existence and multiplicity of positive solutions for semilinear elliptic systems with sobolev critical exponents abstract in this paper we study the existence and multiplicity of positive solutions to the following system u f u u v e g x v f v u v e h x in u v 0 in and u v 0 on where is a bounded smooth domain in r n f c 1 r 2 r is positively homogeneous of degree g h c 1 0 and e is a positive parameter using sub supersolution method we prove the existence of positive solutions for the above problem by means of the variational approach we prove the multiplicity of positive solutions for the above problem with 2 2

yamabe equations on half spaces where n 2 n 2 is the critical sobolev exponent n n 2 is the critical sobolev exponent on the boundary is the unit outer normal of and h x is the mean curvature this problem is related to the yamabe problem on manifolds with boundary see 7 8 it was proved in 7 8 that if either k x 1 h x 0 or k x 0 h x 1 then eq 1 1 has a classical solution which minimizes the yamabe ratio when k x 6 0 h x 6 0 it is natural to seek for the nehari minimizers this idea works when is not conformal to a ball see 9 however when is a ball the situation is very di erent in fact for certain functions k x and h x eq 1 1 has no positive solution at all therefore solvability conditions on k x and h x are needed to make it more clear we consider the yamabe equation

note on the applicability of the james stein estimator in regional hydrologic studies the applicability of the james stein estimator in regional hydrologic studies which entail the estimation of an n dimensional location parameter is discussed regional studies are frequently characterized by relatively short generally correlated samples drawn from nonsymmetric and bounded i e nonnormal populations by means of computer simulation studies the james stein estimator subject to the lindley modification and adoption of the positive part rule suggested by efron and morris and conditioned on the assumption of independence was shown to be robust in the case of the hydrologically plausible distribution considered here namely weibull distributions with coefficient of skewness ranging from 0 to 10 however in contrast to traditional methods of regionalization the effect of cross correlation is a diminishment of the relative risk advantage of the james stein estimator even in the best case of normal variables this is discussed and illustrated

finite size effects at the yang lee edge singularity and branched polymers in a plate geometry abstract finite size scaling effects are investigated for ising like systems in a hypercube ld near the yang lee edge singularity besides exact results for d 1 we present series in e 1 3 for some universal quantities in dimensions d 6 e gained by field theoretic techniques using the supersymmetric connection between the yang lee theory in dimension d and the statistics of branched polymers in d d 2 we find the animal number in a periodic plate geometry with 2 infinite and d compactified dimensions in particular we exactly calculate the full cross over between three dimensional and two dimensional animals

symmetric solutions for a class of singular biharmonic elliptic systems involving critical exponents this paper deals with a class of singular biharmonic elliptic systems involving critical exponents in a bounded symmetric domain by using the variational method and the symmetric criticality principle of palais we obtain several existence and multiplicity results of g symmetric solutions for the systems

the nehari manifold for systems of nonlinear elliptic equations abstract this paper deals with the existence and multiplicity results of nonlocal positive solutions to the following system p u u p 1 2 u 1 u u 1 v 1 q v v q 2 v 1 u 1 v 1 v together with dirichlet or mixed boundary conditions under some hypotheses on the parameters p p 1 and q more precisely the system considered corresponds to a perturbed eigenvalue equation combined with a second equation having concave and convex nonlinearities the study is based on the extraction of palais smale sequences in the nehari manifold the behaviour of the energy corresponding to these positive solutions with respect to the real parameters and is established

a bayesian surrogate for regional skew in flood frequency analysis the problem of how to best utilize site and regional flood data to infer the shape parameter of a flood distribution is considered one approach to this problem is given in bulletin 17b of the u s water resources council 1981 for the log pearson distribution here a lesser known distribution is considered namely the power normal which fits flood data as well as the log pearson and has a shape parameter denoted by derived from a box cox power transformation the problem of regionalizing is considered from an empirical bayes perspective where site and regional flood data are used to infer the distortive effects of spatial correlation and heterogeneity of site sampling variance of are explicitly studied with spatial correlation being found to be of secondary importance the end product of this analysis is the posterior distribution of the power normal parameters expressing in probabilistic terms what is known about the parameters given site flood data and regional information on this distribution can be used to provide the designer with several types of information the posterior distribution of the t year flood is derived the effect of nonlinearity in on inference is illustrated because uncertainty in is explicitly allowed for the understatement in confidence limits due to fixing analogous to fixing log skew is avoided finally it is shown how to obtain the marginal flood distribution which can be used to select a design flood with specified exceedance probability

