linear maps on algebraic groups abstract let g be an irreducible simple classical algebraic subgroup of sl n c the n n matrices of determinant one we discuss the problem of classifying all invertible linear maps t on m n c such that t g g this has already been solved with two general exceptions we show how to eliminate one of these two cases in general t must have the form t x pxq or t x px t q for suitable invertible matrices p and q

linear preservers between matrix modules over connected commutative rings abstract let r be a connected commutative ring with identity 1 r contains no idempotents except 0 and 1 and let m n r be the r module of all n n matrices over r r is said to be idempotence diagonalizable if every idempotent matrix over r is similar to a diagonal matrix for two arbitrary positive integers n and m we characterize a linear maps from m n r to m m r preserving tripotence when r is any idempotence diagonalizable ring with the units 2 and 3 and b linear maps from m n r to m m r preserving inverses respectively drazin inverses group inverses 1 inverses 2 inverses and 1 2 inverses when r is either any idempotence diagonalizable ring with the units 2 and 3 or any commutative principal ideal domain with at least one unit except for 1 and 2 these characterizations are completed by using an idempotence preserving result obtained by cao linear maps preserving idempotence on matrix modules over some rings j natur sci heilongjiang univ 16 1 1999 1 4 moreover we also give a simple proof of cao s result

linear maps preserving idempotents of tensor products of matrices abstract let f be a field of characteristic not 2 and m n the algebra of all n n matrices over f the aim of this paper is to characterize linear maps m m 1 m l m m 1 m l such that a 1 a l is an idempotent whenever a 1 a l is an idempotent

variational approach and exact solutions for a generalized coupled zakharov kuznetsov system abstract in the present paper we obtain a variational principle for a generalized coupled zakharov kuznetsov system which does not admit any lagrangian formulation in its present form the eminent noether s theorem will then be employed to compensate for this approach in addition exact solutions will be constructed for the generalized coupled zakharov kuznetsov system using the kudryashov method and the jacobi elliptic function method

lie point symmetries of the lane emden systems abstract it is shown that a lie point symmetry of the lane emden system is a noether symmetry if and only if its parameters belong to the critical hyperbola

lane emden systems with negative exponents we study the elliptic system u u pv qin v u rv sin u v 0on in a bounded domain rn n 1 with a smooth boundary p s 0 and q r 0 we investigate the existence non existence and uniqueness of c2 c solutions in terms of p q r and s a necessary and sufficient condition for the c1 regularity of solutions up to the boundary is also obtained

additive operators preserving idempotent matrices over fields and applications abstract suppose f is a field of characteristic not 2 let m n f be the algebra of all n n matrices over f and let a 2 a 3 a 1 and a be the semigroups of all additive operator on m n f that preserve idempotence preserve tripotence preserve inverses of matrices and preserve group inverses of matrices respectively the main result in this paper is that the semigroup a 2 is generated by transposition similarity the operators x x for fixed arbitrary injective endomorphisms on f and the operators x tr x for fixed arbitrary additive maps from f to m n f with 1 o as applications we determine the structures of a 3 a 1 and a when the characteristic of f is also not 3

linear operators preserving certain equivalence relations originating in system theory abstract let f be c or r a finite dimensional linear time invariant system is described in state space form by xdot ax bu y cx du and is identified with the matrix 4 tuple a b c d where x f n u f m y f p and a b c d are matrices of appropriate sizes and with entries in f for fixed n m p let m be the linear space of all systems a b c d equivalence relations can be defined on m based on the possibility of changes of basis inthe state space the input space or the output space and the possibility of state feedback and or output feedback we characterize those nonsingular linear operators on m that satisfy x y whenever x y

linear preserver problems a brief introduction and some special techniques abstract linear preserver problems concern the characterization of linear operators on matrix spaces that leave certain functions subsets relations etc invariant the earliest papers on linear preserver problems date back to 1897 and a great deal of effort has been devoted to the study of this type of question since then we present a brief picture of the subject aiming at giving a gentle introduction to the reader then we describe some techniques used in our recent papers on this type of problem

strongly preserver problems in banach algebras and c algebras abstract let a and b be banach algebras assume that a is unital we prove that an additive map t a b strongly preserves drazin or equivalently group invertibility if and only if t is a jordan triple homomorphism when a and b are c algebras we characterize the linear maps strongly preserving generalized invertibility in the jordan systems sense and as consequence we determine the structure of selfadjoint linear maps strongly preserving moore penrose invertibility

