uncertainty of nitrate n load computations for agricultural watersheds 1 water quality samples for most streams are collected at variable frequencies within monitoring periods of different lengths on the basis of discrete concentration data obtained from these monitoring studies loads of various pollutants passing through a gaging station for selected periods may be calculated using various load estimation methods in this paper nitrate n load estimates were compared with their true values calculated using 6 years of daily nitrate n concentration and average discharge data at an agricultural watershed in central illinois a monte carlo subsampling study was conducted to simulate different sampling scenarios for variable sampling frequencies and different monitoring durations load calculations were compared for each sampling scenario based on rating curve ratio estimator and flow weighted average estimator in addition two bias correction techniques minimum variance unbiased estimator mvue and smearing estimator were applied to the rating curve method the monitoring durations were 1 2 3 and 6 years and the sampling frequencies ranged from weekly to bimonthly the results demonstrated that a desired accuracy of the estimates could be achieved either by sampling more frequently or by monitoring the site longer although the ratio and the flow weighted average estimators had a small negative bias in most cases rating curve estimators were positively biased when applied to the study site also neither of the two bias correction techniques mvue and smearing estimator decreased this positive bias on the contrary those techniques produced a higher bias which resulted in increased root mean square error rmse the rating curve uncorrected for bias the simple ratio and the flow weighted estimator had a significantly smaller rmse for all sampling frequencies and all periods of record than the bias corrected rating curve methods

estimating a percent reduction in load this article extends the work of cohn et al 1989 on estimating constituent loads to the problem of estimating a percent reduction in load three estimators are considered the maximum likelihood mle a bias corrected maximum likelihood bcmle and the minimum variance unbiased mvue in terms of root mean square error both the mvue and bcmle are superior to the mle and for the cases considered here there is no appreciable difference between the mvue and the bcmle the bcmle is constructed from quantities computed by most regression packages and is therefore simpler to compute than the mvue which involves approximating an infinite series all three estimators are applied to a case study in which an agricultural tax in the everglades agricultural area is tied to an observed percent reduction in phosphorus load for typical hydrological data very large sample sizes of the order of 100 observations each in the baseline period and after are required to estimate a percent reduction in load with reasonable precision

a theory of pictures for quasi posets abstract the theory of pictures between posets is known to encode much of the combinatorics of symmetric group representations and related topics such as young diagrams and tableaux many reasons combinatorial e g since semi standard tableaux can be viewed as double quasi posets and topological quasi posets identify with finite topologies lead to extend the theory to quasi posets this is the object of the present article

classical dirichlet forms on topological vector spaces the construction of the associated diffusion process given a minimal classical dirichlet form onl 2 e we construct the associated diffusion process heree is a locally convex topological vector space and is a not necessarily quasi invariant probability measure one the construction is carried out under certain assumptions one and which can be easily verified in many examples in particular we explicitly apply our results to time zero and space time quantum fields with or with out cut off

classical dirichlet forms on topological vector spaces closability and a cameron martin formula abstract we prove a sufficient condition for the closability of classical dirichlet forms on l 2 e which is also necessary if all components of the dirichlet form are closable here e is a locally convex topological vector space and a not necessarily quasi invariant probability measure on e the same condition is shown to imply the existence of a closed extension whose domain can be described explicitly in the special case where is quasi invariant with respect to certain vectors in e our result generalises previous theorems on closability in addition we prove a cameron martin type formula for a large class of measures if e is finite dimensional our characterisation of closability is the analogue of the corresponding one dimensional result applications to quantum fields and the connection with the well studied case of abstract wiener spaces are discussed

