on the spaces lp x ω and wm p x ω in this paper we present some basic results on the generalized lebesgue spaces l p x omega and generalized lebesgue sobolev spaces w m w p x omega these results provide the necessary framework for the study of variational problems and elliptic equations with non standard p x growth conditions c 2001 academic press

local factorization of trajectory lifting morphisms for single input affine control systems trajectory preserving and lifting maps have been implicitly used in many recursive or hierarchical control design techniques well known systems theoretic concepts such as differential flatness or more recent ones such as simulation and bisimulation can be also understood through the trajectory lifting maps they define in this paper we initiate a study of trajectory preserving and lifting maps between affine control systems our main result shows that any trajectory lifting map between two single input control affine systems can be locally factored as the composition of two special trajectory lifting maps a projection onto a quotient system followed by a differentially flat output with respect to another control system we use this decomposition result to show that under mild regularity conditions trajectory preserving maps between single input affine control systems also lift trajectories as an additional application of the main result we also show how the hierarchical stabilization method known as back stepping can be used based on the existence of a trajectory preserving and lifting map having a feedback stabilizable control system as codomain

a connection between simulation relations and feedback transformations in nonlinear control systems abstract the recent introduction of simulation and bisimulation relations in the study of nonlinear control systems provides a broad potential framework for the study and classification of such systems this paper reviews the definitions of simulation and bisimulation relations and develops connections between them and the well established notions of feedback transformations and feedback equivalences

quotients of fully nonlinear control systems in this paper we introduce and study quotients of fully nonlinear control systems our definition is inspired by categorical definitions of quotients as well as recent work on abstractions of affine control systems we show that quotients exist under mild regularity assumptions and characterize the structure of the quotient state input space this allows one to understand how states and inputs of the quotient system are related to states and inputs of the original system we also introduce a notion of projectability which turns out to be equivalent to controlled invariance this allows one to regard previous work on symmetries partial symmetries and controlled invariance as leading to special types of quotients we also show the existence of quotients that are not induced by symmetries or controlled invariance such decompositions have a potential use in a theory of hierarchical control based on quotients

a stochastic index flow model of flow duration curves 1 annual flow duration curves afdcs are used increasingly because unlike traditional period of record flow duration curves fdcs they provide confidence intervals for the median afdc they enable one to assign return periods to individual afdcs and they offer opportunities for developing a generalized stochastic model of daily streamflow previous stochastic models of fdcs and afdcs were unable to reproduce the variance of afdcs we introduce an index flow approach to modeling the relationship between an fdc and afdcs of daily streamflow series which is able to reproduce the fdc as well as the mean median and variance of the afdcs without resorting to assumptions regarding the seasonal or persistence structure of daily streamflow series our approach offers additional opportunities for the regionalization of flow duration curves and for the generation of time series of daily streamflows at ungauged sites our approach is tested on three river basins in eastern central italy

the first non zero neumann p fractional eigenvalue abstract in this work we study the asymptotic behavior of the first non zero neumann p fractional eigenvalue 1 s p as s 1 and as p we show that there exists a constant k such that k 1 s 1 s p goes to the first non zero neumann eigenvalue of the p laplacian while in the limit case p we prove that 1 1 s 1 p goes to an eigenvalue of the holder laplacian

estimation of distributional parameters for censored trace level water quality data 1 estimation techniques a recurring difficulty encountered in investigations of many metals and organic contaminants in ambient waters is that a substantial portion of water sample concentrations are below limits of detection established by analytical laboratories several methods were evaluated for estimating distributional parameters for such censored data sets using only uncensored observations their reliabilities were evaluated by a monte carlo experiment in which small samples were generated from a wide range of parent distributions and censored at varying levels eight methods were used to estimate the mean standard deviation median and interquartile range criteria were developed based on the distribution of uncensored observations for determining the best performing parameter estimation method for any particular data det the most robust method for minimizing error in censored sample estimates of the four distributional parameters over all simulation conditions was the log probability regression method with this method censored observations are assumed to follow the zero to censoring level portion of a lognormal distribution obtained by a least squares regression between logarithms of uncensored concentration observations and their z scores when method performance was separately evaluated for each distributional parameter over all simulation conditions the log probability regression method still had the smallest errors for the mean and standard deviation more but the lognormal maximum likelihood method had the smallest errors for the median and interquartile range when data sets were classified prior to parameter estimation into groups reflecting their probable parent distributions the ranking of estimation methods was similar but the accuracy of error estimates was markedly improved over those without classification less

from nonlinear to hamiltonian via feedback mechanical control systems are an especially interesting and important class of nonlinear control systems they possess a rich mathematical structure and yet physical considerations are extremely important for the solution of a large class of control problems we broaden the applicability of design methodologies developed for mechanical control systems by rendering nonlinear control systems mechanical by a proper choice of feedback in particular we characterize which control systems can be transformed to hamiltonian control systems by a feedback transformation

