

on minimal compensators for decoupling control abstract the general construction of minimal regular compensators for decoupling a nonlinear system is given by means of vector subspaces which are generated by differential vectors of outputs and states and the minimal dimension of a decoupling compensator is expressed in intrinsic characterization the equivalence relation of all minimal regular compensators is established though these compensators may have different dynamic behavior from each other

nonlinear decoupling via feedback a differential geometric approach the paper deals with the nonlinear decoupling and noninteracting control problems a complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems the paper also includes algorithms concerned with the actual construction of the appropriate control laws

the differential field associated to a general analytic nonlinear dynamical system a rigorous and detailed construction of the differential field k sub sigma u y associated in a differential algebraic context to a nonlinear system sigma described in state space form with analytic coefficients is presented the field k sub sigma u y represents an input output description of sigma and its study is of key importance in problems concerning the input output behavior of sigma technically the basic step of the construction of k sub sigma u y consists in proving that the differential ideal associated to the state evolution equation of sigma is prime

development of a formal likelihood function for improved bayesian inference of ephemeral catchments 1 the application of formal bayesian inferential approaches in hydrologic modeling is often criticized for requiring explicit assumptions to be made about the distribution of the errors via the likelihood function these assumptions can be adequate in some situations but often little attention is paid to the selection of an appropriate likelihood function this paper investigates the application of bayesian methods in modeling ephemeral catchments we consider two modeling case studies including a synthetically generated data set and a real data set of an arid australian catchment the case studies investigate some typical forms of the likelihood function which have been applied widely by previous researchers as well as introducing new implementations aimed at better addressing likelihood function assumptions in dry catchments the results of the case studies indicate the importance of explicitly accounting for model residuals that are highly positively skewed due to the presence of many zeros zero inflation arising from the dry spells experienced by the catchment specifically the form of the likelihood function was found to significantly impact the calibrated parameter posterior distributions which in turn have the potential to greatly affect the uncertainty estimates in each application the likelihood function that explicitly accounted for the nonconstant variance of the errors and the zero inflation of the errors resulted in 1 equivalent or better fits to the observed discharge in both timing and volume 2 superior estimation of the uncertainty as measured by the reliability and sharpness metrics and 3 more linear quantile quantile plots indicating the errors were more closely matched to the assumptions of this form of the likelihood function

a fuzzy flight controller combining linguistic and model based fuzzy control in this paper we address the design of a fuzzy flight controller that achieves stable and robust aggressive manoeuvrability for an unmanned helicopter the fuzzy flight controller proposed consists of a combination of a fuzzy gain scheduler and linguistic mamdani type controller the fuzzy gain scheduler is used for stable and robust altitude roll pitch and yaw control the linguistic controller is used to compute the inputs to the fuzzy gain scheduler i e desired values for roll pitch and yaw at given desired altitude and horizontal velocities the flight controller is obtained and tested in simulation using a realistic nonlinear mimo model of a real unmanned helicopter platform the apid mk

design of a minimal precompensator for the decoupling problem abstract for right invertible linear time invariant systems which cannot be decoupled row by row using regular static state feedback laws we propose a new algorithmic procedure for designing a minimal precompensator leading to a compensated system which can be decoupled by regular static state feedback

immersion of discrete time nonlinear system by regular dynamic state feedback into a linear system necessary and sufficient conditions for local solvability of the title problem around a given trajectory are obtained the proposed conditions are less restrictive than those obtained by lee and marcus for the problem of immersion a nonlinear system into a linear system via static state feedback instrumental in the problem solution is the inversion structure algorithm for a discrete time nonlinear system the solvability conditions are expressed in terms of the inversion algorithm moreover the construction of both the dynamic state feedback and the immersion map relies on this algorithm finally it is shown that for locally right invertible systems the considered problem unlike the problem of immersion via static state feedback is always solvable