the malliavin calculus a functional analytic approach in his groundbreaking articles s 91 malliavin introduced a technique for obtaining elliptic regularity results using function space calculus in his formulation the function space calculus on which his theory rests is the martingale calculus coming from the ornstein uhlenbeck process on wiener space cf 121 for a detailed discussion of malliavin s theory from this point of view although this formulation has a great deal to recommend it and is particularly pleasing to afficionados of the so called brownian sheet most analysts including those who are reasonably facile with the machinery of probability theory are unlikely to find the technical difficulties inherent in this approach outweighed by the eventual rewards shigekawa 111 discovered that there is an alternative formulation of malliavin s theory in shigekawa s formulation no mention need be made of the ornstein uhlenbeck process instead what he relies on is a sobolev type extension of the frechet dervative with wiener measure playing the role played by lebesgue measure in the finite dimensional context a third formulation of malliavin s theory was recently provided by bismut l bismut s idea is to exploit the quasi invariance of wiener measure as it is manifested in a beautiful relation due to haussmann 4 the present article has two aims in the first place section 1 2 and 3 are devoted to yet another formulation of malliavin s calculus although the end results are precisely the same as those obtained in 121 no reference is made to the ornstein uhlenbeck process on which the original theory depended instead the machinery is entirely that of elementary functional analysis and is devoid of any sophisticated martingale calculus it has been my intent that these three sections should be readily accessible to any analyst who has had some acquintance with wiener measure

blocks of cyclotomic hecke algebras abstract this paper classifies the blocks of the cyclotomic hecke algebras of type g r 1 n over an arbitrary field rather than working with the hecke algebras directly we work instead with the cyclotomic schur algebras the advantage of these algebras is that the cyclotomic jantzen sum formula gives an easy combinatorial characterization of the blocks of the cyclotomic schur algebras we obtain an explicit description of the blocks by analyzing the combinatorics of jantzen equivalence we remark that a proof of the classification of the blocks of the cyclotomic hecke algebras was announced in 1999 unfortunately cox has discovered that this previous proof is incomplete

heisenberg algebras and rational double affine hecke algebras in this paper we categorify the heisenberg action on the fock space via the category o of cyclotomic rational double affine hecke algebras this permits us to relate the filtration by the support on the grothendieck group of o to a representation theoretic grading defined using the heisenberg action this implies a recent conjecture of etingof

comment on forest and floods a new paradigm sheds light on age old controversies by younes alila et al 1 the paper by alila et al 2009 hereafter referred to as aksh presents a technique for analyzing altered peak flow frequencies after logging the paper suggests that the established method of chronologically pairing peak flows by corresponding hydrologic input at control and treated watersheds is inappropriate leading to irrelevant research hypotheses and impeding scientific progress in general we agree that analyses of changes in flood frequency are useful for evaluating the effects of watershed disturbance and that simple regression models often provide inadequate descriptions of posttreatment peak flow responses however the proposed method and accompanying discussion have several problems that undercut the strength of the paper s conclusions 2 1 the recovery adjustment used by the method augments the effect the analysis is attempting to detect 3 2 even in the absence of impacts the frequency distribution of observed peaks is expected to have greater variance than that of predicted peaks thereby introducing an artificial shift when comparing upper quantiles of observed and expected frequency distributions 4 3 a more appropriate analysis of uncertainty is needed if the utility of the method is to be validly assessed 5 4 frequency pairing does not overcome the problem of low power in testing for changes in very large events prior to forest regrowth 6 5 the relative merits of alternative statistical approaches are mischaracterized

energy image density property and the lent particle method for poisson measures abstract we introduce a new approach to absolute continuity of laws of poisson functionals it is based on the energy image density property for dirichlet forms the associated gradient is a local operator and gives rise to a nice formula called the lent particle method which consists in adding a particle and taking it back after some calculation

cauchy problems for keller segel type time space fractional diffusion equation abstract this paper investigates cauchy problems for nonlinear fractional time space generalized keller segel equation d t 0 c 2 b 0 where caputo derivative d t 0 c models memory effects in time fractional laplacian 2 represents levy diffusion and b s n r n x y x y n 2 y d y is the riesz potential with a singular kernel which takes into account the long rang interaction we first establish l r l q estimates and weighted estimates of the fundamental solutions p x t y x t or equivalently the solution operators s t t t then we prove the existence and uniqueness of the mild solutions when initial data are in l p spaces or the weighted spaces similar to keller segel equations if the initial data are small in critical space l p c r n p c n 2 we construct the global existence furthermore we prove the l 1 integrability and integral preservation when the initial data are in l 1 r n l p r n or l 1 r n l p c r n finally some important properties of the mild solutions including the nonnegativity preservation mass conservation and blowup behaviors are established