flood frequency censoring errors associated with daily read flood observations 1 the effects of daily read discharges discharges derived from a single daily observation say at 9 am are examined in the context of flood frequency analysis these discharges underestimate the true peak discharge because the actual peak is unlikely to occur at the single observation time the resultant error in discharge estimates can be quite large up to a factor of 10 several maximum likelihood methods are proposed to deal with these daily read or censored discharges three methods are evaluated censored as gauged cag which treats daily read discharges as the true peak binomial censoring bc which uses binomial censoring and random dependent censoring rdc which incorporates the dependence between the the daily read and true peak discharges the performance of the methods is evaluated using a monte carlo study the rdc method is found preferable to the cag method because it provides better performance in terms of root mean squared error and bias and is theoretically sound the bc method performs very poorly and is not recommended

consistent abstractions of affine control systems in this paper we consider the problem of constructing abstractions of affine control systems that preserve reachability properties and in particular local accessibility in this framework showing local accessibility of the higher level abstracted model is equivalent to showing local accessibility of the more detailed lower level model given an affine control system and a smooth surjective map we present a canonical construction for extracting an affine control system describing the trajectories of the abstracted variables we then obtain conditions on the abstraction maps that render the original and abstracted system equivalent from a local accessibility point of view such consistent hierarchies of accessibility preserving abstractions of nonlinear control systems are then considered for various classes of affine control systems including linear bilinear drift free and strict feedback systems

using partial probability weighted moments to fit the extreme value distributions to censored samples the estimation of floods of large return periods from lower bound censored samples may often be advantageous because interpolation and extrapolation are made by exploring the trend of larger floods in each of the records the method of partial probability weighted moments partial pwms is an useful technique for fitting distributions to censored samples in this paper partial pwms are redefined along with a brief discussion on the definition of ordinary pwms the expression for partial pwms is derived for the extreme value type i or gumbel distribution combined with those for the extreme value type ii and iii distributions an unified expression for partial pwms is presented for the generalized extreme value gev distribution the equations for solving the distribution parameters are provided monte carlo simulation shows that lower bound censoring at a moderate level does not unduly reduce the efficiency of high quantile estimation even if the samples have come from a true gev distribution

integration by parts formula for regional fractional laplacian we obtain the integration by parts formula for the regional fractional laplacian which are generators of symmetric stable processes on a subset of mathbb r n 0 2 in this formula a local operator appears on the boundary connected with the regional fractional laplacian on domain hence this formula can be understood as the green formula for the regional fractional laplacian the similar integration by parts formula is also given for more general nonlocal operators the reflected stable like processes are studied

confidence intervals for expected moments algorithm flood quantile estimates historical and paleoflood information can substantially improve flood frequency estimates if appropriate statistical procedures are properly applied however the federal guidelines for flood frequency analysis set forth in bulletin 17b rely on an inefficient weighting procedure that fails to take advantage of historical and paleoflood information this has led researchers to propose several more efficient alternatives including the expected moments algorithm ema which is attractive because it retains bulletin 17b s statistical structure method of moments with the log pearson type 3 distribution and thus can be easily integrated into flood analyses employing the rest of the bulletin 17b approach the practical utility of ema however has been limited because no closed form method has been available for quantifying the uncertainty of ema based flood quantile estimates this paper addresses that concern by providing analytical expressions for the asymptotic variance of ema flood quantile estimators and confidence intervals for flood quantile estimates monte carlo simulations demonstrate the properties of such confidence intervals for sites where a 25 to 100 year streamgage record is augmented by 50 to 150 years of historical information the experiments show that the confidence intervals though not exact should be acceptable for most purposes

probability plot goodness of fit and skewness estimation procedures for the pearson type 3 distribution uniform flood frequency guidelines in the united states currently recommend fitting a pearson p3 distribution to the logarithms of annual maximum flood flows as a result a plethora of procedures have been recommended for obtaining unbiased plotting positions and unbiased estimates of the skew coefficient and for inverting the cumulative distribution function of a p3 variate these developments are precisely the ingredients required for the construction of p3 probability plots using monte carlo simulation we develop a probability plot correlation coefficient ppcc hypothesis test for the p3 distribution power studies are performed to evaluate the ability of the test to discriminate among competing distributional alternatives and to enhance our understanding of why the p3 distribution often appears to provide such a good fit to observed flood flow data a new estimator of the skew coefficient is presented which unlike the biased and unbiased moment estimators is unbounded and has significantly lower root mean square error than the moment estimators for highly skewed samples

flood frequency analysis with systematic and historical or paleoflood data based on the two parameter general extreme value models historical and paleoflood data have become an important source of information for flood frequency analysis a number of studies have been proposed in the literature regarding the value of historical and paleoflood information for estimating flood quantiles these studies have been generally based on computer simulation experiments in this paper the value of using systematic and historical paleoflood data relative to using systematic records alone is examined analytically by comparing the asymptotic variances of flood quantiles assuming a two parameter general extreme value marginal distribution type 1 and type 2 censored data and maximum likelihood estimation method the results of this study indicate that the value of historical and paleoflood data for estimating flood quantiles can be small or large depending on only three factors the relative magnitudes of the length of the systematic record n and the length of the historical period m the return period t of the flood quantile of interest and the return period h of the threshold level of perception for instance for n 50 m 50 and t 500 the statistical gain for type 2 censoring becomes significantly larger than for type 1 censoring as h becomes greater than 100 years in addition computer experiments have shown that the results regarding the statistical gain based on asymptotic considerations are valid for the usual sample sizes

