rank 1 preserving linear maps on nest algebras in this paper we characterize rank 1 preserving linear maps between nest algebras acting on real or complex banach spaces as applications we show that every weakly continuous and surjective local automorphism or anti automorphism on a nest algebra with an additional property is either an automorphism or an anti automorphism furthermore every weakly continuous and surjective local inner automorphism on such nest algebras is in fact an inner automorphism

linear preservers of minimal rank abstract it is proved that a linear transformation on the vector space of upper triangular matrices that maps the set of matrices of minimal rank 1 into itself and either has the analogous property with respect to matrices of full minimal rank or is bijective is a triangular equivalence or a flip about the south west north east diagonal followed by a triangular equivalence the result can be regarded as an analogue of marcus moyls theorem in the context of triangular matrices

additive mappings decreasing rank one abstract let b x be the algebra of bounded operators on a real or complex banach space x and f x a subalgebra of finite rank operators a complete description of additive mappings f x f x which map rank one operators to operators of rank at most one is given

linear transformations on symmetric matrices that preserve commutativity it is shown that if a nonsingular linear transformation t on the space of n square real symmetric matrices preserves the commutativity where n 3 then t a qaqt q a in for all symmetric matricesa for some scalar orthogonal matrix q and linear functional q

multiplicative mappings at some points on matrix algebras let mn be the algebra of all n n matrices and let mn mn be a linear mapping we say that is a multiplicative mapping at g if st s t for any s t mn with st g fix g mn we say that g is an all multiplicative point if every multiplicative linear bijection at g with in in is a multiplicative mapping in mn where in is the unit matrix in mn we mainly show in this paper the following two results 1 if g mn with detg 0 then g is an all multiplicative point in mn 2 if is an multiplicative mapping at in then there exists an invertible matrix p mn such that either s psp 1 for any s mn or t pttrp 1 for any t mn

comparison between weibull and gamma distributions to derive synthetic unit hydrograph using horton ratios the two parameter weibull distribution 2pwd similar to an instantaneous unit hydrograph iuh is parameterized in terms of horton catchment ratios on the basis of a geomorphologic model of catchment response for this the shape and scale parameters of the weibull distribution are expressed analytically in terms of horton s catchment ratios the two parameters of the iuh derived using nash s model which is a two parameter gamma distribution 2pgd are also expressed analytically in terms of horton ratios the performance of the proposed methods is tested for describing a synthetic unit hydrograph suh under limited data conditions a comparison is made with the unit hydrographs derived from the event data of two real catchments and with the existing geomorphological based 2pgd for developing suh given by rosso 1984 the sensitivity analysis of the 2pwd to the nondimensional parameter of the uh a product of peak discharge and time to peak shows to be more sensitive to the shape parameter a than the scale parameter b further examination to find any similarity between the behavior of 2pwd and 2pgd showed that a in 2pwd corresponds to the shape parameter n in the 2pgd and b behaves similar to the scale parameter k in the 2pgd finally practical applicability of the proposed approach to ungauged catchments is tested using field data less

nash model relation to horton order ratios the nash model of the instantaneous unit hydrograph iuh is parameterized in terms of horton order ratios of a catchment on the basis of a geomorphologic model of catchment response the shape parameter of the nash model is found to depend on horton s numbers ra rb and rl of a catchment thus catchment geomorphology can provide a synthesis of the shape of the hydrologic response the scale parameter of the nash model results to be a time varying character depending on both geomorphology and average streamflow velocity along the stream network thus the time scale of the iuh could account for the variability of the hydrologic response for different storms and throughout a storm

operators preserving the strong birkhoff james orthogonality on b h abstract we characterize the class of surjective conjugate linear mappings b h b h that preserve the strong birkhoff james orthogonality in both directions we also give characterizations of rank one operators as well as coisometries in terms of the strong birkhoff james orthogonality

definition of new equivalent indices of horton strahler ratios for the derivation of the geomorphological instantaneous unit hydrograph 1 the horton strahler concept has been important in river basin geomorphology it describes scaling properties and identifies giuh but has also attracted criticisms because it depends on the threshold area s which is used to extract the channel network from digital elevation models dem on the position of the outlet and on the few number of ratios used to identify the scaling laws to overcome these limitations this paper proposes new indices independently of s and which have similar properties than the horton strahler ratios applications were conducted on seven french basins the methodology consists on analyzing the morphometric properties such as the drained area the number of sources and the length of the channel network as a function of s the results show that horton strahler ratios vary considerably with s particularly while the order length l is a staircase function of s results show that the channel network is articulated around two main nodes independent of s which are descriptors of l then we compared the properties of horton strahler laws to those obtained from self similarity analysis which enables to define new indices independent of s these indices are calculated automatically from dem have similar properties as the horton strahler ratios and are used to calculate the giuh independently of s the four new descriptors rbe rle rae and le which have similar properties as rb rl ra and l respectively are equivalent to those of horton strahler s laws and can be used as indicators of hydrological similarity for catchment comparison and regionalization

