on graded polynomial identities with an antiautomorphism let g be a commutative monoid with cancellation and let r be a strongly g graded associative algebra with finite g grading and with antiautomorphism suppose that r satisfies a graded polynomial identity with antiautomorphism we show that r is a pi algebra

functional identities in superalgebras abstract the aim of this paper is to establish the theory of functional identities in superalgebras as an application of this theory k supercommuting maps in superalgebras are investigated

generalized functional identities with anti automorphisms and derivations on prime rings i abstract the concept of a generalized functional identity gfi with anti automorphisms and derivations is a generalization of the notion of a generalized polynomial identity gpi with anti automorphisms and derivations in the present paper we show that either a prime ring is gpi or such gfis have only the obvious solutions our results simultaneously generalize the results of martindale rowen lanski kharchenko and chuang on gpis and a number of earlier results on gfis

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

tests of sphericity of normal distributions and the analysis of repeated measures designs the locally best invariant test statistic for testing sphericity of normal distributions is shown to be a simple function of the box geisser greenhouse degrees of freedom correction factor in a repeated measures design because of this relationship it provides a more intuitively appealing test of the necessary and sufficient conditions for valid f tests in repeated measures analysis of variance than the likelihood ratio test the properties of the two tests are compared and tables of the critical values of the box geisser greenhouse correction factor are given

k commuting maps on triangular algebras abstract in this paper k commuting maps on certain triangular algebras are determined as an application we show that every k commuting map on an upper triangular matrix algebra over a unital commutative ring of 2 torsion free or a nest algebra is proper

on herstein s lie map conjectures i first published in transactions american mathematical society in vol 353 no 10 pp 4235 4260 published by the american mathematical society

non parametric detection of the number of signals hypothesis testing and random matrix theory detection of the number of signals embedded in noise is a fundamental problem in signal and array processing this paper focuses on the non parametric setting where no knowledge of the array manifold is assumed first we present a detailed statistical analysis of this problem including an analysis of the signal strength required for detection with high probability and the form of the optimal detection test under certain conditions where such a test exists second combining this analysis with recent results from random matrix theory we present a new algorithm for detection of the number of sources via a sequence of hypothesis tests we theoretically analyze the consistency and detection performance of the proposed algorithm showing its superiority compared to the standard minimum description length mdl based estimator a series of simulations confirm our theoretical analysis

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

lie isomorphisms in prime rings with involution abstract let r and r be prime rings with involutions of the first kind and with respective lie subrings of skew elements k and k furthermore assume rc c 1 4 9 16 25 64 where c is the extended centroid of r it is shown that any lie isomorphism of k onto k can be extended uniquely to an associative isomorphism of k onto k where k and k are respectively the associative subrings generated by k and k

on herstein s lie map conjectures iii abstract in the two papers on herstein s lie map conjectures i and ii solutions of all of herstein s problems concerning lie isomorphisms and derivations were given under the assumption that the algebras involved were of sufficiently high dimension in the present paper we remove this restriction thereby solving herstein s problems in full generality

on lie admissible algebras whose commutator lie algebras are lie subalgebras of prime associative algebras abstract we describe third power associative multiplications on noncentral lie ideals of prime algebras and skew elements of prime algebras with involution provided that x y y x x y for all x y and the prime algebras in question do not satisfy polynomial identities of low degree we also obtain necessary and sufficient conditions for these multiplications to be fourth power associative or flexible

centralizing maps on invertible or singular matrices over division rings abstract let d be a division ring and let m n d be the ring of all n n matrices over d with center z where n 2 is an integer we describe the additive map f m n d m n d such that f x x x f x z for all invertible singular x m n d

event based state estimation with time synchronous updates to reduce the amount of data transfer in networked systems measurements are usually taken only when an event occurs rather than at each synchronous sample instant however this complicates estimation problems considerably especially in the situation when no measurement is received anymore the goal of this paper is therefore to develop a state estimator that can successfully cope with event based measurements and attains an asymptotically bounded error covariance matrix to that extent a general mathematical description of event sampling is proposed this description is used to set up a state estimator with a hybrid update i e when an event occurs the estimated state is updated using the measurement while at synchronous instants the update is based on knowledge that the sensor value lies within a bounded subset of the measurement space furthermore to minimize computational complexity of the estimator the algorithm is implemented using a sum of gaussians approach the benefits of this implementation are demonstrated by an illustrative example of state estimation with event sampling

on additive isomorphisms of prime rings preserving polynomials we study additive isomorphisms of prime rings preserving a multilinear polynomial of degree 2 our main theorem generalizes a number of results obtained for jordan n jordan lie and lie triple isomorphisms of prime rings

characterization of k commuting additive maps on rings abstract let k be a positive integer and r a ring having unit 1 denote by z r the center of r assume that the characteristic of r is not 2 and there is an idempotent element e r such that r satisfies a r e 0 a 0 a r 1 e 0 a 0 z e r e k z e r e and z 1 e r 1 e k z 1 e r 1 e then every additive map f r r is k commuting if and only if f x x h x for all x r where z r and h is an additive map from r into z r as applications all k commuting additive maps on prime rings and von neumann algebras are characterized

centralizing maps in prime rings with involution abstract let r be a prime ring with involution of characteristic 2 with center z skew elements k and extended centroid c theorem suppose k k 0 and k k is an additive map such that x x z for all x k then unless r is an order in a 16 dimensional central simple algebra there exists c and an additive map k c such that x x x for all x k

spectrum sensing in the presence of multiple primary users we consider multi antenna cooperative spectrum sensing in cognitive radio networks when there may be multiple primary users a detector based on the spherical test is analyzed in such a scenario based on the moments of the distributions involved simple and accurate analytical formulae for the key performance metrics of the detector are derived the false alarm and the detection probabilities as well as the detection threshold and receiver operation characteristics are available in closed form simulations are provided to verify the accuracy of the derived results and to compare with other detectors in realistic sensing scenarios

commuting traces of multiadditive mappings abstract letrbe a prime ring andmann additive mapping onrsuch that m x x x 0 for allx r if char r 0 or n then there exist mappings iofrinto the extended centroidcofrsuch that m x x i 0 n i x x n i for allx r if in addition ris not algebraic of bounded degree n then for eachithere exists ani additive mappingmiofriintocsuch that i x mi x x for allx r

on functional identities in prime rings with involution abstract let a be a prime ring with involution let s be the symmetric elements let k be the skew elements let q ml be the maximal left ring of quotients x 1 x m noncommuting variables and e i f j g k h l a m 1 q ml i j k l 1 2 m we study functional identities of the form m i 1 e i i x i m j 1 x j f j j m k 1 g k k x k m l 1 x l h l l 0 for all x 1 x m a where e i i means e i x 1 x i x m etc in case s k is not algebraic of bounded degree 2 m definitive results are obtained as an application k commuting traces of symmetric n additive maps of either s or k into q ml are characterized