superconvergence analysis for maxwell s equations in dispersive media in this paper we consider the time dependent maxwell s equations in dispersive media on a bounded three dimensional domain global superconvergence is obtained for semi discrete mixed finite element methods for three most popular dispersive media models the isotropic cold plasma the one pole debye medium and the two pole lorentz medium global superconvergence for a standard finite element method is also presented to our best knowledge this is the first superconvergence analysis obtained for maxwell s equations when dispersive media are involved

dynamic decoupling for right invertible nonlinear systems abstract it is shown that every system with more inputs than outputs that is right invertible in the sense of 5 can be decoupled via a dynamic state feedback that can be computed using a given algorithm this result generalizes the one of 2 and completes the results of 3

on dynamic input output linearization of discrete time nonlinear systems this paper studies the problem of linearizing the input output map of an analytic discrete time nonlinear system locally around a given trajectory necessary and sufficient conditions are given for the existence of a regular dynamic state feedback control law under which the input dependent part of the response of a nonlinear system becomes linear in the input and independent of the initial state the proposed conditions are less restrictive than those obtained by lee and marcus for linearizing the input output map via a static state feedback instrumental in the problem solution is the inversion structure algorithm for a discrete time nonlinear system firstly the solvability conditions are expressed in terms of the inversion algorithm secondly the proof of the existence and construction of the dynamic state feedback compensator relies on this algorithm

decoupling with dynamic compensation for strong invertible affine non linear systems abstract in this paper we tackle for affine non linear systems the morgan problem i e the scalar input scalar output decoupling problem for square systems with dynamic compensation the result provided here theorem 3 1 generalizes that one previously given by wang 1970 for linear systems

a remark on nonlinear accessibility conditions and infinite prolongations the lie rank condition for strong nonlinear accessibility is interpreted via the differential geometry of jets and prolongations of infinite order it yields to a new lie algebraic criterion and to the consideration of first integrals which apply to nonlinear systems in quite general form the latter characterization in particular is valid without distinguishing between the system variables and is independent of time scalings weak accessibility is also considered

noninteracting control with stability for a class of nonlinear systems abstract in this paper we address the problem of noninteracting control with stability for the class of nonlinear square systems for which noninteraction can be achieved without stability by means of invertible static state feedback the use of both static state feedback and dynamic state feedback is investigated we prove that in both cases the asymptotic stabilizability of certain subsystems is necessary to achieve noninteraction and stability we use this and some recent results to state a complete set of necessary and sufficient conditions in order to solve the problem

comparison of joint versus postprocessor approaches for hydrological uncertainty estimation accounting for error autocorrelation and heteroscedasticity the paper appraises two approaches for the treatment of heteroscedasticity and autocorrelation in residual errors of hydrological models both approaches use weighted least squares wls with heteroscedasticity modeled as a linear function of predicted flows and autocorrelation represented using an ar 1 process in the first approach heteroscedasticity and autocorrelation parameters are inferred jointly with hydrological model parameters the second approach is a two stage postprocessor scheme where stage 1 infers the hydrological parameters ignoring autocorrelation and stage 2 conditionally infers the heteroscedasticity and autocorrelation parameters these approaches are compared to a wls scheme that ignores autocorrelation empirical analysis is carried out using daily data from 12 us catchments from the mopex set using two conceptual rainfall runoff models gr4j and hbv under synthetic conditions the postprocessor and joint approaches provide similar predictive performance though the postprocessor approach tends to underestimate parameter uncertainty however the mopex results indicate that the joint approach can be nonrobust in particular when applied to gr4j it often produces poor predictions due to strong multiway interactions between a hydrological water balance parameter and the error model parameters the postprocessor approach is more robust precisely because it ignores these interactions practical benefits of accounting for error autocorrelation are demonstrated by analyzing streamflow predictions aggregated to a monthly scale where ignoring daily scale error autocorrelation leads to significantly underestimated predictive uncertainty and by analyzing one day ahead predictions where accounting for the error autocorrelation produces clearly higher precision and better tracking of observed data including autocorrelation into the residual error model also significantly affects calibrated parameter values and uncertainty estimates the paper concludes with a summary of outstanding challenges in residual error modeling particularly in ephemeral catchments