best linear unbiased design hyetograph under the conditions of system linearity and stationarity of the precipitation process we derive the hyetograph associated with any given flood discharge q using best linear unbiased estimation blue theory the blue hyetograph depends explicitly on the correlation characteristics of the rainfall process and the instantaneous unit hydrograph iuh of the basin when the correlation time of the rainfall process is short relative to the dispersion of the iuh the shape of the blue hyetograph is the mirror image of the iuh itself in the opposite case the design hyetograph is the mirror image of the rainfall correlation function the procedure is extended from lumped to semidistributed and distributed basins in the latter case we obtain simultaneous design hyetographs for each subbasin or each site in the basin the analytical findings and the possibility of regionalization are verified using synthetic and recorded rainfall time series with excellent agreement in both cases because of its simplicity robustness and theoretical basis the proposed procedure should be appealing for practical use particularly when not only the peak but the entire flood hydrograph is required

adaptive calibration of a conceptual model for flash flood forecasting the adaptive use of a conceptual model for real time flow forecasting is investigated maximum likelihood and ordinary least squares estimation criteria are considered and the performance of maximum likelihood techniques for autocorrelated amle and heteroscedastic hmle errors is analyzed jointly with that provided by the commonly used ordinary least squares estimation olse technique streamflow forecasts are compared for three rivers in central italy obtained by amle hmle and olse adaptive calibration of a simple conceptual model describing the rainfall runoff transformation by accounting for hortonian infiltration and linear basin response to rainfall excess although model residuals display both autocorrelation and heteroscedasticity olse is found to provide a rather satisfactory performance because the olse technique also requires less computational effort compared to that for amle and hmle one could consider olse as a suitable option for real time model operation

linear maps preserving the minimum and surjectivity moduli of hilbert space operators abstract let b h be the algebra of all bounded linear operators on a complex infinite dimensional hilbert space h for every t b h let m t and q t denote the minimum modulus and surjectivity modulus of t respectively let b h b h be a surjective linear map in this paper we prove that the following assertions are equivalent i m t m t for all t b h ii q t q t for all t b h iii there exist two unitary operators u v b h such that t u t v for all t b h this generalizes the result of mbekhta 7 theorem 3 1 to the non unital case

a spectral characterization of operators having rank k abstract let a b x the algebra of all bounded linear operators on a complex banach space x and let k be a positive integer it is proved that a has rank k if and only if i k 1 m 1 t c m a t for every t b x and some nonzero scalars c 1 c k 1 and ii k m 1 t c m a t for some t b x and some distinct scalars c 1 c k

on the use of digital elevation model data for hortonian and fractal analyses of channel networks a common method of channel network extraction from digital elevation model dem data is based on specification of a threshold area ath that is the minimum support area required to drain to a point for a channel to form current efforts to predict ath from dem data are inconclusive and usually an arbitrary constant ath value is chosen for channel network extraction in this paper we study the effects of threshold area selection on the morphometric properties such as drainage density length of drainage paths and external and internal links and scaling properties such as horton s laws and fractal dimension of a channel network we also study the related problem of dem data resolution and its effect on estimation of scaling properties the results indicate that morphometric properties vary considerably with ath and thus values reported without their associated ath are meaningless and should be used in hydrologic analysis with caution also the completeness of a channel network in terms of having the outlet stream flowing directly into a higher order stream is found to depend on ath in a random unpredictable way even if only the complete channel networks are used in the analysis the statistical variability of scaling properties estimates due to ath selection is significant and can be of comparable size to the variability due to dem resolution and variability between estimates of different river networks our analysis highlights the need to carefully study the problem of network source representation or channel initiation scale from dems which will point to an appropriate ath for channel network extraction and estimation of morphometric properties

