maps on idempotent matrices over division rings abstract let d be an arbitrary division ring and p n d the set of all n n idempotent matrices over d under some mild conditions we give a complete description of maps on p n d that preserve either commutativity or order or orthogonality we give examples showing that our assumptions cannot be relaxed much further as an application we will prove a quaternionic analogue of ovchinnikov s result that is important in quantum mechanics other applications of our theorems include results on automorphisms of operator and matrix semigroups local automorphisms linear preserver problems and geometry of matrices and grassmannians

mappings that preserve pairs of operators with zero triple jordan product abstract let f be a field and n 3 suppose s 1 s 2 m n f contain all rank one idempotents the structure of surjections s 1 s 2 satisfying aba 0 a b a 0 is determined similar results are also obtained for a subsets of bounded operators acting on a complex or real banach space x b the space of hermitian matrices acting on n dimensional vectors over a skew field d c subsets of self adjoint bounded linear operators acting on an infinite dimensional complex hilbert space it is then illustrated that the results can be applied to characterize mappings on matrices or operators such that f aba f a b a for all a b for functions f such as the spectral norm schatten p norm numerical radius and numerical range etc

preservers of eigenvalue inclusion sets for a square matrix a let s a be an eigenvalue inclusion set such as the gershgorin region the brauer region in terms of cassini ovals and the ostrowski region characterization is obtained for maps on n n matrices satisfying s a b s a b for all matrices a and b from these results one can deduce the structure of additive or real linear maps satisfying s a s a for every matrix a

preservers of spectral radius numerical radius or spectral norm of the sum on nonnegative matrices abstract let m n be the set of entrywise nonnegative n n matrices denote by r a the spectral radius perron root of a m n characterization is obtained for maps f m n m n such that r f a f b r a b for all a b m n in particular it is shown that such a map has the form a s 1 as or a s 1 a tr s for some s m n with exactly one positive entry in each row and each column moreover the same conclusion holds if the spectral radius is replaced by the spectrum or the peripheral spectrum similar results are obtained for maps on the set of n n nonnegative symmetric matrices furthermore the proofs are extended to obtain analogous results when spectral radius is replaced by the numerical range or the spectral norm in the case of the numerical radius a full description of preservers of the sum is also obtained but in this case it turns out that the standard forms do not describe all such preservers

preservers of eigenvalue inclusion sets of matrix products abstract for a square matrix a let s a be an eigenvalue inclusion set such as the gershgorin region the union of cassini ovals and the ostrowski s set characterization is obtained for maps on n n matrices satisfying s a b s ab for all matrices a and b

more on matrix semigroup homomorphisms abstract we study non degenerate irreducible homomorphisms from the multiplicative semigroup of all 2 by 2 complex matrices to the semigroup of n by n complex matrices if such a homomorphism maps a cyclic unipotent to a cyclic unipotent it is the composition of a symmetric power a field homomorphism used entrywise and a matrix conjugation in the case n 4 we characterise all non degenerate irreducible homomorphisms

nonlocal growth equations a test case for dynamic renormalization group analysis abstract in this paper we discuss nonlocal growth equations such as the generalization of the kardar parisi zhang kpz equation that includes long range interactions also known as the nonlocal kardar parisi zhang nkpz equation and the nonlocal version of the molecular beam epitaxy nmbe equation we show that the steady state strong coupling solution for nonlocal models such as nkpz and nmbe can be obtained exactly in one dimension for some special cases using the fokker planck form of these equations the exact results we derive do not agree with previous results obtained by dynamic renormalization group drg analysis this discrepancy is important because drg is a common method used extensively to deal with nonlinear field equations while difficulties with this method for d 1 has been realized in the past it has been believed so far that drg is still safe in one dimension our result shows differently the reasons for the failure of drg to recover the exact one dimensional results are also discussed

multiplicative mappings of operator algebras nest algebras are the natural analogues of upper triangular matix algebras in an infinite dimensional hilbert space in this paper we study multiplicative isomorphisms of subalgebras of nest algebras which contain all finite rank operators but might contain no idempotents we prove that such multiplicative mappings are automatically additive and linear or conjugate linear