on a neumann problem with critical exponents and hardy potentials abstract in this paper we consider the neumann problem of the potential elliptic system with hardy terms and critical exponents on a bounded domain using the critical point theory we first find infinitely many solutions for the corresponding perturbed subcritical problem analyzing concentration points in the bubbles carefully which appear in the approximate solutions we establish the concentration estimates and then obtain infinitely many solutions with positive energy by passing to a limit

existence of multiple positive solutions for a p q laplacian system with critical nonlinearities abstract in this paper our main purpose is to establish the existence of multiple positive solutions of a p q laplacian system with convex and sobolev critical nonlinearities by some standard variational methods whose key is to construct homotopies between and levels of the functional j and some analytical techniques

regional flood quantile estimation for a weibull model estimation of annual flood quantiles at a given site based on a regional weibull model with independence in space and time is considered a common shape parameter over sites motivated by an index flood assumption was assumed an exact simple formula for the cramer rao lower bound for the variance of unbiased estimators of the quantile is obtained and the gain of regional flood frequency analysis over single site analysis can be quantified via this formula the estimation techniques of the method of moments the method of probability weighted moments and the method of maximum likelihood are compared

the nehari manifold for a semilinear elliptic system involving sign changing weight functions abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system e with sign changing weight function with the help of the nehari manifold we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters belongs to a certain subset of r 2

infinitely many solutions for some nonlinear scalar system of two elliptic equations abstract in this paper we consider the elliptic system of two equations in h 1 r n h 1 r n u a x u 2 u 2 u v v b x v 2 u v 2 v where 1 satisfy 2 n n 2 n 3 the potentials a x b x are regular functions such that lim inf x a x a 0 and lim inf x b x b 0 moreover a x b x verify suitable decay assumptions but not requiring any symmetry property by means of the standard critical point theory we find infinitely many approximate solutions in bounded balls then we obtain infinitely many solutions for the original elliptic system by analyzing the structures of the approximate solutions carefully and by passing to a limit

a remark on the existence of multiple solutions to a multiparameter nonlinear elliptic system abstract in this work motivated by t f wu the nehari manifold for a semilinear elliptic system involving sign changing weight function nonlinear anal 68 2008 1733 1745 and using recent ideas from brown and wu k j brown t f wu a semilinear elliptic system involving nonlinear boundary condition and sign changing weight function j math anal appl 337 2008 1326 1336 we prove the existence of nontrivial nonnegative solutions to the nonlinear elliptic system p u m x u p 2 u u 2 u c x u 2 u v x p v m x v p 2 v v 2 v c x u v 2 v x u 0 v x here p denotes the p laplacian operator defined by p z div z p 2 z p 2 r n is a bounded domain with smooth boundary 1 1 2 p p p p n n p if n p p if n p n is the outer normal derivative r 2 0 0 the weight m x is a bounded function with m 0 and c x is a continuous function which changes sign in

multiple solutions of an inhomogeneous neumann problem for an elliptic system with critical sobolev exponent abstract in this paper we prove the existence of two solutions for the inhomogeneous neumann problem with critical sobolev exponent

multiple positive solutions for a critical quasilinear elliptic system with concave convex nonlinearities abstract in this paper we consider a quasilinear elliptic system with both concave convex nonlinearities and critical growth terms in bounded domains the existence and multiplicity results of positive solutions are obtained by variational methods

simulation bayes and bootstrap in statistical hydrology statistical simulation in hydrology is discussed from a bayesian perspective the inherent difficulties in both parametric simulation based on a parent distribution and classical nonparametric simulation based on the bootstrap are discussed as an alternative to these procedures a nonparametric bayesian simulation methodology polya resampling is introduced it consists of simulating from a nonparametric predictive distribution obtained from the analysis of a reference sample and it is asymptotically equivalent to the bootstrap the method is generalized to take into account a prior hypothesis on the parametric distribution of a variable a hybrid simulation model is then obtained that includes parametric and nonparametric simulation as particular cases an extensive application is presented in a related paper fortin et al 1997 where polya resampling is used to compare statistical models for flood frequency analysis in this paper an example is used to demonstrate how polya resampling can help assess the influence of a distribution hypothesis on simulation results

multiple positive solutions of nonhomogeneous elliptic systems involving critical sobolev exponents abstract in this paper we study the existence of multiple positive solutions to the following elliptic system u 2 u u 2 v e f x v 2 u v v 2 e g x in u v 0 in and u v 0 on where is a bounded domain in r n n 3 f g c 1 and 1 for the subcritical and critical cases we prove that problem has at least two solutions for any e 0 e 0 and has no solution for any e e e 0 e in the supercritical case we find that the existence of solutions to problem is closely related to the existence of nonnegative solutions for two linear elliptic problems