plotting positions for historical floods and their precision plotting positions are needed for situations where in addition to a systematically recorded annual flood series one would have a record of any large floods which occurred during an extended historical period if they occurred many of the published estimators are based on uncensored sampling theory which is not appropriate for such data sets here such historical and systematic flood records are viewed as resulting from a partially censored sampling experiment plotting positions are derived for such experiments using both classical and bayesian viewpoints in general it is impossible to construct highly accurate estimates of the exceedance probabilities of the largest floods using only their rank the number of observed historical floods and the lengths of the historical period and the systematic record for the largest flood the coefficient of variation of exceedance probability estimators is of the order of 1 as it is for complete systematic records examples illustrate the bias and precision of a variety of plotting position formulas the differences among the different plotting positions are generally small in comparison to the sampling variability however plotting positions which are unbiased with uncensored samples are often the most biased when used with a combination of historical and systematic data three appendices consider the effect of misspecification of the length of the historical period the effect of misspecification of the threshold of perception or observation level and plotting positions for situations with several perception thresholds

equivalence of dynamical systems by bisimulation a general notion of bisimulation is defined for linear input state output systems using analogies with the theory of concurrent processes a characterization of bisimulation and an algorithm for computing the maximal bisimulation relation is derived using geometric control theory bisimulation is shown to be a notion which unifies the concepts of state space equivalence and state space reduction and which allows to study equivalence of systems with nonminimal state space dimension the notion of bisimulation is especially powerful for nondeterministic dynamical systems and leads in this case to a notion of equivalence which is finer than equality of external behavior for abstractions of systems it is shown how the results specialize to previously obtained results by other authors extensions of the main results to the nonlinear case are provided

contractibility of overlapping decentralized control abstract the purpose of this paper is to generalize the concept of contractibility of decentralized control laws in the inclusion principle after a system with overlapping subsystems is expanded into a larger space and decentralized control laws are formulated for the disjoint subsystems the laws need to be contracted for implementation in the original space we propose broader definitions of restriction and aggregation in the framework of inclusion which provide more flexibility in the contraction phase of the expansion contraction process in particular we discuss contractibility conditions for dynamic output controllers including state observers which have been of special interest in applications

nonlocal equations with measure data we develop an existence regularity and potential theory for nonlinear integrodifferential equations involving measure data the nonlocal elliptic operators considered are possibly degenerate and cover the case of the fractional p laplacean operator with measurable coefficients we introduce a natural function class where we solve the dirichlet problem and prove basic and optimal nonlinear wolff potential estimates for solutions these are the exact analogs of the results valid in the case of local quasilinear degenerate equations established by boccardo and gallouet j funct anal 87 149 169 1989 partial differ equ 17 641 655 1992 and kilpelainen and mal ann scuola norm sup pisa cl sci iv 19 591 613 1992 acta math 172 137 161 1994 as a consequence we establish a number of results that can be considered as basic building blocks for a nonlocal nonlinear potential theory fine properties of solutions calderon zygmund estimates continuity and boundedness criteria are established via wolff potentials a main tool is the introduction of a global excess functional that allows us to prove a nonlocal analog of the classical theory due to campanato ann mat pura appl iv 69 321 381 1965 our results cover the case of linear nonlocal equations with measurable coefficients and the one of the fractional laplacean and are new already in such cases

optimal chained aggregation for reduced order modeling in this paper a theory is proposed for a new optimal process to perform chained aggregation in reduced order modelling notions of almost invariant subspaces and approximate aggregation are introduced in the proposed theory and are shown to be useful concepts in model reduction to derive an exact aggregated model from the approximately aggregated model obtained by optimal chained aggregation an algorithm is presented which is a variant of the well known shifted qr algorithm examples are given to illustrate the theory and its superiority over a previous approach

abstractions of hamiltonian control systems given a control system and a desired property an abstracted system is a reduced system that preserves the property of interest while ignoring modeling detail in previous work abstractions of linear and nonlinear control systems were considered while preserving reachability properties in this paper we consider the abstraction problem for hamiltonian control systems where in addition to the property of interest we also preserve the hamiltonian structure of the control system we show how the hamiltonian structure of control systems can be exploited to simplify the abstraction process we then focus on local accessibility preserving abstractions and provide conditions under which local accessibility properties of the abstracted hamiltonian system are equivalent to the local accessibility properties of the original hamiltonian control system

renormalized solutions for the fractional p x laplacian equation with l1 data abstract we consider the fractional p x laplacian problem with l 1 data based on the approximation and energy methods we prove the existence and uniqueness of nonnegative renormalized solutions for such problems

lh moments for statistical analysis of extreme events statistical analysis of extremes is often conducted for predicting large return period events in this paper lh moments a generalization of l moments that are based on linear combinations of higher order statistics are introduced for characterizing the upper part of distributions and larger events in data using lh moments reduces undesirable influences that small sample events may have on the estimation of large return period events the method of lh moments is formulated for the generalized extreme value gev distribution along with two detailed examples monte carlo simulations are conducted to illustrate the performance of using the method of lh moments to fit the gev distribution to both gev and non gev samples lh moment diagrams are constructed using annual maximum flow data for 107 streams worldwide to examine the ability of the gev distribution to model those series