transformation of wiener measure under anticipative flows lett f be a transformation from the wiener space to itself with the range off assumed to be in the cameron martin space the absolute continuity and the density function associated witht is considered t is assumed to be embedded in or defined through a parameterizationt t f t andf t is assumed to be differentiable int the paper deals first with the case where the range of thet derivative off t is also in the cameron martin space and new representations for the radon nikodym derivative and the carleman fredholm determinant are derived the case where thet derivative off t is not in the cameron martin space is considered next and results on the absolute continuity and the density function under conditions which are considerably weaker than previously known conditions are presented

projection of the infinitesimal generator of a diffusion consider a finite or infinite dimensional space x with a diffusion having an invariant measure a typical example is the wiener space with the ornstein uhlenbeck process another example is the heat process on the wiener space to a nondegenerated map g from x into a finite dimensional manifold v we associate the following invariants 1 a riemannian metric on v 2 a vector field z on v then the image g of the measure through the map g will have a density k with respect to the riemannian volume for k the relation z log k will hold the projected infinitesimal generator will be equal to the sum z where is the riemannian laplacian on the manifold v this result applied to the heat equation on x yields a non autonomous parabolic equation which gives the law g the second order operator involved in this parabolic equation is strictly elliptic the method reduces the study of a hypoelliptic operator to that of a non autonomous elliptic one

uniqueness of generalized schrodinger operators and applications abstract we prove necessary and sufficient conditions on r d r 0 a e so that the operator s 2 1 w1 n has exactly one self adjoint extension on w1 p which generates a sub markovian semigroup on w1 n these conditions are shown to be always fulfilled if d 1 and are verified for a large class of functions if d 1 we also prove an infinite dimensional analogue of this result where r d is replaced by some topological vector space e and the lebesgue measure dx by a gaussian measure the role of is taken by some ornstein uhlenbeck operator with general linear drift and dom s bounded smooth cylinder functions both results are derived as special cases from a general perturbation result we also give the corresponding probabilistic version i e we prove uniqueness for the associated martingale problem we present in some detail applications to the case where is a ground state of a hamiltonian in quantum field theory settling a problem which has been open for some time furthermore we apply our results to prove uniqueness in distribution of the diffusion first constructed by g jona lasinio and p k mitter for the stochastic quantization of f 2 field theory

a decomposition rule for certain tensor product representations of the symmetric groups abstract in this paper we give a combinatorial rule to calculate the decomposition of the tensor product kronecker product of two irreducible complex representations of the symmetric group s n when one of the representations corresponds to a hook n m 1 m

q tensor space and q weyl modules we obtain the irreducible representations of the q schur algebra motivated by the fact that these representations give all the irreducible representations of gln q in the nondescribing characteristic the irreducible polynomial representations of the general linear groups in the describing characteristic are a special case of this construction the theory of polynomial representations of general linear groups is equivalent to the representation theory of schur algebras see green s book 5 and the bibliography therein in 4 we defined q analogues of schur algebras when q 1 these are the usual schur algebras and when q is a prime power representations of q schur algebras give a substantial part of the representation theory of finite general linear groups in the nondescribing characteristic case including all irreducible representations of these groups and important information about decomposition numbers it is natural to ask what features of the classical schur algebras have qanalogues in this paper we define q analogues of tensor space of weyl modules and of weight spaces thereby generalizing the main reslllts which appear in green s book 5 for example we classify the irreducible modules for qschur algebras we determine bases for q weyl modules compatible with weight spaces and we give results on composition multiplicities of the irreducible modules in q weyl modules the proofs are largely self contained so by specializing q to 1 we recover the corresponding results in 5 this paper therefore is relevant to the representation theory of symmetric groups and to the representation theory of general linear groups in the describing and in the nondescribing characteristics 1 the q schur algebra let r be a natural number let r be an integral domain and let q be a unit in r we denote the symmetric group on r letters by er the hecke algebra z is the r free r algebra with basis twlw e er where the multiplication is determined by the following rule if a i i 1 is a basic transposition in received by the editors august 15 1989 1980 mathematics subject classification 198 5 revision primary 1 6a64 1 6a6 5 secondary 20c30 this research was supported in part by nsf grant no dms 8802290 the authors gratefully acknowledge support received from nato grant no 0222 87 r 1991 american mathematical society 0002 9947 91 1 00 25 per page