a new error analysis of characteristics mixed fems for miscible displacement in porous media the method of characteristics type is especially effective for convection dominated diffusion problems due to the nature of characteristic temporal discretization the method allows one to use a large time step in many practical computations while all previous theoretical analyses always required certain restrictions on the time stepsize here we present a new analysis to establish unconditionally optimal error estimates for a modified method of characteristics with a mixed finite element approximation to the miscible displacement problem in mathbb r d d 2 3 for this purpose we introduce a new characteristic time discrete system we prove that the l 2 error bound the characteristic time discrete systemof the fully discrete method of characteristics to the time discrete system is tau independent and the numerical solution is bounded in w 1 infty norm unconditionally with the boundedness optimal error estimates are established in a traditional manner numerical results confirm our th

on the inversion of a class of nonlinear systems this paper deals with the inversion problem of affine square multi input multi output mimo nonlinear systems it presents a new algorithm unifying the construction of the inverse of a dynamical system with a regular or a singular characteristic matrix this algorithm is based on the determination of a projector on the fibre bundle of the state space and incorporates a regularization of the singular case it has the advantage of avoiding the input derivatives numerical examples are given to illustrate the proposed approach

on a singular limit problem for nonlinear maxwell s equations in this paper we study the following nonlinear maxwell s equations eet x e e h f ht e 0 where x s is a monotone graph of s it is shown that the system has a unique weak solution moreover the limit of the solution as e 0 converges to the solution of quasi stationary maxwell s equations

fully discrete finite element scheme for maxwell s equations with non linear boundary condition abstract we study a full maxwell s system accompanied with a non linear degenerate boundary condition which represents a generalization of the classical silver muller condition for a non perfect conductor the relationship between the normal components of electric e and magnetic h field obeys the following power law h e 1 e for some 0 1 we establish the existence and uniqueness of a weak solution in a suitable function spaces under the minimal regularity assumptions on the boundary and the initial data e 0 and h 0 we design a non linear time discrete approximation scheme and prove convergence of the approximations to a weak solution we also derive the error estimates for the time discretization as a next step we study the fully discrete problem using curl conforming edge elements and derive the corresponding error estimates finally we present some numerical experiments

dynamic input output decoupling of nonlinear control systems the problem of dynamic input output decoupling of nonlinear control systems is studied based on an analytic algorithm the authors obtain necessary and sufficient conditions for the solvability of this problem the solution of the problem is constructed by applying a series of simple precompensations and linking maps some interesting connections with other approaches in nonlinear control theory are discussed the authors also give a few simple examples to illustrate the methods used

solving metamaterial maxwell s equations via a vector wave integro differential equation in this paper we discuss the time domain metamaterial maxwell s equations one major contribution of this paper is that after some effort we find that the metamaterial maxwell s equations can be beautifully reduced to a vector wave integro differential equation involving just one unknown which is quite similar to that obtained from the standard maxwell s equations in vacuum then we study the existence and uniqueness of this new modeling equations and propose a fully discrete finite element method to solve this model numerical results justifying our analysis are presented this discovery shall make simulation of metamaterials much more efficient than the previous works