on self similarity and self affinity of drainage basins an approach is proposed which allows consideration from common positions the self similar and self affine properties of river drainage basins and which introduces respective characteristics of their fractal structure horton s 1945 model has been assumed as the basis of this study it is shown that self similarity of river drainage basins is characterized by the self similarity dimension ds ln rb ln rl in the case of self affinity two scaling indices dl ln rb ln rl and dw ln rb ln ra rl are required the combinations of which determine the hurst h dl dw index characterizing the degree of drainage basins self affinity and the lacunary dimension dg 2dldw dl dw characterizing the degree of lacunarity or noncompactness of drainage basins on the basis of analysis of published data from rivers in the united states italy russia and romania the conclusion is drawn that river drainage basins are generally noncompact dg 2 and self affine h 1 fractal objects besides for a quantitative description of river drainage basins a new parameter is introduced which characterizes the degree to which a large catchment is filled with smaller ones

fractal relation of mainstream length to catchment area in river networks institute of hydraulics university of genoa italymandelbrot s 1982 hypothesis that river length is fractal has been recently substantiated byhjelmfelt 1988 using eight rivers in missouri the fractal dimension of river length d is derived herefrom the horton s laws of network composition this results in a simple function of stream length andstream area ratios that is d max 1 2 log rl og ra three case studies are reported showing thisestimate to be coherent with measurements of d obtained from map analysis the scaling properties ofthe network as a whole are also investigated showing the fractal dimension of river network d todepend upon bifurcation and stream area ratios according to d min 2 2 log rb log ra theseresults provide a linkage between quantitative analysis of drainage network composition and scalingproperties of river networks

additive maps on standard operator algebras preserving invertibilities or zero divisors let a and b be standard operator algebras on infinite dimensional complex banach spaces x and y respectively and let be an additive surjection from a onto b we prove that if is unital and preserves any one of left right invertibility left right zero divisors left right topological divisors of zero quasi affinity injectivity surjectivity range density lower boundedness and left right maximal ideals in both directions then it has one of the following forms isomorphism conjugate isomorphism anti isomorphism and conjugate anti isomorphism we also show that preserves zero products in both directions if and only if is either an isomorphism or a conjugate isomorphism

a geomorphoclimatic theory of the instantaneous unit hydrograph the instantaneous unit hydrograph is conceived as a random function of climate and geomorphology varying with the characteristics of the rainfall excess the probability density functions of the peak and time to peak of the iuh are analytically derived as functions of the rainfall characteristics and the basin geomorphological parameters the main characteristics of these pdf s are studied and a new approach to hydrologic similarity is initiated under the concept of the geomorphoclimatic iuh for a given set of geomorphologic characteristics and a particular intensity and duration of rainfall the peak and time to peak of the iuh corresponding to those values can be easily estimated

convergence and approximation of semigroups of lipschitz operators abstract a convergence theorem and an approximation theorem for semigroups of lipschitz operators are given these theorems are applied to a semi discrete approximation problem for a quasi linear wave equation with damping and a finite difference method for a quasi linear equation of kirchhoff type

linear preservers on triangular matrices abstract let t n f denote the vector space of all n n upper triangular matrices over a field f we characterize those linear transformations t on t n f that satisfy one of the following properties 1 t preserves rank one matrices 2 t preserves both singular and nonsingular matrices 3 t is nonsingular and t adj a adj t a for all a t n f

linear operators preserving adjoint matrix between matrix spaces abstract we characterize the linear operators from the linear space of n n matrices into the linear space of m m matrices over any field f that preserve adjoint matrix where n 3

what controls the width function shape and can it be used for channel network comparison and regionalization 1 the width function captures the essential features of the catchment s giuh s response this paper aims to identify the morphometric properties which control the shape of the width function and assess whether these properties can be used as similarity indices for catchment comparison a new deterministic iterative model of the width function is proposed on the basis of a conceptualization of the topology of the channel network and exploiting the morphometric characteristics of internal and external nodes tests are carried out on eleven french catchments and compared to the reference peano catchment results show that the morphometric properties of three main internal and external nodes such as the drained area the distance to the outlet and the position on the channel network are useful descriptors for modeling the width function and for representing the scaling properties of a channel network while the giuhs based on horton strahler ratios are strongly related to the method used to extract the channel network from the dem the new indices are independent of the method used they are sufficient descriptors to reproduce the main shape of the width function the peak the time to peak and the main properties such as non negativity non stationarity and power law decay of the spectrum they may be used to establish catchment typology to compare catchments and to classify the width function peaks for catchment regionalization

linear additive preservers of rank 2 on spaces of alternate matrices over fields abstract let kn f be the linear space of all n n alternate matrices over a field f and let k n 2 f be its subset consisting of all rank 2 matrices an operator kn f kn f is said to be additive if a b a b for any a b kn f linear if is additive and aa af a for every a f and a kn f and a preserver of rank 2 on kn f if k n 2 f k n 2 f when n 4 we characterize all linear respectively additive preservers of rank 2 on kn f over any field respectively any field that is not isomorphic to a proper subfield of itself