self consistent expansion for the kardar parisi zhang equation with correlated noise a minor modification of the self consistent expansion sce for the kardar parisi zhang kpz system with uncorrelated noise is used to obtain the exponents in systems where the noise has spatial long range correlations for d dimensional systems with correlations of the form d stackrel ensuremath rightarrow r ensuremath r ensuremath t ensuremath t ensuremath 2d 0 stackrel ensuremath rightarrow r ensuremath r ensuremath 2 ensuremath rho ensuremath d ensuremath delta t ensuremath t ensuremath ensuremath rho g0 we find a lower critical dimension d 0 ensuremath rho 2 2 ensuremath rho above which a perturbative edwards wilkinson ew solution appears below the lower critical dimension two solutions exist each in a different distinct region of ensuremath rho for small ensuremath rho s the solution of kpz with uncorrelated noise is recovered for large ensuremath rho s a ensuremath rho dependent solution is found the existence of only one solution in each region of ensuremath rho is not a result of a competition between two solutions but a direct outcome of the sce equation

jordan triple maps abstract let a be a standard operator algebra on a banach space of dimension 1 and b be an algebra over the field of rational numbers let k be a non zero rational number in this note we prove that if a bijection a b satisfies kaba k a b a for all a b a or k abc cba k a b c c b a for all a b c a then is additive

adjacency preserving maps on upper triangular matrix algebras abstract let n be an integer n 3 and t n the algebra of all real n n upper triangular matrices we describe the general form of maps on t n that preserve the adjacency in both directions we apply this result to characterize the semigroup of injective continuous maps on t n preserving the adjacency in one direction only

automorphisms of the poset of skew projections abstract any automorphism of the poset b of all idempotents of the algebra b h of all bounded linear operators in a hilbert space h dim h 3 is shown to be of the form p apa 1 or p ap a 1 with a c where c is the set of all semi linear bijections a h h if h is finite dimensional and the set of all continuous invertible linear or conjugate linear operators in h if h is infinite dimensional further applications of the method are outlined

orthogonality preserving transformations on indefinite inner product spaces generalization of uhlhorn s version of wigner s theorem abstract we present an analogue of uhlhorn s version of wigner s theorem on symmetry transformations for the case of indefinite inner product spaces this significantly generalizes a result of van den broek the proof is based on our main theorem which describes the form of all bijective transformations on the set of all rank one idempotents of a banach space which preserve zero products in both directions

commuting traces of biadditive mappings commutativity preserving mappings and lie mappings biadditive mappings b r r r where r is a prime ring with certain additional properties satisfying b x x x xb x x for all x r are characterized as an application we determine the structures of commutativity preserving mappings lie isomorphisms and lie derivations of certain prime rings

strong commutativity preserving maps on lie ideals abstract let a be a prime ring and let r be a noncentral lie ideal of a an additive map f r a is called strong commutativity preserving scp on r if f x f y x y for all x y r in this paper we show that if f is scp on r then there exist c 2 1 and an additive map r z a such that f x x x for all x r where c is the extended centroid of a unless char a 2 and a satisfies the standard identity of degree 4

additive maps preserving jordan zero products on nest algebras abstract let alg n and alg m be nest algebras associated with the nests n and m on banach spaces assume that n n and m m are complemented whenever n n and m m let alg n alg m be a unital additive surjection it is shown that preserves jordan zero products in both directions that is a b b a 0 ab ba 0 if and only if is either a ring isomorphism or a ring anti isomorphism particularly all unital additive surjective maps between hilbert space nest algebras which preserves jordan zero products are characterized completely

multiplicative semigroup automorphisms of upper triangular matrices over rings abstract suppose r is a ring with 1 and c a central subring of r let tn r be the c algebra of upper triangular n n matrices over r recently several authors have shown that if r is sufficiently well behaved then every c automorphism of tn r is the composites of an inner automorphism and an automorphism induced from a c automorphism of r see 1 5 to generalize these results in this paper we prove that if n 2 and r is a semiprime ring or a ring in which all idempotents are central then f tn r tn r tn r is only regarded as a multiplicative semigroup is a multiplicative semigroup automorphism if and only if there exist a nonsingular matrix p in tn r and a ring automorphism of r such that f a p 1 a p a a ij n n n r where a aij n n