improving probabilistic prediction of daily streamflow by identifying pareto optimal approaches for modeling heteroscedastic residual errors reliable and precise probabilistic prediction of daily catchment scale streamflow requires statistical characterization of residual errors of hydrological models this study focuses on approaches for representing error heteroscedasticity with respect to simulated streamflow i e the pattern of larger errors in higher streamflow predictions we evaluate 8 common residual error schemes including standard and weighted least squares the box cox transformation with fixed and calibrated power parameter and the log sinh transformation case studies include 17 perennial and 6 ephemeral catchments in australia and usa and two lumped hydrological models performance is quantified using predictive reliability precision and volumetric bias metrics we find the choice of heteroscedastic error modelling approach significantly impacts on predictive performance though no single scheme simultaneously optimizes all performance metrics the set of pareto optimal schemes reflecting performance trade offs comprises box cox schemes with of 0 2 and 0 5 and the log scheme 0 perennial catchments only these schemes significantly outperform even the average performing remaining schemes e g across ephemeral catchments median precision tightens from 105 to 40 of observed streamflow and median biases decrease from 25 to 4 theoretical interpretations of empirical results highlight the importance of capturing the skew kurtosis of raw residuals and reproducing zero flows paradoxically calibration of is often counterproductive in perennial catchments it tends to overfit low flows at the expense of abysmal precision in high flows the log sinh transformation is dominated by the simpler pareto optimal schemes listed above recommendations for researchers and practitioners seeking robust residual error schemes for practical work are provided this article is protected by copyright all rights reserved

extending the applicability of the generalized likelihood function for zero inflated data series proper uncertainty estimation for data series with a high proportion of zero and near zero observations has been a challenge in hydrologic studies this technical note proposes a modification to the generalized likelihood function that accounts for zero inflation of the error distribution zi gl we compare the performance of the proposed zi gl with the original generalized likelihood function using the entire data series gl and by simply suppressing zero observations gly 0 these approaches were applied to two interception modeling examples characterized by data series with a significant number of zeros the zi gl produced better uncertainty ranges than the gl as measured by the precision reliability and volumetric bias metrics the comparison between zi gl and gly 0 highlights the need for further improvement in the treatment of residuals from near zero simulations when a linear heteroscedastic error model is considered aside from the interception modeling examples illustrated herein the proposed zi gl may be useful for other hydrologic studies such as for the modeling of the runoff generation in hillslopes and ephemeral catchments

unconditionally optimal error estimates of a crank nicolson galerkin method for the nonlinear thermistor equations this paper focuses on unconditionally optimal error analysis of an uncoupled and linearized crank nicolson galerkin finite element method for the time dependent nonlinear thermistor equations in d dimensional space d 2 3 in our analysis we split the error function into two parts one from the spatial discretization and one from the temporal discretization by introducing a corresponding time discrete elliptic system we present a rigorous analysis for the regularity of the solution of the time discrete system and error estimates of the time discretization with these estimates and the proved regularity optimal error estimates of the fully discrete crank nicolson galerkin method are obtained unconditionally numerical results confirm our analysis and show the efficiency of the method

approximate linearization of nonlinear control systems abstract the paper address the problem of approximate linearization of a nonlinear control system by state feedback or dynamic feedback the main result proved is that if the fast k d relative degrees are equal to each other then the input output response of a nonlinear control system can be linearized to degree k any system having linear d relative degree can be linearized to any degree by dynamic feedbacks one example of signal tracking using dynamic feedback linearization method to improve the performance is also given

a sufficient condition for nonlinear noninteracting control with stability via dynamic state feedback a sufficient condition is given to solve the problem of achieving local noninteracting control with asymptotic stability via dynamic state feedback for a nonlinear affine system the condition which is automatically satisfied in the case of linear systems although only sufficient is helpful in overcoming some of the geometric obstructions pointed out in the literature an example in which the author assumptions are satisfied is given clearly showing how to construct a decoupling and stabilizing dynamic state feedback and how the condition can weaken the requirement that the p dynamics be locally asymptotically stable

an intrinsic sufficient condition for regular decoupling abstract this paper introduces an intrinsic regularity property namely regular invertibility which requires that a sequence of vector spaces has constant dimension after a certain order thus allowing some degeneracies in the beginning it corresponds to the system and its tangent having the same defect using the constant rank theorem this property is shown to be sufficient condition for regular decoupling