spectrum preserving linear maps abstract let x and y be banach spaces we show that a spectrum preserving surjective linear map from b x to b y is either of the form t ata 1 for an isomorphism a of x onto y or the form t bt b 1 for an isomorphism b of x onto y

linear transformations between matrix spaces that map one rank specific set into another we characterize in several instances those linear transformations from the linear space of m n matrices into the linear space of p q matrices that map the set of matrices having a fixed rank into the set of matrices having a fixed rank examples are given showing that in contrast with the case of linear transformations on the linear space of m n matrices mapping a rank specific set into itself in the more general case of linear transformations between two full matrix spaces often one cannot expect neat and predictable results

additive rank one preserving surjections on symmetric matrix spaces we characterize additive rank one preserving surjections on symmetric matrix spaces over a field of characteristic not 2 or 3 as applications the invertibility preservers the determinant preservers and characteristic polynomial preservers have been characterized

linear preservers and representations with a 1 dimensional ring of invariants we determine the group of linear transformations on a vector space v that preserve a polynomial function f on v for several interesting pairs v f using the theory of semisimple algebraic groups in an 1897 paper fro97 frobenius proved that every linear transformation of the n by n real matrices that preserves the determinant is of the form x 7 axb or x 7 ax t b for some a b gln r such that det ab 1 this is the basic example of a linear preserver problem lpp one is given a finite dimensional vector space v over a field k and a polynomial function f v k and one wants to determine the linear transformations of v that preserve f since frobenius many such prob lems have been solved see for example the surveys lp01 pll 92 lt92 and mar62 we develop here a general method that solves several new problems see examples 3 14 and 3 15 and corollaries 7 10 8 3 8 7 8 5 8 8 and 8 11 our method is to introduce an auxiliary group g gl v that is semisimple and such that v is an irreducible representation or weyl module of g in section 2 we determine the normalizer ngl v g of g in gl v we prove in theorem 3 2 that this subgroup equals the stabilizer of a closed g orbit o in the projective space p v i e stabgl v o ngl v g using this result in sections 7 and 8 we solve two families of lpps by reducing the problems in each family to determining this stabilizer these two families consist of representations v with a 1 dimensional ring of g invariant functions generated by f and are examples of prehomogenous vector spaces of parabolic type the two families correspond to the cases where the unipotent radical u of the parabolic subgroup is abelian i e u u 0 or u u is 1 dimensional respectively and we use the general results on representations in these families from rrs92 roh93 and hel12 besides obtaining new results we also recover many known solutions to linear preserver problems the generality of our method is in contrast to many of the proofs in the literature which typically are highly dependent on the particular choice of v and f the arguments in pd95 and gur97 are notable exceptions further we require only very weak assumptions about the field k at most we require that the characteristic is 6 2 3 and determine the preserver precisely and not just its identity component or lie algebra

approximation of semigroups of lipschitz operators abstract this paper is devoted to an approximation theorem of semigroups of lipschitz operators which are closely related with the abstract cauchy problem and an application of the obtained result to the projection method for the two dimensional navier stokes equations

linear operators that preserve pairs of matrices which satisfy extreme rank properties a supplementary version abstract a pair of m n matrices a b is said to be rank sum maximal if a b a b and rank sum minimal if a b a b we characterize the linear operators preserving the set of rank sum maximal pairs over any field and the linear operators preserving the set of rank sum minimal pairs over any field except for 0 1 the linear preservers of the set of rank sum maximal pairs are characterized by using a result about rank preservers proposed by li and pierce amer math monthly 108 2001 591 605 and thereby the linear preservers of the set of rank sum minimal pairs are characterized the paper can be viewed as a supplementary version of several related results

fractal structure and properties of stream networks this paper studies the fractal structure and properties of stream networks through a comparison between stream networks and loopless random aggregate trees five fractal dimensions are recognized for stream networks namely topological dimension dt minimum path dimension dm fractal dimension of stream networks as a whole df diffusion dimension dw and spectral dimension ds mathematical definitions and derivations of the fractal dimensions are proposed which provide a theoretical basis for some recognized empirical relationships in drainage basin geomorphology relationships among the fractal dimensions are examined and the average values of the fractal dimensions for natural stream networks are estimated the hydrological implications of the fractal dimensions of stream networks are also discussed

additive rank one preserving mappings on triangular matrix algebras abstract we classify surjective additive maps on the space of block upper triangular matrices that preserve matrices of rank one as well as linear maps preserving matrices of rank one on fairly general subspaces of matrices