stochastic system identification with noisy input output measurements using polyspectra two new classes of parametric frequency domain approaches are proposed for estimation of the parameters of scalar linear errors in variables models i e linear systems where measurements of both input and output of the system are noise contaminated the first approach consists of linear estimators where using the bispectrum or the integrated polyspectrum of the input and the cross bispectrum or the integrated cross polyspectrum the system transfer function is first estimated at a number of frequencies exceeding one half the number of unknown parameters the estimated transfer function is then used to estimate the unknown parameters using an overdetermined linear system of equations in the second class of approaches quadratic transfer function matching criteria are optimized by using the results of the linear estimators as initial guesses both classes of the parameter estimators are shown to be consistent in any measurement noise that has symmetric probability density function when the bispectral approaches are used the proposed parameter estimators are shown to be consistent in gaussian measurement noise when trispectral approaches are used

on 2 local isometries on continuous vector valued function spaces article history received 24 july 2008 available online 24 december 2008 submitted by j d m wright a not necessarily linear mapping from a banach space x to a banach space y is said to be a 2 local isometry if for any pair x y of elements of x t here is as urjective linear isometry t x y such that tx x and ty y we show that under certain conditions on locally compact hausdorff spaces q k and a banach space e e very 2 local isometry on c0 q e to c0 k e is linear and surjective we also show that every 2 local isometry on p is linear and surjective for 1 p p 2 but this fails for the hilbert space 2

adjacency preservers on invertible hermitian matrices ii abstract fundamental theorem of geometry of hermitian matrices characterizes all bijective maps on the space of all hermitian matrices which preserve adjacency in both directions in this and subsequent paper we characterize maps on the set of all invertible hermitian matrices over a finite field which preserve adjacency in one direction in this first paper it is shown that maps that preserve adjacency on the set of all invertible hermitian matrices over a finite field are necessarily bijective so the corresponding graph on invertible hermitian matrices where edges are defined by the adjacency relation is a core besides matrix theory the proof relies on results from several other mathematical areas including spectral and chromatic graph theory and finite geometry

automorphisms of certain groups and semigroups of matrices characterizations are given for automorphisms of semigroups of nonnegative matrices including doubly stochastic matrices row column stochastic matrices positive matrices and nonnegative monomial matrices the proofs utilize the structure of the automorphisms of the symmetric group realized as the group of permutation matrices and alternating group furthermore for each of the above semi groups of matrices a larger semi group of matrices is obtained by relaxing the nonnegativity assumption characterizations are also obtained for the automorphisms on the larger semi groups and their subgroups subsemigroups as well

system reconstruction based on selected regions of discretized higher order spectra we consider the problem of system reconstruction from arbitrarily selected slices of the nth order output spectrum we establish that unique identification of the impulse response of a system can be performed up to a scalar and a circular shift based on any two one dimensional 1 d slices of the discretized nth order output spectrum n spl ges 3 as long as the distance between the slices and the grid size satisfy a simple condition for the special case of real systems one slice suffices for system reconstruction the ability to choose the slices to be used for reconstruction enables us to avoid regions of the nth order spectrum where the estimation variance is high or where the ideal polyspectrum is expected to be zero as is the case for bandlimited systems we show that the obtained system estimates are asymptotically unbiased and consistent we propose a mechanism for selecting slices that result in improved system estimates we also demonstrate via simulations the superiority in terms of estimation bias and variance of the proposed method over existing approaches in the case of bandlimited systems

adjacency preserving maps on matrices and operators we characterize injective continuous maps on the space of real or complex rectangular matrices preserving adjacent pairs of matrices we also extend hua s fundamental theorem of the geometry of rectangular matrices to the infinite dimensional case an application in the theory of local automorphisms is presented

strong commutativity preserving maps in prime rings with involution abstract let a be a prime ring of characteristic not 2 with center z a and with involution let s be the set of symmetric elements of a suppose that f s a is an additive map such that f x f y x y for all x y s then unless a is an order in a 4 dimensional central simple algebra there exists an additive map s z a such that f x x x for all x s or f x x x for all x s