branched polymers on the two dimensional square lattice with attractive surfaces using the renormalization group approach an analysis is given of the asymptotic properties of branched polymers situated on the two dimensional square lattice with attractive impenetrable surfaces we modeled branched polymers as site lattice animals with loops and site lattice animals without loops on the simple square lattice we found the gyration radius critical exponent 0 6511 0 0003 and 0 6513 0 0003 for branched polymers with and without loops respectively our results for the crossover exponent 0 502 0 003 for branched polymers with loops and 0 503 0 003 for branched polymers without loops satisfy the recent hyperuniversality conjecture frac 1 2 in addition we have studied partially directed site lattice animals

collapse transition of randomly branched polymers renormalized field theory we present a minimal dynamical model for randomly branched isotropic polymers and we study this model in the framework of renormalized field theory for the swollen phase we show that our model provides a route to understand the well established dimensional reduction results from a different angle for the collapse transition we uncover a hidden becchi rouet stora supersymmetry signaling the sole relevance of tree configurations we correct the long standing one loop results for the critical exponents and we push these results on to two loop order for the collapse transition we find a runaway of the renormalization group flow which lends credence to the possibility that this transition is a fluctuation induced first order transition our dynamical model allows us to calculate for the first time the fractal dimension of the shortest path on randomly branched polymers in the swollen phase as well as at the collapse transition and related fractal dimensions

two component extreme value distribution for flood frequency analysis theoretical considerations supported by statistical analysis of 39 annual flood series afs of italian basins suggest that the two component extreme value tcev distribution can be assumed as a parent flood distribution i e one closely representative of the real flood experience this distribution belongs to the family of distributions of the annual maximum of a compound poisson process which is a solid theoretical basis for afs analysis however the two parameter distribution of this family obtained on the assumption of identically distributed floods does not account for the high variability of both observed skewness and largest order statistics so that a significant number of observed floods qualify as outliers under this distribution the more general tcev distribution assumes individual floods to arise from a mixture of two exponential components its four parameters can be estimated by the maximum likelihood method a regionalized tcev distribution with parameters representative of a set of 39 italian afs s was shown to closely reproduce the observed distribution of skewness and that of the largest order statistic

elliptic systems involving the critical exponents and potentials abstract in this paper we investigate a singular elliptic system which involves the critical sobolev exponent and multiple hardy type terms by employing variational methods the existence of its positive solutions is established by the moser iteration method some asymptotic properties of its nontrivial solutions at the singular points are verified

existence of multiple positive solutions to singular elliptic systems involving critical exponents abstract this paper is devoted to investigate multiple positive solutions to a singular elliptic system where the nonlinearity involves a combination of concave and convex terms by exploiting the effect of the coefficient of the critical nonlinearity and a variational method we establish the main result which is based on the argument of the compactness

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

quasilinear elliptic system with coupling on nonhomogeneous critical term abstract we study the existence of multiple solutions for a quasilinear elliptic system of gradient type with the possibility of coupling on the critical and subcritical terms which are not necessarily homogeneous the solutions are obtained from a version of the symmetric mountain pass theorem a version of the concentration compactness principle for this class of systems allows us to verify that the palais smale condition is satisfied below a certain level

multiple positive solutions for a quasilinear elliptic system with critical exponent and sign changing weight abstract in this paper our main purpose is to establish the existence of multiple positive solutions of a quasilinear elliptic system with sobolev critical nonlinearities and sign changing weight by some standard variational methods by using the n ehari manifold fibering maps and the lusternik schnirelmann category we study the topology of the global maximum set f of f x and show the system has at least c a t f f 1 distinct positive solutions where cat f f denotes the lusternik schnirelmann category of f in f

problemes de neumann non lineaires sur les varietes riemanniennes nonlinear neumann problems on riemannian manifolds let m g be a c compact riemannian manifold of dimension n 2 whose boundary b is an n 1 dimensional submanifold and let m m b be the interior of m study of neumann problems of the form x 0 in m d dn g y 0 on b where for every t x y r m b t x and g t y are bounded by c 1 t a or c exp t a application to the determination of a conformal metric for which the scalar curvature of m and the mean curvature of b take prescribed values

symmetry properties in systems of semilinear elliptic equations abstract we investigate symmetry properties of solutions of systems of semilinear elliptic equations the two main tools we use consist of the maximum principle and the device of moving parallel planes to a critical position and then showing that the solution is symmetric about the limiting plane an application to the belousov zhabotinskii chemical reaction is given