unconditional convergence and optimal error estimates of a galerkin mixed fem for incompressible miscible flow in porous media in this paper we study the unconditional convergence and error estimates of a galerkin mixed fem with the linearized semi implicit euler scheme for the equations of incompressible miscible flow in porous media we prove that the optimal l 2 error estimates hold without any time step convergence conditions while all previous works require certain time step restrictions our theoretical results provide a new understanding on commonly used linearized schemes the proof is based on a splitting of the error into two parts the error from the time discretization of the pdes and the error from the finite element discretization of corresponding time discrete pdes the approach used in this paper can be applied to more general nonlinear parabolic systems and many other linearized semi implicit time discretizations

stabilization by output feedback of multivariable invertible nonlinear systems in this paper the problem of global stabilization of a rather general class of mimo nonlinear systems is addressed the systems considered in the paper are invertible have a trivial zero dynamics and possess a normal form in which certain multipliers are functions of the state vector of a special kind while special structural dependence of such multipliers on the components state vector has been exploited before in the context of achieving stabilization via full state feedback though the novelty in the approach of this paper is that a peculiar structure is identified which happens to be intimately related to the property of uniform complete observability thus making the design of observers possible and to the property of uniform invertibility relations never established before in the literature as a result for this class of mimo nonlinear systems a dynamic output feedback law can be designed yielding semiglobal and even global under appropriate assumptions asymptotic stability

asymptotic model matching for nonlinear systems this paper investigates the problem of designing a compensating control law for a square invertible nonlinear plant so that the response of the closed loop system asymptotically matches that of a prescribed driven nonlinear model a set of necessary conditions for achieving asymptotic model matching is established one of these involves the stability properties for subdynamics which are common to every model matching closed loop these subdynamics called the fixed dynamics are intrinsically characterized based on these results a new set of sufficient conditions for achieving asymptotic model matching is given the interrelation between the minimum phase and vector relative degree properties of a plant and a matchable model are studied

generalized state variable representation for a simplified crane description recent theoretical advances in nonlinear systems theory insist on the relevance of dynamics where control derivatives appear we discuss here a simplified model of a crane which exhibits such a description

orthogonal decomposition and asymptotic behavior for nonlinear maxwell s equations abstract we consider nonlinear maxwell s equations in which the electric conductivity strongly depends on the electric field acting like a switch like function for the electromagnetic field we combine multiplier techniques and nakao s method to show that the solution decays at polynomial rates if the conductivity satisfies suitable conditions under more restrictive hypotheses exponential decay is obtained as a byproduct we also obtain the decay of the solution of quasi stationary maxwell s equations

necessary conditions for asymptotic tracking in nonlinear systems in the literature it has been shown that if a single input single output analytic nonlinear plant 1 has a well defined relative degree and 2 is minimum phase it is possible to achieve asymptotic tracking for an open set of output trajectories containing the origin in c sup n 0 spl infin the space of n times continuously differentiable functions taking values in r when either of these sufficient conditions is not met various authors have investigated approximate analytic solutions discontinuous solutions and solutions for restricted sets of trajectories in this paper it is shown that conditions 1 and 2 are necessary for the existence of an analytic compensator which yields asymptotic tracking for an open set of output trajectories analogous results are established for multi input multi output systems

a new approach to the structure at infinity of nonlinear systems abstract zeros at infinity for nonlinear systems are defined by using differential algebra this approach can be viewed as a nonlinear generalization of silverman s structure algorithm the connection with the problem of inverting input output systems is briefly described

bayesian inference of uncertainties in precipitation streamflow modeling in a snow affected catchment 1 bayesian inference is used to study the effect of precipitation and model structural uncertainty on estimates of model parameters and confidence limits of predictive variables in a conceptual rainfall runoff model in the snow fed rudback catchment 142 ha in southern finland the ihacres model is coupled with a simple degree day model to account for snow accumulation and melt the posterior probability distribution of the model parameters is sampled by using the differential evolution adaptive metropolis dream zs algorithm and the generalized likelihood function precipitation uncertainty is taken into account by introducing additional latent variables that were used as multipliers for individual storm events results suggest that occasional snow water equivalent swe observations together with daily streamflow observations do not contain enough information to simultaneously identify model parameters precipitation uncertainty and model structural uncertainty in the rudback catchment the addition of an autoregressive component to account for model structure error and latent variables having uniform priors to account for input uncertainty lead to dubious posterior distributions of model parameters thus our hypothesis that informative priors for latent variables could be replaced by additional swe data could not be confirmed the model was found to work adequately in 1 day ahead simulation mode but the results were poor in the simulation batch mode this was caused by the interaction of parameters that were used to describe different sources of uncertainty the findings may have lessons for other cases where parameterizations are similarly high in relation to available prior information