additive mappings preserving operators of rank one abstract let b x be the algebra of all bounded linear operators on a nontrivial real or complex banach space and let f x be the subalgebra of all finite rank operators a characterization of additive mappings on f x which preserve operators of rank one or projections of rank one is given in the real case such mappings are automatically linear

linear rank and corank preserving maps on b h and an application to semigroup isomorphisms of operator ideals abstract we characterize linear rank k nonincreasing rank k preserving and corank k preserving maps on b h the algebra of all bounded linear operators on the hilbert space h this unifies and extends finite dimensional results and results on linear rank 1 non increasing and rank 1 preserving maps in the infinite dimensional case we conclude with an application to semigroup isomorphisms of operator ideals

spectrum preserving additive maps abstract let x and y be complex banach spaces we show that a spectrum preserving surjective additive map from b x to b y is either of the form f ata 1 for a linear isomorphism a of x onto y or of the form t bt b 1 for a linear isomorphism b of x onto y

a trotter kato type result for a second order difference inclusion in a hilbert space abstract a trotter kato type result is proved for a class of second order difference inclusions in a real hilbert space the equation contains a nonhomogeneous term f and is governed by a nonlinear operator a which is supposed to be maximal monotone and strongly monotone the associated boundary conditions are also of monotone type one shows that if a n is a sequence of operators which converges to a in the sense of resolvent and f n converges to f in a weighted l 2 space then under additional hypotheses the sequence of the solutions of the difference inclusion associated to a n and f n is uniformly convergent to the solution of the original problem

approximation of abstract cauchy problems for dissipative operators with respect to metric like functionals abstract this paper discusses approximation of semigroups of locally lipschitz operators by discrete semigroups of local quasi contractions with respect to metric like functionals the main approximation result not only extends a product formula for contractive semigroups generated by maximal dissipative operators in real hilbert spaces but also gives an algorithm for solving a mixed problem for the kirchhoff equation to which the contractive semigroup theory or kato s quasilinear theory cannot directly apply

on a spectral characterization of rank one matrices abstract let a be an n n complex matrix with a 2 0 it is proved that a has rank one if and only if t a t ca t for every rank one matrix t and some fixed scalar c 0 or 1 the condition a 2 0 cannot be dropped in case n 4

linear additive preservers of ranks 2 and 4 on alternate matrix spaces over fields abstract let kn f be the linear space of all n n alternate matrices over a field f an operator f kn f kn f is said to be additive if f a b f a f b for any a b kn f linear if f is additive and f aa af a for every a f and a kn f and a preserver of ranks 2 and 4 on kn f if rank f x rank x for every x kn f with rank x 2 or 4 when n 4 we characterize all linear respectively additive preservers of ranks 2 and 4 on kn f over any field respectively any field that is not isomorphic to a proper subfield of itself furthermore it is also shown that the condition f is not isomorphic to a proper subfield of itself is necessary for the obtained conclusion on additive preservers of ranks 2 and 4 on kn f

a note on fractal channel networks this paper studies the relation between the structure of river networks and the features of their geomorphologic hydrologic response a mathematical formulation of connectivity of a drainage network is proposed to relate contributing areas and the network geometry in view of the connectivity conjecture horton s bifurcation ratio r b tends for high values of strahler s order omega of the basin to the area ratio r a and horton s length ratio r l equals in the limit the single order contributing area ratio r a the relevance of these arguments is examined by reference to data from real basins well known empirical results from the geomorphological literature melton s law hack s relation moon s conjecture are viewed as a consequence of connectivity it is found that in hortonian networks the time evolution of contributing areas exhibits a multifractal behavior generated by a multiplicative process of parameter 1 r b the application of the method of the most probable distribution in view of connectivity contributes new inroads toward a general formulation of the geomorphologic unit hydrograph in particular generalizing its width function formulation a quantitative example of multifractal hydrologic response of idealized networks based on peano s construct for which r b r a 4 r l 2 closes the paper

additive mappings that preserve rank one nilpotent operators let b x be the algebra of bounded operators on a complex infinite dimensional banach space x and f x be the subalgebra of all finite rank operators in b x a characterization of additive mappings on f x which preserve rank one nilpotent operators in both directions is given as applications of this result some additive preservers are described

on positive linear maps preserving invertibility theorem a positive linear map 4 between two c algebras is a jordan homomorphism if d preserves invertibility and the range of is a c algebra a counterexample is given for the case that the range of q is not assumed to be a c algebra this answers a question raised by b russo proc amer math sot 17