applying projective geometry to transformations on rank one idempotents abstract we present a short proof of molnar s characterization of bijective transformations on the set of all rank one idempotent operators on a banach space which preserve zero products in both directions an improvement in the finite dimensional case is given we apply these results to describe automorphisms of standard operator semigroups and to improve uhlhorn s version of wigner s theorem

the cumulant theory of cyclostationary time series ii development and applications for pt i see ibid vol 42 no 12 p 3387 3408 1994 the development of the theory of nonlinear processing of cyclostationary time series that is initiated in part i is continued a new type of cumulant for complex valued variables is introduced and used to generalize the temporal and spectral moments and cumulants for cyclostationary time series from real valued to complex valued time series the relations between the temporal and spectral moments and cumulants at the inputs and outputs of several signal processing operations are determined formulas for the temporal and spectral cumulants of complex valued pulse amplitude modulated time series are derived estimators for the temporal moments and cumulants and for the cyclic polyspectra are presented and their properties are discussed the performance of these estimators is illustrated by several computer simulation examples for pulse amplitude modulated time series the theory is applied to the problems of weak signal detection and interference tolerant time delay estimation

commutativity preserving linear maps on central simple algebras abstract let f be a field with char f 0 and let a be a finite dimensional central simple algebra over f with dim f a 4 if a linear map a a satisfies x 2 x x x 2 for all x a in particular if preserves commutativity then is either a standard commutativity preserving map or its range is commutative

anomalous dynamic scaling of the non local growth equations abstract the anomalous dynamic scaling behavior of the d 1 dimensional non local growth equations is investigated based on the scaling approach the growth equations studied include the non local kardar parisi zhang nkpz non local sun guo grant nsgg and non local lai das sarma villain nldv equations the anomalous scaling exponents in both the weak and strong coupling regions are obtained respectively our results show that non local interactions can affect anomalous scaling properties of surface fluctuations

nonparametric polyspectral estimators for kth order almost cyclostationary processes second and higher order almost cyclostationary processes are random signals with almost periodically time varying statistics the class includes stationary and cyclostationary processes as well as many real life signals of interest cyclic and time varying cumulants and polyspectra are defined for discrete time real kth order cyclostationary processes and their interrelationships are explored smoothed polyperiodograms are proposed for cyclic polyspectral estimation and are shown to be consistent and asymptotically normal asymptotic covariance expressions are derived along with their computable forms higher than second order cyclic cumulants and polyspectra convey time varying phase information and are theoretically insensitive to any stationary for nonzero cycles as well as additive cyclostationary gaussian noise for all cycles

additivity of jordan maps on standard operator algebras abstract in this paper we prove that a bijective map form a a standard operator algebra on a banach space of dimension 1 onto a ring that satisfies ab ba a b b a a b a is additive

maps on matrix spaces it is well known that every automorphism of the full matrix algebra is inner we give a short proof of this statement and discuss several extensions of this theorem including structural results for multiplicative maps on matrix algebras characterizations of monotone and orthogonality preserving maps on idempotent matrices some nonlinear preserver results and some recent theorems concerning geometry of matrices we show that all these topics are closely related and point out the connections with physics and geometry several open problems are posed

preservers of radial unitary similarity functions on products of operators abstract let s be a subset of the algebra l h of all bounded linear operators on an infinite dimensional complex hilbert space h and let f s 0 be a radial unitary similarity invariant function under some assumption on s and f characterizations are obtained for surjective maps on s satisfying f t s f t s t s s where the binary operation stands for the product or the jordan semi triple product on operators analogous descriptions are obtained for the finite dimensional case without the surjectivity assumption on

multiplicative maps preserving the higher rank numerical ranges and radii abstract let m n be the semigroup of n n complex matrices under the usual multiplication and let s be different subgroups or semigroups in m n including the special unitary group special general linear group the semigroups of matrices with bounded ranks suppose k a is the rank k numerical range and r k a is the rank k numerical radius of a m n multiplicative maps s m n satisfying r k a r k a are characterized from these results one can deduce the structure of multiplicative preservers of k a