the hierarchical lattices of a finite machine the concept of dynamical consistency is introduced to define a high level transition function for an arbitrary partition of the state space of a finite input state machine m the existence of a dynamically consistent transition from a partition member xi to a member xj corresponds to the existence for every state x in xi of some x dependent control sequence which takes that state directly into xj this paper analyses what are termed in block controllable partition machines and between block controllable partition machines and establishes the existence of the associated in block controllable hierarchical lattice ibcp m it is shown that any partition machine in ibcp m is between block controllable if and only if the base machine m is controllable this setting allows the specification of state to state control trajectories of m to be decomposed into high level and low level components

hierarchically consistent control systems large scale control systems typically possess a hierarchical architecture in order to manage complexity higher levels of the hierarchy utilize coarser models of the system resulting from aggregating the detailed lower level models in this layered control paradigm the notion of hierarchical consistency is important as it ensures the implementation of high level objectives by the lower level system in this paper we define a notion of modeling hierarchy for continuous control systems and obtain characterizations for hierarchically consistent linear systems with respect to controllability objectives as an interesting byproduct we obtain a hierarchical controllability criterion for linear systems from which we recover the best of the known controllability algorithms from numerical linear algebra

comprehensive at site flood frequency analysis using monte carlo bayesian inference in flood frequency applications where the design flood is required to have a specified exceedance probability expected probability should be used its computation however presents formidable difficulties this study presents a monte carlo bayesian method for computing the expected probability distribution as well as quantile confidence limits for any flood frequency distribution using data on gauged flows possibly corrupted by rating curve error and on censored flows this is achieved by a three step process 1 formulate the likelihood function for the given data 2 approximate the likelihood function using a multinomial distribution and 3 integrate the expected probability integral using importance sampling the flike software for performing this is described and an example is given

hierarchical trajectory refinement for a class of nonlinear systems trajectory generation for nonlinear control systems is an important and difficult problem in this paper we provide a constructive method for hierarchical trajectory refinement the approach is based on the recent notion of f related control systems given a control affine system satisfying certain assumptions we construct a f related control system of smaller dimension trajectories designed for the smaller abstracted system are guaranteed by construction to be feasible for the original system constructive procedures are provided for refining trajectories from the coarser to the more detailed system

low flow analysis with a conditional weibull tail model estimates of low flow quantiles such as the 7 day 10 year low flow which are usually obtained by statistical modeling of observed data series are widely used in water quality management this paper presents a conditional modeling approach to low flow analysis that employs only those data values which are less than or equal to a ceiling value modeling in this fashion has been motivated by the observation that annual low flows may derive from mixed processes and by the subjective nature of graphical methods such as those employed by the u s geological survey which are often employed in such cases results of monte carlo experiments demonstrate that the conditional modeling approach yields a low flow quantile estimator whose bias and rmse are comparable to more conventional modeling approaches of fitting a classical textbook probability distribution on the basis of all observed data values even when the underlying population is of a well behaved form since the complex forms of mixed low flow data distributions are not capable of being represented by classical textbook distributions and since the conditional modeling approach performs comparably to those models even when the data derive from well behaved probability distributions these results imply that the conditional modeling approach is worthy of consideration for use by hydrologists the conditional modeling approach also leads rather naturally to a scheme much like that used in index flood methods whereby a regional low flow estimator might be devised an application of the conditional modeling approach to 48 low flow data series in alabama is presented

l moment diagrams should replace product moment diagrams it is well known that product moment ratio estimators of the coefficient of variation c skewness and kurtosis exhibit substantial bias and variance for the small n 100 samples normally encountered in hydrologic applications consequently l moment ratio estimators termed l coefficient of variation 2 l skewness 3 and l kurtosis 4 are now advocated because they are nearly unbiased for all underlying distributions the advantages of l moment ratio estimators over product moment ratio estimators are not limited to small samples monte carlo experiments reveal that product moment estimators of c and are also remarkably biased for extremely large samples n 1000 from highly skewed distributions a case study using large samples n 5000 of average daily streamflow in massachusetts reveals that conventional moment diagrams based on estimates of product moments c and reveal almost no information about the distributional properties of daily streamflow whereas l moment diagrams based on estimators of 2 3 and 4 enabled us to discriminate among alternate distributional hypotheses

discrete approximation and supervisory control of continuous systems addresses the following hybrid control problem a continuous plant its state evolving in euclidean space is to be controlled via symbolic output feedback both measurement and control signal live on finite sets of symbols we adopt the following approach the hybrid problem is first translated into a purely discrete problem by approximating the continuous plant model by a nondeterministic finite state machine by taking into account past measurement and control symbols approximation accuracy can be improved and adjusted to the specification requirements supervisory control theory for discrete event systems des is then applied to find the optimal controller which enforces the specifications as the behavior of the approximating automaton is guaranteed to contain the behavior of the underlying continuous plant model the controller also forces the latter to obey the specifications

projection and deflation method for partial pole assignment in linear state feedback two projection methods are proposed for partial pole placement in linear control systems these methods are of interest when the system is very large and only a few of its poles must be assigned the first method is based on computing an orthonormal basis of the left invariant subspace associated with the eigenvalues to be assigned and then solving a small inverse eigenvalue problem resulting from projecting the initial problem into that subspace the second method can be regarded as a variant of the weilandt deflation technique used in eigenvalue methods