approximate decoupling and asymptotic tracking for mimo systems this paper presents an algorithm for approximate input output decoupling of nonlinear mimo systems that are either numerically ill posed or exhibit nearly singular behavior in the application of decoupling algorithms although the systems considered are regular so that the exact decoupling algorithms are applicable in this case they require inversion of an ill conditioned matrix and yield high gain feedback solutions that may result in actuator saturation and cancellation of high frequency zeros the approximate algorithms of this paper are numerically robust and provide solutions that do not cancel far off right half plane zeros this latter characteristic is especially valuable when some of the far off right half plane zeros are unstable the algorithms are inspired by and are generalizations of some examples in the flight control literature

a note on the invertibility of nonlinear input output differential systems abstract a new conceptual framework employing differential algebra is proposed for solving the long standing problem of inverting nonlinear input output differential systems simple characterizations of left and right invertibility are given which rest upon an invariant integer which for constant linear systems turns out to be the rank of the transfer matrix

a canonical dynamic extension for noninteraction with stability for affine nonlinear square systems we study the problem of noninteracting control with stability via dynamic feedback for continuous affine nonlinear square systems given a system which may not be decouplable via static state feedback but is decouplable via dynamic feedback a canonical dynamic extension is constructed we show that every dynamic extension contains this canonical one hence the mix dynamics as defined by wagner of the canonical extension is contained in every other dynamic extension following wagner s result the stability of this mix dynamics is necessary for noninteraction with internal stability the results in this paper show that under some regularity assumptions in the investigation of noninteraction with stability one can assume without loss of generality that the system is decouplable via static state feedback

multi objective optimal trajectory design and tracking with non periodic tracking transition switching for non minimum phase linear systems abstractin this paper the problem of trajectory design and tracking of non periodic tracking transition switching for non minimum phase linear systems is considered such a problem exists in various applications where the output trajectory consists of application dependent tracking sessions and to be designed transition sessions the challenge arises when multiple control objectives are considered including the smooth transition from one output tracking session to the next one without large oscillations during the transition smooth tracking transition switching without inducing pre and or post switching oscillations input energy minimisation without saturation under amplitude constraint and furthermore minimisation of the overall transition time the proposed approach extends the previous work that attained smooth output transition and smooth tracking transition switching to further achieve amplitude constrained input energy minimisation and transition time minimisation first the constrained inp

global approximate output tracking for nonlinear systems addresses the global output tracking problem for nonlinear systems with singular points for nonlinear systems which satisfy a suitable observability condition the authors identify a class of smooth output trajectories which the system can track using continuous open loop controls this class includes all output trajectories generated by smooth state feedback they then study the problem of approximate output tracking using discontinuous time varying feedback controllers given a smooth output trajectory for which exact tracking is possible the authors construct a discontinuous feedback controller which achieves robust tracking of the desired output trajectory in the face of perturbations finally it is shown that their results can be applied to the control of a chain system and some numerical results are presented to illustrate the performance of their controller

fixed modes and nonlinear noninteracting control with stability the existence of a fixed internal dynamics inherent to the noninteraction requirement is identified when unstable this represents an obstruction to the achievement of noninteracting control with stability by means of static state feedback remarkably whenever one leaves the class of linear systems this obstruction cannot in general be removed by dynamic state feedback

approximation by regular input output maps the authors study approximate dynamic input output linearization in the sense of j hauser et al 1989 for multiinput multioutput mimo nonlinear systems which exhibit singularities in the dynamic extension process