on hua s fundamental theorem of the geometry of rectangular matrices abstract we show that hua s fundamental theorem of the geometry of rectangular matrices can be proved without the bijectivity assumption when the underlying field is the field of real numbers we also give a counterexample showing that this generalization is not possible in the complex case

spectrum and commutativity preserving mappings on triangular matrices we give the description of continuous mappings on the algebra of all upper triangular complex matrices that preserve spectrum and commutativity

identification of systems with cyclostationary input and correlated input output measurement noise an alternative approach to wiener s optimum filtering theory for stationary random time series that is applicable when the system input exhibits cyclostationarity is presented this alternative approach can in principle eliminate performance degradation due to input output corruption this method of system identification is called the speccorr spectral correlation ratio method since the cross spectra in the ratio are actually spectral correlation functions an application to interference tolerant time difference of arrival estimation is described and illustrated by simulation results showing its effectiveness for system identification with severely corrupted input output measurements a comparison of wiener s method to the speccorr method shows the superior performance of the latter

schur multiplicative maps preserving unitarily invariant norms characterizations are obtained for maps on real or complex matrices which preserve both the schur hadamard product and a given unitarily invariant norm

general preservers of invariant subspace lattices let b x be the space of all bounded linear operators on a banach space x and let lata be the lattice of invariant subspaces of the operator a b x we characterize some maps b x b x with one of the following preserving properties lat a b lat a b or lat a b lat ab or lat a b b a lat ab ba or lat a b a lat aba or lat a b lat a b

generalized symmetry transformations on quaternionic indefinite inner product spaces an extension of quaternionic version of wigner s theorem uhlhorn s extension of wigner s unitary antiunitary theorem has been recently generalized by molnar to indefinite inner product spaces we present the quaternionic version of this result

non linear maps preserving solvability let mn be the algebra of all n n complex matrices and let l be the general linear lie algebra gl n c or the special linear lie algebra sl n c a bijective not necessarily linear map l l preserves solvability in both directions if both and 1 map every solvable lie subalgebra of l into some solvable lie subalgebra if n 3 then every such map is either a composition of a bijective lattice preserving map with a similarity transformation and a map aij f aij induced by a field automorphism f c c or a map of this type composed with the transposition we also describe the general form of such maps in the case when n 2 using lie s theorem we will reduce the proof of this statement to the problem of characterizing bijective maps on mn preserving triangularizability of matrix pairs in both directions as a byproduct we will characterize bijective maps on mn that preserve inclusion for lattices of invariant subspaces in both directions

automorphisms of mn partially ordered by rank subtractivity ordering let mn be the space of all n n matrices with coefficients in r or c where n 3 the rank subtractivity or minus partial order on mn is defined by a rsb iff rankb ranka rank b a we characterize bijective mappings on mn such that a rsb iff a rs b a b mn

nonlocal kardar parisi zhang equation with spatially correlated noise the effects of spatially correlated noise on a phenomenological equation equivalent to a nonlocal version of the kardar parisi zhang kpz equation are studied via the dynamic renormalization group drg techniques the correlated noise coupled with the long ranged nature of interactions prove the existence of different phases in different regimes giving rise to a range of roughness exponents defined by their corresponding critical dimensions finally self consistent mode analysis is employed to compare the non kpz exponents obtained as a result of the long range interactions with the drg results

circular lattice filtering using pagano s method recently pagano has found a one to one relationship between multivariate autoregression and scalar periodic autoregressions and derived a set of fundamental yule walker yw type equations for estimating the parameters of the periodic autoregressions in this paper we first obtain a levinson type recursive algorithm for solving the above mentioned yw equations then using this recursion we show a circular lattice structure of the process this enables us to obtain a burg type algorithm which guarantees the filter stability lastly we modify it to an adaptive form for on line computation this circular lattice filter simultaneously performs whitening and orthogonalization of the components of multivariate input samples the most salient feature of the algorithm is that it consists of calculations of scalar quantities thus completely avoiding matrix manipulations accompanying usual multivariate processing methods