a new approach to function based hypothesis testing in location scale families motivated by two applications in the mining industry we introduce a new approach to testing the hypothesis that two sampled distributions are simply location and scale changes of one another the test applicable to both paired data and two sample data is based on the empirical characteristic function more conventional techniques founded on the empirical distribution function suffer from serious drawbacks when used to test for location scale families in the motivating applications knowing that the distributions differ only in location and scale has significant operational and economic advantages enabling protocols for one type of data to be applied directly to another supplementary material in the form of matlab code is available online

linear maps preserving idempotence on matrix modules over principal ideal domains abstract let r be a commutative principal ideal domain t m n r m m r an r linear map which preserves idempotence we determine the forms of t when n m and r f 2 and solve some of beasley s open problems as a consequence we prove that the set l r of all r linear maps on m n r which preserve both idempotence and nonidempotence is a proper subset of f r the set of all linear maps on m n r that preserve idempotence when the characteristic of r is 2

a test for normality based on the empirical characteristic function our aim in the present paper is to suggest a simple test of the composite hypothesis of normality against the alternative that the underlying distribution is long tailed the test is based on the behaviour of the empirical characteristic function in the neighbourhood of the origin and is very competitive with several well known tests for normality only a table of critical points is required for its implementation we begin by describing the philosophy behind the test let q be the characteristic function of the sampling distribution and set

linear operators preserving idempotent matrices over fields abstract suppose f is a field we show that if the characteristic of the field is not 2 then the semigroup of linear operators on the n n matrices over f that preserve idempotence is the group g f generated by transposition and similarity chan lim and tan have previously established that theorem for the real and complex fields by other methods we also show that the semigroup l f of linear operators on the n n matrices over f that preserve both idempotence and nonidempotence is g f when the characteristic of f is not 2 we determine the structure of l f when the characteristic of f is 2 and present some open problems

linear maps preserving drazin inverses of matrices over fields abstract let f be a field with at least five elements m n f the n n full matrix algebra over f in this paper we determine the forms of linear maps from m n f to m m f preserving drazin inverses of matrices under ch f 2 and m n 1 and also determine the forms of linear bijections from m n f to itself preserving drazin inverses of matrices under ch f 2 and n 1

symmetry analysis of the bidimensional lane emden systems abstract we carry out a complete group classification of the nonlinear lane emden systems in dimension two the noether symmetries are found and their corresponding conservation laws are established

positive solutions of lane emden systems with negative exponents existence boundary behavior and uniqueness abstract we study the existence boundary behavior and uniqueness of solutions for the singular elliptic system u u p v q v u r v s u 0 v 0 x u v 0 where is a bounded domain with smooth boundary in r n p s 0 and q r 0 our results are obtained in a range of p q r s different from those in m ghergu lane emden systems with negative exponents j funct anal 258 2010 3295 3318

a test for normality based on the empirical characteristic function summary an omnibus test of normality is proposed which has high power against many alternative hypotheses the test uses a weighted integral of the squared modulus of the difference between the characteristic functions of the sample and of the normal distribution together with the one to one correspondence between t and f x suggest utilizing kn t in statistical inference here we use n t to test the composite hypothesis that f x is normal let 00 t exp it1 1t2 a2 be the characteristic function under the null hypothesis with 1u and u2 the unspecified mean and variance the test introduced here is based on a weighted integral over t of the squared modulus of kn t o t where 0 t depends on sample estimates of ju and a2 we compare the power of the test with that of prominent tests based on order statistics and on sample moments heathcote 1972 and feigin heathcote 1977 have previously considered using either the real or imaginary part alone of 4n t in tests of simple hypotheses their tests relied on the fact that for given t either component of 4n t is asymptotically normal with mean given by its population counterpart if the alternative hypothesis is also simple it may be possible to find a value of t that maximizes the power of the test in large samples epps singleton pulley 1982 showed how the sample moment generating function may be employed to test composite hypotheses that the data come from one or the other of two separate families of distributions murota takeuchi 1981 have recently proposed a location and scale invariant test based on the statistic an t i n t s 12 where s is the sample standard deviation applied to the problem of testing normality an t was found to have high power in the vicinity of t 10 against members of six families of symmetric alternatives but its

nonparametric confidence bands for a quantile comparison function this article develops statistical methods useful for comparing the marginals f and g of a bivariate distribution such comparisons are appropriate in the analysis of matched pair data involving a treatment and a control or two treatments the quantile comparison functionq g 1 f proposed by lehmann as a generalized measure of treatment effect in fully randomized experiments is shown to be applicable and also useful in the analysis of matched pair data nonparametric simultaneous confidence bands for q are constructed using asymptotic and permutation methods the copula of the bivariate distribution plays a significant role in the methodology application of the results is illustrated on a dataset from an industrial experiment