the validity of a simple statistical model for estimating fluvial constituent loads an empirical study involving nutrient loads entering chesapeake bay we consider the appropriateness of rating curves and other log linear models to estimate the fluvial transport of nutrients split sample studies using data from tributaries to the chesapeake bay reveal that a minimum variance unbiased estimator mvue based on a simple log linear model provides satisfactory load estimates even in some cases where the model exhibited significant lack of fit for total nitrogen tn the average difference between the mvue estimates and the observed loads ranges from 8 to 2 at the four sites the corresponding range for total phosphorus tp is 6 to 5 none of these differences is statistically significant the observed variability of the mvue load estimates for tn and tp which ranges from 7 to 25 depending on the case is accurately predicted by statistical theory

application of the lent particle method to poisson driven sdes we apply the dirichlet form theory to stochastic differential equations with jumps as extension of malliavin calculus reasoning as in the continuous case this weakens significantly the assumptions on the coefficients of the sde thanks to the flexibility of the dirichlet forms language this approach brings also an important simplification which was neither available nor visible previously an explicit formula giving the carre du champ matrix i e the malliavin matrix following this formula a new procedure appears called the lent particle method which shortens the computations both theoretically and in concrete examples in this paper which uses the construction done in bouleau and denis j funct analysis 257 1144 1174 2009 we restrict ourselves to the existence of densities smoothness will be studied separately

equivariant littlewood richardson skew tableaux we give a positive equivariant littlewood richardson rule also discovered independently by molev our proof generalizes a proof by stembridge of the classical littlewood richardson rule we describe a weight preserving bijection between our indexing tableaux and trapezoid puzzles which restricts to a bijection between positive indexing tableaux and knutson tao puzzles

an evaluation of methods for the estimation of tributary mass loads tributary loading estimation methods were evaluated by conducting retrospective studies with comprehensive sets of field data for flow rates nutrients heavy metals and polychlorinated biphenyls three broad classes of loading estimation methods were investigated simple averaging methods ratio estimation methods and regression methods estimators were evaluated using monte carlo sampling studies in which random subsamples of complete loading records were used to estimate annual loadings these estimates were then compared to true loadings determined by calculations using the entire record no group of estimators were found to be superior for all test cases considered however individual estimation approaches within each group often provided low error estimates results were inconsistent among test cases and these inconsistencies appeared to be related to specific test case characteristics such as the strength and form of the flow concentration relationship and the nature of the annual hydrograph ratio estimators appeared to be more robust to sources of bias than other estimation approaches

on the absolute continuity of levy processes with drift we consider the problem of absolute continuity for the one dimensional sde xt x 0ta xs ds zt where z is a real levy process without brownian part and a a function of class mathcal c 1 with bounded derivative using an elementary stratification method we show that if the drift a is monotonous at the initial point x then xt is absolutely continuous for every t 0 if and only if z jumps infinitely often this means that the drift term has a regularizing effect since zt itself may not have a density we also prove that when zt is absolutely continuous then the same holds for xt in full generality on a and at every fixed time t these results are then extended to a larger class of elliptic jump processes yielding an optimal criterion on the driving poisson measure for their absolute continuity

coincidences among skew schur functions new sufficient conditions and necessary conditions are developed for two skew diagrams to give rise to the same skew schur function the sufficient conditions come from a variety of new operations related to ribbons also known as border strips or rim hooks the necessary conditions relate to the extent of overlap among the rows or among the columns of the skew diagram