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

lifting of trajectories of control systems related by smooth mappings abstract given a pair of control systems x f x u and y h y v whose state spaces are differentiable manifolds m and n respectively we focus on situations where there exists a mapping m n that induces some type of correspondence between the trajectories of the systems an important instance of this situation occurs when f is a complex system for example one having many states h is a subsystem of f presumably with fewer states and a simpler structure than f and is a mapping from the full state space m to a reduced state space n some recent research has concentrated on the concept of related systems where it is required that send trajectories of f onto trajectories of h here we approach the problem from a different direction and ask under what conditions trajectories of the subsystem h can be lifted to trajectories of the full system f we provide computable sufficient conditions for the local and global lifting of trajectories from n to m connections between the lifting problem and the problem of global f g invariance are also discussed briefly

flood frequency analysis with historical and paleoflood information an investigation is made of flood quantile estimators which can employ historical and paleoflood information in flood frequency analyses two categories of historical information are considered censored data where the magnitudes of historical flood peaks are known and binomial data where only threshold exceedance information is available a monte carlo study employing the two parameter lognormal distribution shows that maximum likelihood estimators mles can extract the equivalent of an additional 10 30 years of gage record from a 50 year period of historical observation the mle routines are shown to be substantially better than an adjusted moment estimator similar to the one recommended in bulletin 17b of the united states water resources council hydrology committee 1982 the mle methods performed well even when floods were drawn from other than the assumed lognormal distribution

robust flood frequency models the concept of a robust model is briefly explored in the context of flood frequency analysis two necessary properties of a robust model are advanced namely resistance and efficiency strategies for seeking more robust models are discussed because of its versatility the five parameter wakeby distribution can credibly be considered a parent flood distribution four regionalized wakeby parents are employed in simulation studies to search for robust models these parents were shown by houghton to be representative of u s flood experience in the sense that certain raw flood data characteristics could be reproduced a limited range of sampling experiments were undertaken the results suggest that of the site specific estimators considered the two parameter log normal maximum likelihood estimator is most resistant with gumbel estimators employing either maximum likelihood or probability weighted moments displaying comparable resistance several estimators which utilize regional flood information were compared included were empirical bayes estimators which are structurally similar to james stein rules and regionalized estimators based on the flood index method these estimators exhibited substantial improvements in aggregate risk performance over their site specific counterparts particularly for short record lengths regionalized estimators appear to be preferable for short record lengths while estimators which combine both site and regional flood information are preferable for longer record lengths when such estimation procedures are considered other distributional models such as log pearson type iii and wakeby become practical alternatives to the two parameter log normal model

nonparametric variable kernel estimation with historical floods and paleoflood information extending a data record back in time using historical or paleoflood data has the potential to provide a considerable amount of information on very large floods parametric estimation methods are readily applicable to flood frequency analysis when historical or paleoflood estimates are available however all parametric approaches need an assumption about the underlying parent distribution which is never known exactly in recent years nonparametric methods of estimating probability density functions have been developed each of these involves the use of a suitable smoothing function known as a kernel a new nonparametric variable kernel estimation model is proposed results obtained from a limited amount of real data and from simulation experiments show that quantiles estimated by the nonparametric method are better than those estimated by some selected parametric models both in descriptive ability and in predictive ability the uncertainty in the choice of the threshold value of perception of a historical flood is also discussed

practical aspects of low flow frequency analysis this paper considers some practical aspects concerning the application of the weibull distribution to low flow frequency analysis two and three parameter forms of the distribution are fitted to a total of 987 distributions derived from the daily flow data of 134 catchments located in southeastern australia the relative performance of three estimation methods moments maximum likelihood and probability weighted moments is investigated and it is found that the different estimation methods provide distinct sets of quantile estimates the method of probability weighted moments is more likely to give unsatisfactory estimates of the smallest drought and in general tends to yield less severe estimates of drought volumes relative to the other two methods the method of maximum likelihood however occasionally provides estimates of drought volumes that are many times greater than that yielded by the methods moments or probability weighted moments in addition the differences between low flow frequency estimates based on calendar and hydrologic years is investigated and recommendations are given for the selection of an appropriate subset of the data to be fitted

renormalized solutions for a nonlinear parabolic equation with variable exponents and l 1 data abstract we prove the well posedness existence and uniqueness of a renormalized solution to nonlinear parabolic equations with variable exponents and l 1 data the functional setting involves lebesgue sobolev spaces with variable exponents

censored data correlation and principal component dynamic programming a principal component stochastic dynamic programming algorithm for stochastic multireservoir hydropower system operation optimization was proposed by saad and turgeon 1988 the dimension of the state space of the system is reduced by using only the major principal components of the system s state as determined by a principal component analysis of the results of a deterministic optimization a significant refinement of the procedure is to employ censored data principal component analysis the more sophisticated statistical analysis provides a better model of the full dynamic range of the reservoir system s state explains more observed variability of the reservoir volumes and provides more accurate estimates of the statistical description s parameters in an example presented of a four reservoir system the first component of the censored data principal component analysis for a given month explained all but 7 of the uncensored system s variability whereas the standard analysis for the same month left 12 of the observed system s variability unexplained

reflected symmetric α stable processes and regional fractional laplacian in this paper we investigate the reflected symmetric stable processes and their generators we show that the generators are regional fractional laplacians on the closed region in the case of 1 2 their existence requires that open image in new window on the boundary among other things we obtain the integration by parts formula of the regional fractional laplacian and the semi martingale decomposition of the reflected symmetric stable processes