uncertain destination dynamics certain dynamical systems exhibit a sensitivity to initial conditions in which the asymptotic state is selected from an infinite number of possible states the phase space of such systems is foliated with attractors each of which is associated with a particular set of initial conditions the associated uncertain destination dynamics can be analyzed by an appropriate reduction of the full system to a subsystem that explicitly yields the dynamics s1063 651x 99 09909 2 pacs number s 05 45 2a recent studies of high dimensional dynamical systems have revealed many new modes of complex evolution such as synchronization 1 on off intermittency 2 and fractal riddled and intermingled basins 3 many of these studies have raised fundamental questions concerning the relationship between model systems and the real systems they attempt to describe 4 in this paper we report on another gross complexity in the evolution of high dimensional systems for many dynamical systems governed by evolution equations of the form

mappings preserving spectrum and commutativity on hermitian matrices the general form of a continuous mapping acting on the real vector space of all n n complex hermitian or real symmetric matrices and preserving spectrum and commutativity is derived it turns out that is either linear or its image forms a commutative set

effect of long range interactions in the conserved kardar parisi zhang equation the conserved kardar parisi zhang equation in the presence of long range nonlinear interactions is studied by the dynamic renormalization group method the long range effect produces new fixed points with continuously varying exponents and gives distinct phase transitions depending on both the long range interaction strength and the substrate dimension d the long range interaction makes the surface width less rough than that of the short range interaction in particular the surface becomes a smooth one with a negative roughness exponent at the physical dimension d 2

coherence invariant mappings on block triangular matrix spaces abstract in this paper we classify bijective mappings on the space of block upper triangular matrices such that both and 1 preserve pairs of matrices whose differences have rank one applications to rank one preservers and semi isomorphisms are considered

matrix semigroup homomorphisms from dimension two to three abstract we characterise all non degenerate homomorphisms from the multiplicative semigroup of all 2 2 matrices over an arbitrary field to the semigroup of 3 3 matrices over the same field in the case of a field of real numbers every irreducible non degenerate homomorphism is a conjugation of the symmetric square

commutativity preserving maps we briefly describe several techniques that have been developed to solve the problem of characterizing commutativity preserving maps we prove a new result describing the general form of injective continuous commutativity preserving maps on full matrix algebras

hua s fundamental theorems of the geometry of matrices and related results abstract we briefly survey some recent improvements of hua s fundamental theorem of the geometry of rectangular matrices then we discuss possible further generalizations as well as some related open problems in the theory of preservers we solve one such open problem using ovchinnikov s characterization of automorphisms of the poset of idempotent matrices using ovchinnikov s result we obtain a short proof of the fundamental theorem of the geometry of square matrices

on the perturbation expansion of the kpz equation we present a simple argument to show that the function of the d dimensional kpz equation d 2 is to all orders in perturbation theory given by beta g r d 2 g r 2 8 pi d 2 text gamma 2 d 2 g r 2 neither the dynamical exponent z nor the roughness exponent have any correction in any order of perturbation theory this shows that standard perturbation theory cannot attain the strong coupling regime and in addition breaks down at d 4 we also calculate a class of correlation functions exactly

hua s fundamental theorem of the geometry of matrices abstract let m n f be the space of all n n matrices over the field f n 2 two matrices a b m n f are adjacent if rank a b 1 hua s fundamental theorem of the geometry of square matrices characterizes bijective maps on m n f that preserve adjacency in both directions in this paper we treat a long standing open problem whether the result of hua holds true under the weaker assumption of preserving the adjacency in one direction only we answer this question in the affirmative in the case that every nonzero homomorphism f f f is surjective for example the field of real numbers has this property in order to prove this result we have to improve ovchinnikov s characterization of automorphisms of the poset of idempotent matrices

on the minimal rank in non reflexive operator spaces over finite fields let u and v be vector spaces over a field k and s be an n dimensional linear subspace of l u v the space s is called algebraically reflexive whenever it contains every linear map g u v such that for all x u there exists f s with g x f x a theorem of meshulam and semrl states that if s is not algebraically reflexive then it contains a non zero operator of rank at most 2n 2 provided that k has more than n 2 elements in the present article we prove that the provision on the cardinality of the underlying field is unnecessary to do so we demonstrate that the above result holds for all finite fields