estimating contaminant loads in rivers an application of adjusted maximum likelihood to type 1 censored data 1 this paper presents an adjusted maximum likelihood estimator amle that can be used to estimate fluvial transport of contaminants like phosphorus that are subject to censoring because of analytical detection limits the amle is a generalization of the widely accepted minimum variance unbiased estimator mvue and monte carlo experiments confirm that it shares essentially all of the mvue s desirable properties including high efficiency and negligible bias in particular the amle exhibits substantially less bias than alternative censored data estimators such as the mle tobit or the mle followed by a jackknife as with the mle and the mvue the amle comes close to achieving the theoretical frechet cramer rao bounds on its variance this paper also presents a statistical framework applicable to both censored and complete data for understanding and estimating the components of uncertainty associated with load estimates this can serve to lower the cost and improve the efficiency of both traditional and real time water quality monitoring

a littlewood richardson rule for the macdonald inner product and bimodules over wreath products abstract we prove a littlewood richardson type formula for s s t k t the pairing of two skew schur functions in the macdonald inner product at q t k for positive integers k this pairing counts graded decomposition numbers in the representation theory of wreath products of the algebra c x x k and symmetric groups

properties of convergence in dirichlet structures abstract in univariate settings we prove a strong reinforcement of the energy image density criterion for local dirichlet forms admitting square field operators this criterion enables us to redemonstrate some classical results of dirichlet forms theory ancona 1976 2 besides when x x 1 x p belongs to the d domain of the dirichlet form and when its square field operator matrix x t x is almost surely definite we prove that l x is a rajchman measure this is the first result in full generality in the direction of bouleau hirsch conjecture moreover in multivariate settings we study the particular case of sobolev spaces we prove that a convergence for the sobolev norm w 1 p r d r p toward a non degenerate limit entails convergence of push forward measures in the total variation topology our proofs are based on a new kind of integration by parts which is of independent interest

bases for coordinate rings of conjugacy classes of nilpotent matrices abstract a general conjecture is given for an explicit basis of the coordinate ring of the closure of the conjugacy class of a nilpotent matrix this conjecture is proven when the partition given by the transpose jordan type of the nilpotent matrix is a hook or has two parts

a littlewood richardson rule for factorial schur functions we give a combinatorial rule for calculating the coefficients in the expansion of a product of two factorial schur functions it is a special case of a more general rule which also gives the coefficients in the expansion of a skew factorial schur function applications to capelli operators and quantum immanants are also given

estimating constituent loads several recent articles have called attention to the problem of retransformation bias which can arise when log linear regression models are used to estimate sediment or other constituent loads in some cases the bias can lead to underestimation of constituent loads by as much as 50 and several procedures have been suggested for reducing or eliminating it however some of the procedures recommended for reducing the bias can actually increase it this paper compares the bias and variance of three procedures that can be used with log linear regression models the traditional rating curve estimator a modified rating curve method and a minimum variance unbiased estimator mvue analytical derivations of the bias and efficiency of all three estimators are presented it is shown that for many conditions the traditional and the modified estimator can provide satisfactory estimates however other conditions exist where they have substantial bias and a large mean square error these conditions commonly occur when sample sizes are small or when loads are estimated during high flow conditions the mvue however is unbiased and always performs nearly as well or better than the rating curve estimator or the modified estimator provided that the hypothesis of the log linear model is correct since an efficient unbiased estimator is available there seems to be no reason to employ biased estimators

sobolev algebras on lie groups and riemannian manifolds we prove that on any connected unimodular lie group g the space l p g l g where l p g is the sobolev space of order 0 associated with a sublaplacian is an algebra under pointwise product this generalizes results due to strichartz in the euclidean case to bohnke in the case of stratified groups and others a global version of this fact holds for groups with polynomial growth we give similar results for riemannian manifolds with ricci curvature bounded from below respectively nonnegative