generalized extreme value distribution fitted by lh moments for low flow frequency analysis 1 this study introduces a method based on lh moments to use the generalized extreme value gev distribution for low flow frequency analysis and investigates the capability of the gev distribution fitted by lh moments to effectively model the lower tail of the low flow frequency curve without explicitly censoring the data sample the performance of the gev l moment the gev distribution fitted by l moments and gev lh moment the gev distribution fitted by lh moments methods are assessed by evaluating the bias mean square error and relative accuracy of quantile estimates through monte carlo simulations it is shown that when both frequent low flows and extreme low flows can be adequately described by an assumed parent distribution both gev l2 moment and gev l moment methods make equally accurate quantile estimates however when frequent low flows and extreme low flows do not follow a single trend the bias of the gev l2 moment estimator is negligible while the bias of the gev l moment estimator is significant at large annual recurrence intervals on average the gev l2 moment quantile estimator displays less bias than the gev l moment quantile estimator furthermore as the annual recurrence interval increases the relative accuracy of the gev l2 moment method consistently improves over the gev l moment method the gev lh moment method is thus considered to be the more suitable method to model low flows

l moment diagrams for censored observations observed data sets containing values above or below the analytical threshold of measuring equipment are referred to as censored such data are frequently encountered in quality and quantity monitoring applications of water soil and air samples most of the previous literature on the statistical analysis of censored data relates to the problems of moment parameter and quantile estimation methods such estimation methods usually assume an underlying probability distribution few goodness of fit methods exist for censored data we introduce l moment diagrams for the evaluation of the goodness of fit of alternative distributional hypotheses for left censored data experiments with artificial censored data sets document the conditions under which l moment diagrams should be useful our approach like hosking s 1995 approach for right censoring derived l moment diagrams for left censored observations from partial probability weighted moments

hierarchical hybrid control systems a lattice theoretic formulation the notion of dynamical consistency is extended to hybrid systems so as to define the set of dynamically consistent hybrid partition machines associated with a continuous system s following the formulation of the notions of between block and in block controllable hybrid partition machines the lattice hibc s of hybrid in block controllable partition machines is defined and investigated based on these constructions the definition and properties of hierarchical hybrid control systems are presented together with an example

estimation of moments and quantiles using censored data censored data sets are often encountered in water quality investigations and streamflow analyses a monte carlo analysis examined the performance of three techniques for estimating the moments and quantiles of a distribution using censored data sets these techniques include a lognormal maximum likelihood estimator mle a log probability plot regression estimator and a new log partial probability weighted moment estimator data sets were generated from a number of distributions commonly used to describe water quality and water quantity variables a robust fill in method which circumvents transformation bias in the real space moments was implemented with all three estimation techniques to obtain a complete sample for computation of the sample mean and standard deviation regardless of the underlying distribution the mle generally performed as well as or better than the other estimators though the moment and quantile estimators using all three techniques had comparable log space root mean square errors rmse for censoring at or below the 20th percentile for samples sizes of n 10 the 40th percentile for n 25 and the 60th percentile for n 50 comparison of the log space rmse and real space rmse indicated that a log space rmse was a better overall metric of estimator precision

on the cauchy problem for boltzmann equations global existence and weak stability we study the large data cauchy problem for boltzmann equations with general collision kernels we prove that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in l to a solution from this stability result we deduce global existence of a solution to the cauchy problem our method relies upon recent compactness results for velocity averages a new formulation of the boltzmann equation which involves nonlinear normalization and an analysis of subsolutions and supersolutions it allows us to overcome the lack of strong a priori estimates and define a meaningful collision operator for general configurations

robust flood frequency analysis performance of ema with multiple grubbs beck outlier tests flood frequency analysis generally involves the use of simple parametric probability distributions to smooth and extrapolate the information provided by short flood records to estimate extreme flood flow quantiles parametric probability distributions can have difficulty simultaneously fitting both the largest and smallest floods a danger is that the smallest observations in a record can distort the exceedance probabilities assigned to the large floods of interest the identification and treatment of such potentially influential low floods pilfs frees a fitting algorithm to describe the distribution of the larger observations this can allow parametric flood frequency analysis to be both efficient and also robust to deviations from the proposed probability model s lower tail historically pilf identification involved subjective judgement we propose a new multiple grubbs beck outlier test mgbt for objective pilf identification mgbt pilf identification rates akin to type i errors are reported for the lognormal ln distribution and the log pearson type iii lp3 distribution with a variety of skew coefficients mgbt pilf identification generally matched subjective identification from a recent california flood frequency study monte carlo results show that censoring of pilfs identified by the mgbt algorithm improves the extreme quantile estimator efficiency of the expected moments algorithm ema for negatively skewed lp3 distributions and has little effect for zero or positive skews simultaneously it protects against deviations from the lp3 in the lower tail as illustrated by distorted ln examples thus mgbt generally makes flood frequency analysis based on the lp3 distribution with ema both more accurate and more robust