the cumulant theory of cyclostationary time series i foundation the problem of characterizing the sine wave components in the output of a polynomial nonlinear system with a cyclostationary random time series input is investigated the concept of a pure nth order sine wave is introduced and it is shown that pure nth order sine wave strengths in the output time series are given by scaled fourier coefficients of the polyperiodic temporal cumulant of the input time series the higher order moments and cumulants of narrowband spectral components of time series are defined and then idealized to the case of infinitesimal bandwidth such spectral moments and cumulants are shown to be characterized by the fourier transforms of the temporal moments and cumulants of the time series it is established that the temporal and spectral cumulants have certain mathematical and practical advantages over their moment counterparts to put the contributions of the paper in perspective a uniquely comprehensive historical survey that traces the development of the ideas of temporal and spectral cumulants from their inception is provided

a computationally efficient and interference tolerant nonparametric algorithm for lti system identification based on higher order cyclostationarity a new nonparametric algorithm for the identification of linear time invariant systems is proposed the method is based on the cyclic correlations of the input and output signals with a nonlinear transformation of the input signal consequently although it exploits the higher order cyclostationarity properties of the input and output signals its computational complexity is comparable with that of methods based on second order statistics the proposed estimator of the system transfer function is inherently immune to the presence of noise and interference on both input and output signal measurements and turns out to be asymptotically unbiased and consistent moreover bias and variance of the estimate exhibit a rate of convergence to zero equal to that of estimates based on second order statistics finally simulation results show that the proposed algorithm significantly outperforms in terms of both bias and variance of the estimates several nonparametric identification algorithms previously presented in the literature

reflexivity algebraic reflexivity and linear interpolation introduction this paper was motivated by a discovery that most finite dimensional subalgebras of b h for h an infinite dimensional hilbert space are reflexive with the only obstructions to reflexivity being finite rank considerations proofs section 2 do not depend on multiplicative structure nor on topology so extend to linear subspaces of transformations in an abstract setting abstract reflexivity has been studied in 3 4 7 primarily for singly generated algebras reflexivity properties can be interpreted as linear interpolation properties and we shall adopt this point of view the results of section 2 extend in section 3 to algebraic reflexivity counterparts for countably generated algebraically linear subspaces of bounded linear transformations acting on a banach space as consequences in section 4 we obtain generalizations of two single operator results one is a multivariate version of the result due to kaplansky 10 theorem 15 that a bounded locally algebraic operator acting on a banach space is algebraic the other is a multivariate version of the result due to douglas and foias 5 for hilbert space and to hadwin 7 for a general banach space extending work of fillmore 6 that a bounded non algebraic operator acting on a banach space is topologically algebraically reflexive in section 5 we give an application kindly suggested by d hadwin concerning joint strong similarity orbits of n tupules of operators we wish to thank e azoff k davidson j erdos d hadwin j kraus c lance and a sourour for conversations and some correspon

characterization of jordan homomorphisms on mn using preserving properties abstract let o mn mn n 3 be a continuous mapping preserving spectrum and commutativity in both directions neither linearity nor multiplicativity of i is assumed then i is either an automorphism or an antiautomorphism the same result holds if i preserves spectrum commutativity and rank one matrices

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

generalization of wigner s unitary antiunitary theorem for indefinite inner product spaces we present a generalization of wigner s unitary antiunitary theorem for pairs of ray transformations as a particular case we get a new wigner type theorem for non hermitian indefinite inner product spaces

transformations on the set of all n dimensional subspaces of a hilbert space preserving principal angles wigner s classical theorem on symmetry transformations plays a fundamental role in quantum mechanics it can be formulated for example in the following way every bijective transformation on the set of all 1 dimensional subspaces of a hilbert space h which preserves the angle between the elements of is induced by either a unitary or an antiunitary operator on h the aim of this paper is to extend wigner s result from the 1 dimensional case to the case of n dimensional subspaces of h with n fixed