development of regional regression relationships with censored data when no discharge record is available for a site a regional regression relationship can be used to estimate low flow quantiles problems arise in the derivation of such models when some at site quantile estimates are reported as zero one concern is that quantile estimates reported as zero may be in the range from zero to the measurement threshold a second concern is that a logarithmic transformation cannot be used with zero quantile estimates so traditional log linear least squares estimators cannot be computed this paper uses visual examples and monte carlo simulation to compare the performance of techniques for estimating the parameters of a regional regression model when some at site quantile estimates are zero ordinary least squares ols techniques employed in practice include adding a small constant to all at site quantile estimates denoted olsc or neglecting all observation reported as zero denoted olsd olsc and olsd performed poorly compared to the use of a tobit model which is a maximum likelihood estimator mle procedure that represents the below threshold estimates as a range from zero to the threshold level for a small amount of censoring the olsd method can be acceptable a weighted tobit model that accounts for the heteroscedasticity of the residuals in the regression model provided relatively little gain over the ordinary tobit model

the hopf algebra of finite topologies and t partitions a noncommutative and noncocommutative hopf algebra on finite topologies h t is introduced and studied freeness cofreeness self duality generalizing stanley s definition of p partitions associated to a special poset we define the notion of t partitions associated to a finite topology and deduce a hopf algebra morphism from h t to the hopf algebra of packed words wqsym generalizing stanley s decomposition by linear extensions we deduce a factorization of this morphism which induces a combinatorial isomorphism from the shuffle product to the quasi shuffle product of wqsym it is strongly related to a partial order on packed words here described and studied

combinatorics of representations of u_q widehat mathfrak s mathfrak l n atq 0 theq 0 combinatorics for u q widehat mathfrak s mathfrak l n is studied in connection with solvable lattice models crystal bases of highest weight representations of u q widehat mathfrak s mathfrak l n are labelled by paths which were introduced as labels of corner transfer matrix eigenvectors atq 0 it is shown that the crystal graphs for finite tensor products ofl th symmetric tensor representations of u q widehat mathfrak s mathfrak l n approximate the crystal graphs of levell representations of u q widehat mathfrak s mathfrak l n the identification is made between restricted paths for the rsos models and highest weight vectors in the crystal graphs of tensor modules for u q widehat mathfrak s mathfrak l n

girsanov theorem for anticipative shifts on poisson space we study the absolute continuity of the image measure of the canonical poisson probability measure under nonlinear shifts the radon nykodim density function is expressed using a carleman fredholm determinant and a divergence operator results are obtained for non necessarily invertible transformations under almost sure differentiability hypothesis

green s and dirichlet spaces associated with fine markov processes this is the second paper in a series devoted to green s and dirichlet spaces in the first paper we have investigated green s space k and the dirichlet space h associated with a symmetric markov transition function pt x b now we assume that p is a transition function of a fine markov process x and we prove that a the space h can be built from functions which are right continuous along almost all paths b the positive cone k in k can be identified with a cone m of measures on the state space c the positive cone h in h can be interpreted as the cone of green s potentials of measures m to every measurable set b in the state space e there correspond a subspace k b of k and a subspace h b of h the orthogonal projections of k onto k and of h onto h b can be expressed in terms of the hitting probabilities of b by the markov process x as the main tool we use additive functionals of x corresponding to measures m

formes de dirichlet generales et densite des variables aleatoires reelles sur l espace de wiener abstract it is shown that the main properties of dirichlet spaces can be proved without the classical local compacity hypothesis to this purely measurable framework we extend the functional calculus and the energy image density property these results are then applied to the ornstein uhlenbeck semi group on wiener space where it is obtained that the real random variables which are solutions of lipschitzian stochastic differential equations always have probability densities after perhaps an initial deterministic phase

on the contraction property of energy forms on infinite dimensional space abstract we prove that certain energy forms on infinite dimensional space with polynomial domain have the contraction or dirichlet property some consequences are discussed