correlated rating curve error in flood frequency inference an incremental rating curve error model is proposed to describe the systematic error introduced when a rating curve is extended by methods such as slope conveyance log log extrapolation or fitting to indirect discharge estimates extension can introduce a systematic or highly correlated error which is anchored by the more extensively measured part of the rating curve a likelihood function is developed which explicitly accounts for such error and accepts both gauged and binomial censored data a sampling experiment based on the three parameter generalized extreme value distribution was conducted to assess the performance of maximum likelihood quantile estimators this experiment revealed that substantial and in some cases massive degradation in the performance of quantile estimators can occur in the presence of correlated rating curve error rating error comparison of maximum likelihood estimators allowing for and ignoring rating error produced mixed results as rating error impact and or information content increased estimators allowing for rating error tended to perform better and in some cases significantly better than estimators ignoring rating error it is also shown that in the presence of rating error the likelihood surface may have multiple optima that may result in nonunique solutions for hill climbing search methods moreover in the presence of multiple optima and constraints on parameters the likelihood surface may be poorly described by asymptotic approximations

the relationship between monte carlo estimators of heterogeneity and error for daily to monthly time steps in a small minnesota precipitation gauge network precipitation quantile estimates are used in engineering agriculture and a variety of other disciplines index flood regional frequency methods pool normalized gauge data in the case of homogeneity among the constituent gauges of the region unitless regional quantile estimates are outputted and rescaled at each gauge because violation of the homogeneity hypothesis is a major component of quantile estimation error in regional frequency analysis heterogeneity estimators should be reasonable proxies of the error of quantile estimation in this study three monte carlo heterogeneity statistics tested in hosking and wallis 1997 are plotted against monte carlo estimates of quantile error for all five or more gauge regionalizations in a 12 gauge network in the twin cities region of minnesota upper tail quantiles with nonexceedance probabilities of 0 75 and above are examined at time steps ranging from daily to monthly a linear relationship between heterogeneity and error estimates is found and quantified using pearson s r score two of hosking and wallis s 1997 heterogeneity measures incorporating the coefficient of variation in one case and additionally the skewness in the other are found to be reasonable proxies for quantile error at the l moment ratio values characterizing these data this result in addition to confirming the utility of a commonly used coefficient of variation based heterogeneity statistic provides evidence for the utility of a heterogeneity measure that incorporates skewness information

plotting positions of annual flood extremes considering extraordinary values a generalized plotting position formula for estimation of the recurrence interval or its reciprocal the exceedance probability of hydrologic events in an incomplete data sample containing both extraordinarily large and small historical values is derived the derivation is based on order statistics analysis and is independent of the probability distribution of the hydrologic variable it is shown that the weibull formula is a special case of the generalized formula

inferences about the mean from censored water quality data several methods which are commonly used for making inferences about the levels of many metals and organic contaminants in ambient waters from type i censored data are critically evaluated and their applications are illustrated using the concentrations of polychlorinated biphenyls in water samples from the niagara river difficulties encountered in the application of all the methods except the method of maximum likelihood include ignoring the information available about the analytical detection limit and the unavailability of the standard errors for these estimates under the assumption that the distribution of the data is lognormal the log regression method is modified to produce estimates of the censored values which use the detection limit information and the properties of the maximum likelihood estimates for the lognormal mean are derived furthermore an approximate confidence interval for the lognormal mean is given and its use for estimating the load to and from the niagara river is illustrated the above methods along with a modification to the method of maximum likelihood are evaluated using monte carlo simulation

bisimilar control affine systems the notion of bisimulation plays a very important role in theoretical computer science where it provides several notions of equivalence between models of computation these equivalences are in turn used to simplify verification and synthesis for these models as well as to enable compositional reasoning in systems theory a similar notion is also of interest in order to develop modular verification and design tools for purely continuous or hybrid control systems in this paper we introduce two notions of bisimulation for nonlinear systems we present differential geometric characterizations of these notions and show that bisimilar systems of different dimensions are obtained by factoring out certain invariant distributions furthermore we also show that all bisimilar systems of different dimension are of this form

robin fractional problems with symmetric variable growth in this paper we study the fractional p laplacian and we introduce the corresponding nonlocal conormal derivative for this operator we prove the basic properties of the corresponding function space and we establish a nonlocal version of the divergence theorem for such operators in the second part of this paper see sec iv we prove the existence of weak solutions of corresponding p robin boundary problems with sign changing potentials by applying variational tools

comparisons of two moments based estimators that utilize historical and paleoflood data for the log pearson type iii distribution 1 the expected moments algorithm ema cohn et al 1997 and the bulletin 17b interagency committee on water data 1982 historical weighting procedure b17h for the log pearson type iii distribution are compared by monte carlo computer simulation for cases in which historical and or paleoflood data are available the relative performance of the estimators was explored for three cases fixed threshold exceedances a fixed number of large floods and floods generated from a different parent distribution ema can effectively incorporate four types of historical and paleoflood data floods where the discharge is explicitly known unknown discharges below a single threshold floods with unknown discharge that exceed some level and floods with discharges described in a range the b17h estimator can utilize only the first two types of historical information including historical paleoflood data in the simulation experiments significantly improved the quantile estimates in terms of mean square error and bias relative to using gage data alone ema performed significantly better than b17h in nearly all cases considered b17h performed as well as ema for estimating x100 in some limited fixed threshold exceedance cases ema performed comparatively much better in other fixed threshold situations for the single large flood case and in cases when estimating extreme floods equal to or greater than x500 b17h did not fully utilize historical information when the historical period exceeded 200 years robustness studies using gev simulated data confirmed that ema performed better than b17h overall ema is preferred to b17h when historical and paleoflood data are available for flood frequency analysis