the performance of the two component extreme value distribution in regional flood frequency analysis the performance of the regional two component extreme value tcev estimation procedure in estimating both dimensionless regional frequency curves showing the t year flood as a multiple of the mean annual flood and site curves incorporating local and regional information was assessed using computer simulation experiments it was found that the tcev procedure produces estimates of both dimensionless regional curves and scaled site quantiles that are relatively unbiased but very variable when data are drawn from tcev or wakeby parents although estimates are very biased when data follow a gev distribution the tcev procedure is robust in the sense that its worst efforts are less bad than those of the alternatives considered but performance declines significantly as sample sizes reduce

critical growth fractional elliptic systems with exponential nonlinearity abstract we study the existence of positive solutions for the system of fractional elliptic equations of the type 1 2 u p p q f x u p 2 u v q h 1 u v e u 2 v 2 in 1 1 1 2 v q p q f x u p v q 2 v h 2 u v e u 2 v 2 in 1 1 u v 0 in 1 1 u v 0 in r 1 1 where 1 p q 2 h 1 u v 2 u 2 u 2 u v h 2 u v 2 v 2 u v 2 v and 2 here 1 2 is the fractional laplacian operator we show the existence of multiple solutions for suitable range of by analyzing the fibering maps and the corresponding nehari manifold we also study the existence of positive solutions for a superlinear system with critical growth exponential nonlinearity

multiplicity of positive solutions for a p q laplacian system with concave and critical nonlinearities abstract in this paper we consider a p q laplacian system with concave and sobolev critical nonlinearities by using the n ehari manifold fibering maps and the lusternik schnirelman category we prove that the problem has at least cat 1 distinct positive solutions where cat denotes the lusternik schnirelman category of in itself

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

morse theory for symmetric functionals on the sphere and an application to a bifurcation problem abstract this paper uses conley s index to study the cortical points of a function f on a finite dimensional sphere in presence of a symmetry group the authors prove a theorem which leads to a lower bound on the number of critical points of f when the group is finite even if the action is not free this investigation has been motivated by the following bifurcation problem au lambda where a is a variational g equivariant operator an estimated on the number of branches bifurcating from an eigenvalue of a 0 is given author

high energy positive solutions for a critical growth dirichlet problem in noncontractible domains abstract in this paper we consider the dirichlet problem for a critical growth elliptic system of two equations in a noncontractible domain by means of variational method we establish the existence of positive solutions with high energy

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

simulations of lattice animals and trees the scaling behaviour of randomly branched polymers in a good solvent is studied in two to nine dimensions using as microscopic models lattice animals and lattice trees on simple hypercubic lattices as a stochastic sampling method we use a biased sequential sampling algorithm with re sampling similar to the pruned enriched rosenbluth method perm used extensively for linear polymers essentially we start simulating percolation clusters either site or bond re weigh them according to the animal tree ensemble and prune or branch the further growth according to a heuristic fitness function in contrast to previous applications of perm this fitness function is not the weight with which the actual configuration would contribute to the partition sum but is closely related to it we obtain high statistics of animals with up to several thousand sites in all dimension 2 d 9 in addition to the partition sum number of different animals we estimate gyration radii and numbers of perimeter sites in all dimensions we verify the parisi sourlas prediction and we verify all exactly known critical exponents in dimensions 2 3 4 and 8 in addition we present the hitherto most precise estimates for growth constants in d 3 for clusters with one site attached to an attractive surface we verify for d 3 the superuniversality of the cross over exponent at the adsorption transition predicted by janssen and lyssy but not for d 2 there we find 0 480 4 instead of the conjectured 1 2 finally we discuss the collapse of animals and trees arguing that our present version of the algorithm is also efficient for some of the models studied in this context but showing that it is not very efficient for the classical model for collapsing animals

on a conjecture of lin ni for a semilinear neumann problem let q be a bounded domain in rn n 3 and a 0 we consider au au u n 2 n 2 in q2 u 0 in q au av 0 on i2 and show that for a sufficiently small the minimal energy solutions are only constants

on a nonhomogeneous elliptic system with changing sign data abstract in this paper we give some existence results for multiple positive solutions to the following nonhomogeneous elliptic system s u a u 1 u u 1 v 1 f x in v b v 1 u 1 v v 1 g x in u v 0 on where is a regular bounded domain in r n n 3 0 a b nonnegative reals and are positive parameters and f g are given changing sign functions