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

cyclotomic double affine hecke algebras and affine parabolic category o using the orbifold kz connection we construct a functor from an affine parabolic category o of type a to the category o of a cyclotomic rational double affine hecke algebra h then we give several results concerning this functor

improved estimation in lognormal models abstract the estimation of the function exp a b 2 of normal parameters and 2 on the basis of a random sample x 1 xn is considered this class of functions includes the mean the median and all moments of lognormal distribution i show that the minimum variance unbiased estimator suggested by finney 1941 can be substantially improved in terms of mean squared error a similar result is established for the maximum likelihood estimator i suggest for practice use the following generalized bayes estimator when m n 1 2 x y exp ax y k 0 m 2m k k m k 2 y k k 0 m 2m k k m k 2 y k here x i n xj n y2 1 n x1 x 2 and constants and are determined by formulas 2 2 2b 2a n 1 5 b 3a2 2n this estimator is shown to be locally optimal for both small and large values of 2 the results of numerical study of the quadratic risk show the superiority of this estimator over the mentioned traditional procedures

new branching rules induced by plethysm we derive group branching laws for formal characters of subgroups of leaving invariant an arbitrary tensor t of young symmetry type where is an integer partition the branchings and fixing a vector vi a symmetric tensor gij gji and an antisymmetric tensor fij fji respectively are obtained as special cases all new branchings are governed by schur function series obtained from plethysms of the schur function s by the basic m series of complete symmetric functions and the l m 1 series of elementary symmetric functions our main technical tool is that of hopf algebras and our main result is the derivation of a coproduct for any schur function series obtained by plethysm from another such series therefrom one easily obtains generalized newell littlewood formulae and the algebra of the formal group characters of these subgroups is established concrete examples and extensive tabulations are displayed for and showing their involved and nontrivial representation theory the nature of the subgroups is shown to be in general affine and in some instances non reductive we discuss the complexity of the coproduct formula and give a graphical notation to cope with it we also discuss the way in which the group branching laws can be reinterpreted as twisted structures deformed by highly nontrivial 2 cocycles the algebra of subgroup characters is identified as a cliffordization of the algebra of symmetric functions for formal characters modification rules are beyond the scope of the present paper but are briefly discussed

factors affecting the efficiency of some estimators of fluvial total phosphorus load the accuracy of estimating total phosphorus tp loads to receiving waters usually is constrained by availability of concentration data as discharge flow data normally are comparatively abundant using 4 years of daily observations from three tributaries to the great lakes grand saginaw and sandusky rivers annual tp loads were tested for accuracy by five methods including regression ratio and robust estimators monte carlo methods were employed to simulate replicated flow stratified sampling of the datasets with various allocations of sampled to flow strata each of the load calculation methods was applied to each group of simulated samples and response was quantitated as load estimation error computed minus true load the results show the most consistently accurate estimator was beale s stratified ratio estimator it was however the only stratified estimator tested and should have been more accurate most accurate of the unstratified estimators was a straightforward least squares regression log log method the response of estimation bias to flow cut point and sample allocation manipulations indicated 1 beneficial results generally but not always obtained from high flow weighting of sampling and 2 postsampling stratification generally may yield improved accuracy for load estimation and deserves additional research

mean square error of regression based constituent transport estimates estimates of long term transport of constituents commonly are obtained by summing retransformed estimates from regressions of logarithmically transformed response variables typical explanatory variables for these regressions include functions of flow change in flow time and time of year the mean and mean square error of four estimators of long term transport at periodically measured stations are presented as a function of the observed values of the explanatory variables from the long term record and summary statistics of the regression data estimates of the mean square errors can be used in designing sampling strategies to attempt to minimize the uncertainty in the estimation of long term transport subject to a constraint on the number of samples to be taken this uncertainty is expressed in terms of the explanatory variables in the long term record the regression coefficients and standard error of the regression and the mean and covariance structure of the explanatory variables used in the regression

traces of harmonic functions and a new path space for the free quantum field the infinite dimensional ornstein uhlenbeck process associated with the free field of quantum field theory on rd is reconstructed as the traces of random harmonic functions these harmonic functions are the solutions of a generalised dirichlet problem with a random schwartz distribution as boundary data a detailed analysis of the associated trace space which is a subspace of a scaled sobolev space of negative fractional order leads to a new path space for the free field as well as to a convenient regularisation method because of the particular form of the trace space it is possible to give an explicit formula for the transition function of the process furthermore the dependence of the path space on the dimension d is discussed and a formulation of our result in terms of abstract wiener spaces is given