nonlinear elliptic equations with variable exponent old and new abstract in this survey paper by using variational methods we are concerned with the qualitative analysis of solutions to nonlinear elliptic problems of the type div a x u u q x 2 u in u 0 on where is a bounded or an exterior domain of r n and q is a continuous positive function the results presented in this paper extend several contributions concerning the lane emden equation and we focus on new phenomena which are due to the presence of variable exponents

bisimilar linear systems the notion of bisimulation in theoretical computer science is one of the main complexity reduction methods for the analysis and synthesis of labeled transition systems bisimulations are special quotients of the state space that preserve many important properties expressible in temporal logics and in particular reachability in this paper the framework of bisimilar transition systems is applied to various transition systems that are generated by linear control systems given a discrete time or continuous time linear system and a finite observation map we characterize linear quotient maps that result in quotient transition systems that are bisimilar to the original system interestingly the characterizations for discrete time systems are more restrictive than for continuous time systems due to the existence of an atomic time step we show that computing the coarsest bisimulation which results in maximum complexity reduction corresponds to computing the maximal controlled or reachability invariant subspace inside the kernel of the observations map these results establish strong connections between complexity reduction concepts in control theory and computer science

synthesis of supervisory controllers for hybrid systems based on approximating automata the paper concerns the synthesis of supervisory controllers for a class of continuous time hybrid systems with discrete valued input signals that select differential inclusions for continuous valued state trajectories and event valued output signals generated by threshold crossings in the continuous state space the supervisor is allowed to switch the input signal value when threshold events are observed the objective is to synthesize a nonblocking supervisor such that the set of possible sequences of control and threshold event pairs for the closed loop system lies between given upper and lower bounds in the sense of set containment we show how this problem can be converted into a supervisor synthesis problem for a standard controlled discrete event system des a finite representation may not exist for the exact des model of the hybrid system however to circumvent this difficulty we present an algorithm for constructing finite state muller automata that accept outer approximations to the exact controlled threshold event language and we demonstrate that supervisors that solve the synthesis problem for the approximating automata achieve the control specifications when applied to the original hybrid system

an algorithm for computing moments based flood quantile estimates when historical flood information is available this paper presents the expected moments algorithm ema a simple and efficient method for incorporating historical and paleoflood information into flood frequency studies ema can utilize three types of at site flood information systematic stream gage record information about the magnitude of historical floods and knowledge of the number of years in the historical period when no large flood occurred ema employs an iterative procedure to compute method of moments parameter estimates initial parameter estimates are calculated from systematic stream gage data these moments are then updated by including the measured historical peaks and the expected moments given the previously estimated parameters of the below threshold floods from the historical period the updated moments result in new parameter estimates and the last two steps are repeated until the algorithm converges monte carlo simulations compare ema bulletin 17b s united states water resources council 1982 historically weighted moments adjustment and maximum likelihood estimators when fitting the three parameters of the log pearson type iii distribution these simulations demonstrate that ema is more efficient than the bulletin 17b method and that it is nearly as efficient as maximum likelihood estimation mle the experiments also suggest that ema has two advantages over mle when dealing with the log pearson type iii distribution it appears that ema estimates always exist and that they are unique although neither result has been proven ema can be used with binomial or interval censored data and with any distributional family amenable to method of moments estimation

censored stable processes we present several constructions of a censored stable process in an open set d rn i e a symmetric stable process which is not allowed to jump outside d we address the question of whether the process will approach the boundary of d in a finite time we give sharp conditions for such approach in terms of the stability index and the thickness of the boundary as a corollary new results are obtained concerning besov spaces on non smooth domains including the critical exponent case we also study the decay rate of the corresponding harmonic functions which vanish on a part of the boundary we derive a boundary harnack principle in c1 1 open sets

uncorrelated measurement error in flood frequency inference when measurement error me is present the true value of the annual maximum discharge and of the censoring threshold discharge is unknown the impact of using estimated rather than true discharges on the inference of flood quantiles is considered the likelihood function is formulated for data which consist of annual maximum discharges systematic data and occurrences of floods above some threshold discharge binomial censored data the formulation makes explicit allowance for the corruption of discharges by statistically independent me this formulation can be used to get maximum likelihood estimates or perform a bayesian analysis a limited sampling experiment was conducted to assess the performance of two parameter lognormal maximum likelihood quantile estimators in the presence of simple uncorreiated discontinuous me it was found that me reduces the information content of systematic and binomial censored data with the reduction being greatest for distributions with low coefficients of variation when only using systematic data it was found that the performance of estimators making allowance for me was at best only modestly better than that of estimators ignoring me the principal finding however was that the performance of maximum likelihood estimators using binomial censored data but ignoring me can be substantially worse than that of estimators making explicit allowance for me in fact the loss in performance can be so great that in some cases it may be preferable to ignore the binomial censored data finally it is shown that a bayesian analysis of flood data affected by me provides insights not offered by maximum likelihood estimation when the threshold discharge is in error the posterior distribution of the lognormal parameters can become bimodal as the length of the binomial censored record increases indicating an inconsistency between the information in the systematic and binomial censored data