a formal likelihood function for parameter and predictive inference of hydrologic models with correlated heteroscedastic and non gaussian errors estimation of parameter and predictive uncertainty of hydrologic models has traditionally relied on several simplifying assumptions residual errors are often assumed to be independent and to be adequately described by a gaussian probability distribution with a mean of zero and a constant variance here we investigate to what extent estimates of parameter and predictive uncertainty are affected when these assumptions are relaxed a formal generalized likelihood function is presented which extends the applicability of previously used likelihood functions to situations where residual errors are correlated heteroscedastic and non gaussian with varying degrees of kurtosis and skewness the approach focuses on a correct statistical description of the data and the total model residuals without separating out various error sources application to bayesian uncertainty analysis of a conceptual rainfall runoff model simultaneously identifies the hydrologic model parameters and the appropriate statistical distribution of the residual errors when applied to daily rainfall runoff data from a humid basin we find that 1 residual errors are much better described by a heteroscedastic first order auto correlated error model with a laplacian distribution function characterized by heavier tails than a gaussian distribution and 2 compared to a standard least squares approach proper representation of the statistical distribution of residual errors yields tighter predictive uncertainty bands and different parameter uncertainty estimates that are less sensitive to the particular time period used for inference application to daily rainfall runoff data from a semiarid basin with more significant residual errors and systematic underprediction of peak flows shows that 1 multiplicative bias factors can be used to compensate for some of the largest errors and 2 a skewed error distribution yields improved estimates of predictive uncertainty in this semiarid basin with near zero flows we conclude that the presented methodology provides improved estimates of parameter and total prediction uncertainty and should be useful for handling complex residual errors in other hydrologic regression models as well

averaging for superconvergence verification and application of 2d edge elements to maxwell s equations in metamaterials abstract in this paper a simple averaging technique for edge elements is justified to improve the standard convergence rate hence achieving superconvergence when they are used to solve the maxwell s equations for simplicity here we focus on the lowest order triangular edge element which is widely used in practice though there exists no natural superconvergence points for the numerical solution obtained on such an edge element superconvergence can be obtained after a simple average of solutions over the neighboring elements a comprehensive analysis for the lowest order triangular edge element is carried out and one order higher convergence rate than the standard interpolation error estimate is proved for the averaged solution at midpoints of those interior edges of parallelograms formed by two triangles i e superconvergence happens at the parallelogram centers we also provide detailed analysis to explain why several cases do not have superconvergence extensive numerical results consistent with our analysis are presented

a second order numerical scheme for nonlinear maxwell s equations using conforming finite element abstract in this paper we study and analyze a second order numerical scheme for maxwell s equations with nonlinear conductivity using the nedelec finite element method fem a purely explicit treatment of the nonlinear term greatly simplifies the computational effort since we only need to solve a constant coefficient linear system at each time step the curl conforming nature of the nedelec element assures its divergence free property in turn we present the linearized stability analysis for the numerical error function to obtain an optimal l2 error estimate in more details an o 2 h s error estimate in the l2 norm yields the maximum norm bound of the numerical solution so that the convergence analysis could be carried out at the next time step a few numerical examples in the transverse electric te case in two dimensional spaces are also presented which demonstrate the efficiency and accuracy of the proposed numerical scheme

time discretization scheme for quasi static maxwell s equations with a non linear boundary condition we study a time dependent eddy current equation for the magnetic field h accompanied with a non linear degenerate boundary condition bc which is a generalization of the classical silver muller condition for a non perfect conductor more exactly the relation between the normal components of electrical e and magnetic h fields obeys the following power law email protected email protected a email protected for some email protected 0 1 we establish the existence and uniqueness of a weak solution in a suitable function space under the minimal regularity assumptions on the boundary c and the initial data h 0 we design a non linear time discrete approximation scheme based on rothe s method and prove convergence of the approximations to a weak solution we also derive the error estimates for the time discretization