additive idempotence preservers abstract let a be a local matrix algebra over a field of characteristic different from 2 b an arbitrary algebra and x y banach spaces additive mappings a b which preserve idempotents are characterized the result is then used in classifying additive surjections b x b y which preserve idempotents and do not annihilate finite rank operators

duality between some linear preserver problems iii c spectral norms and skew symmetric matrices with fixed singular values abstract let f denote either the complex field c or the real field r let v be sn f or kn f the vector spaces of all n n symmetric and skew symmetric matrices respectively over f for c c1 cn 0 with c1 cn 0 the c spectral norm of a matrix a v is the quantity a c i l n c i i a where 1 a n a are the singular values of a let d d1 dn 0 with d1 dn 0 we study the linear isometries between the normed spaces v c and v d by using the fact that they are dual transformations of the linear operators which map d onto c where c x v x has singular values c 1 c n it is shown that such isometries and hence their dual transformations exist if and only if c and d are scalar multiples of each other in such case we completely determine the structure of such isometries and prove that they and their dual transformations belong to a same class of operators in the proof we obtain characterizations of the extreme points of the unit ball in v for different cases with respect to c which is of independent interest

special conformal groups of a riemannian manifold and lie point symmetries of the nonlinear poisson equation abstract we obtain a complete group classification of the lie point symmetries of nonlinear poisson equations on generic pseudo riemannian manifolds m using this result we study their noether symmetries and establish the respective conservation laws it is shown that the projection of the lie point symmetries on m are special subgroups of the conformal group of m in particular if the scalar curvature of m vanishes the projection on m of the lie point symmetry group of the poisson equation with critical nonlinearity is the conformal group of the manifold we illustrate our results by applying them to the thurston geometries

hierarchy of conservation laws of diffusion convection equations we introduce notions of equivalence of conservation laws with respect to lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or sets of admissible transformations for classes of such systems we also revise the notion of linear dependence of conservation laws and define the notion of local dependence of potentials to construct conservation laws we develop and apply the most direct method which is effective to use in the case of two independent variables admitting possibility of dependence of conserved vectors on a number of potentials we generalize the iteration procedure proposed by bluman and doran wu for finding nonlocal potential conservation laws as an example we completely classify potential conservation laws including arbitrary order local ones of diffusion convection equations with respect to the equivalence group and construct an exhaustive list of locally inequivalent potential systems corresponding to these equations

linear operators preserving the p q numerical range abstract let bd m be h n or c n n the real linear space of all n n hermitian matrices and the complex linear space of all n n complex matrices respectively for 1 p q n the p q numerical radius of a m is defined and denoted by r p q a e p x ax x d n q x x i q where ep y denotes the pth elementary symmetric function on the eigenvalues of y we characterize the linear operators on m that satisfy rp q a rp q a for all a m

lie and noether symmetries for a class of fourth order emden fowler equations a group classification of a fourth order ordinary differential equation is carried out the noether symmetries are considered and some first integrals are established solutions for special lane emden systems are also obtained from the invariant solutions of the investigated equation

comparison of different approaches to conservation laws for some partial differential equations in fluid mechanics abstract the conservation laws for second order scalar partial differential equations and systems of partial differential equations which occur in fluid mechanics are constructed using different approaches the direct method noether s theorem the characteristic method the variational approach multiplier approach for arbitrary functions as well as on the solution space symmetry conditions on the conserved quantities the direct construction formula approach the partial noether approach and the noether approach for the equation and its adjoint are discussed and explained with the help of an illustrative example on a non linear field equation describing the relaxation to a maxwellian distribution the conservation laws for the non linear diffusion equation for the spreading of an axisymmetric thin liquid drop the system of two partial differential equations governing flow in a laminar two dimensional jet and the system of two partial differential equations governing flow in a laminar radial jet are discussed via these approaches

group analysis of a hyperbolic lane emden system in this paper we carry out a complete noether and lie group classification of the radial form of a coupled system of hyperbolic equations from the noether symmetries we establish the corresponding conserved vectors we also determine constraints that the nonlinearities should satisfy in order for the scaling symmetries to be noetherian this led us to a critical hyperbola for the systems under consideration an explicit solution is also obtained for a particular choice of the parameters

a goodness of fit test based on the empirical characteristic function when parameters must be estimated summary the goodness of fit test using the empirical characteristic function proposed by koutrouvelis 1980 is extended to the case where parameters must be estimated the proposed test statistic is shown to have an asymptotic chi squared distribution with degrees of freedom reduced by the number of parameters estimated

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

commutativity preserving operators on symmetric matrices abstract if is a nonsingular linear operator on n n symmetric matrices over a formally real field n 3 and if preserves commutativity then a cu 1 au f a i where u t u and c are scalar and is a linear functional this is an extension of a result of chan and lim

additive drazin inverse preservers let h be a real or complex hilbert space and b h denote the banach algebra of all bounded linear operators on h for t b h if there exists an operator td b h and a positive integer k such that ttd tdt tdttd td tk 1td tk then t is said to be drazin invertible and td is a drazin inverse of t we say a map b h b h preserves drazin inverse if td t d for every drazin invertible operator t b h in this paper we determine the structures of additive maps on b h preserving drazin inverses

linear preservers on matrices abstract let u denote either the vector space of n n matrices or the vector space of n n symmetric matrices over an infinite field f in this paper we characterize linear mappings l on u that satisfy one of the following properties i l adja adjl a for all a in u ii l preserves idempotent matrices and l in in where f is the real field r or the complex field c iii l ea el a for all a in u where f r or c

rank k preservers and preservers of sets of ranks abstract let t be a linear transformation on the set of m n matrices with entries in an algebraically closed field if t maps the set of all matrices whose rank is k into itself and if n 3 k 2 then the rank of a is the rank of t a for every m n matrix

linear preservers on powers of matrices abstract this paper is concerned with linear maps l on n x n matrices such that i l ak l a k for all a where k is a fixed integer 2 or ii l preserves idempotent or tripotent matrices respectively

modular automorphisms preserving idempotence and jordan isomorphisms of triangular matrices over commutative rings abstract suppose r is a commutative ring with 1 and 2 being the units of r let t n r be the n n upper triangular matrix modular over r and let l r be the set of all r module automorphisms on t n r that preserve idempotence the main result in this paper is that f l r if and only if there exist an invertible matrix u t n r and an idempotence e r such that f x u ex 1 e x u 1 for any x x ij t n r where x x n 1 j n 1 i as applications we determine all jordan isomomorphisms of t n r over the ring r

permanent polya problem for additive surjective maps abstract let m n f denote the set of square matrices of size n over a field f with characteristics different from two we say that the map f m n f m n f is additive if f a b f a f b for all a b m n f the main goal of this paper is to prove that for n 2 there are no additive surjective maps t m n f m n f such that per t a det a for all a m n f also we show that an arbitrary additive surjective map t m n f m n f which preserves permanent is linear and thus can be completely characterized

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 k power k potent preservers between matrix spaces abstract suppose f is a field let mn f be the linear space of all n n matrices over f and let sn f be its subspace consisting of all symmetric matrices let m n k be positive integers with k 2 and let v m n f s n f and w m m f s m f a linear map f v w is called a k power preserver if f a k f ak for every a v and a k potent preserver if f a k f a for any a v with ak a we characterize i linear k power preservers from mn f to mm f when ch f k or ch f 0 ii linear k potent preservers from mn f to mm f when f is an algebraically closed field with ch f 0 iii linear k power preservers from sn f to mm f respectively sm f when ch f k 5 or ch f 0 and iv linear k potent preservers from sn f to mm f respectively sm f when f is an algebraically closed field with ch f 0

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

on the efficiency of empirical characteristic function procedures summary the asymptotic normality and arbitrarily high efficiency of some new statistical procedures based on the empirical characteristic function is established under general conditions

idempotent elements determined matrix algebras abstract let m n r be the algebra of all n n matrices over a unital commutative ring r with 2 invertible v be an r module it is shown in this article that if a symmetric bilinear map from m n r m n r to v satisfies the condition that u u e u whenever u 2 u then there exists a linear map f from m n r to v such that x y f x y x y m n r applying the main result we prove that an invertible linear transformation on m n r preserves idempotent matrices if and only if it is a jordan automorphism and a linear transformation on m n r is a jordan derivation if and only if it is jordan derivable at all idempotent points

two guidelines for bootstrap hypothesis testing two guidelines for nonparametric bootstrap hypothesis testing are highlighted the first recommends that resampling be done in a way that reflects the null hypothesis even when the true hypothesis is distant from the null the second guideline argues that bootstrap hypothesis tests should employ methods that are already recognized as having good features in the closely related problem of confidence interval construction violation of the first guideline can seriously reduce the power of a test sometimes this reduction is spectacular since it is most serious when the null hypothesis is grossly in error the second guideline is of some importance when the conclusion of a test is equivocal it has no direct bearing on power but improves the level accuracy of a test