additive mappings on von neumann algebras preserving absolute values abstract given hilbert spaces h and k and a von neumann algebra a b h let denote the class of all additive mappings a b k satisfying a a a a the paper shows that if a contains no nonzero abelian central projection then every preserves the operation the r linear combination and up to a commuting operator multiple i 0 the ring multiplication if a contains a nonzero abelian central projection p and if the dimension of k is at least 2 or 2 rank p according to whether or not p can be chosen to be minimal then there exists an additive mapping a b k such that i is a projection and a a for all a a but is neither multiplicative nor adjoint preserving in case a b h the result was proved by molnar bull aust math soc 53 1996 391 when a contained all finite rank operators and by radjabalipour et al linear algebra appl 327 2001 197 under the redundant restriction i i k i k

an algorithm for global minimization of linearly constrained concave quadratic functions we present an algorithm for the global minimization of a quadratic function x y xtqx htx dty over a polytope x y rn k ax by b x 0 y 0 where x h rn y d rk b rm and where a and b are m n and m k matrices respectively and q is an n n symmetric positive definite matrix we first consider the case where k 0 and construct a tight parallelpiped r containing by using an arbitrary set of q conjugate directions and by solving 2n linear programs we show that the convex envelope of with respect to r is linear and obtain an explicit formula for it we then describe a branch and bound algorithm in which the linearity of the convex envelope allows efficient lower bounding for the subproblems for each subproblem we obtain the linear convex envelope of over a smaller parallelepiped r with facets parallel to those of r then we obtain a lower bound by minimizing this convex envelope over r if is the optimal objective value for each e 0 the algorithm generates a sequence of feasible points zj with nonincreasing function values j and a nondecreasing sequence j of lower bounds to moreover if e 0 there exist j0 such that j j e for all j j0 and if e 0 j j converges to 0 the results are then generalized to the case where k is nonzero and possibly much larger than n preliminary computational results are also presented

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

maps preserving peripheral spectrum of generalized products of operators abstract let a 1 and a 2 be standard operator algebras on complex banach spaces x 1 and x 2 respectively for k 2 let i 1 i m be a sequence with terms chosen from 1 k and assume that at least one of the terms in i 1 i m appears exactly once define the generalized product t 1 t 2 t k t i 1 t i 2 t i m on elements in a i let a 1 a 2 be a map with the range containing all operators of rank at most two we show that satisfies that a 1 a k a 1 a k for all a 1 a k where a stands for the peripheral spectrum of a if and only if is an isomorphism or an anti isomorphism multiplied by an mth root of unity and the latter case occurs only if the generalized product is quasi semi jordan if x 1 h and x 2 k are complex hilbert spaces we characterize also maps preserving the peripheral spectrum of the skew generalized products and prove that such maps are of the form a c u a u or a c u a t u where u b h k is a unitary operator c 1 1

scaling anomalies in the coarsening dynamics of fractal viscous fingering patterns we analyze a recent experiment of sharon et al 2003 on the coarsening due to surface tension of fractal viscous fingering patterns fvfps grown in a radial hele shaw cell we argue that an unforced hele shaw model a natural model for that experiment belongs to the same universality class as model b of phase ordering two series of numerical simulations with model b are performed with the fvfps grown in the experiment and with diffusion limited aggregates as the initial conditions we observed lifshitz slyozov scaling t 1 3 at intermediate distances and slow convergence to this scaling at small distances dynamic scale invariance breaks down at large distances

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

a regularized monotonic fuzzy support vector machine model for data mining with prior knowledge incorporating prior knowledge into data mining is an interesting but challenging problem and this study proposes a novel fuzzy support vector machine svm model to explore this issue it considers the fact that in many applications each input point may not be exactly labeled as one particular class and thus it applies a fuzzy membership to each input point it also utilizes expert knowledge concerning the monotonic relations between the response and predictor variables which is represented in the form of monotonicity constraints we formulate the classification problem of a monotonically constrained fuzzy svm called a monotonic fsvm derive its dual optimization problem and theoretically analyze its monotonic property the tikhonov regularization method is further applied to ensure that the solution is unique and bounded a new measure i e the frequency monotonicity rate is proposed to evaluate the ability of the model to retain the monotonicity the results of the experiments on real world and synthetic datasets show that this method which considers different contributions of each data and the prior knowledge of the monotonicity has a number of advantages with regard to predictive ability and retaining monotonicity over the original fsvm and svm models when applied to classification problems

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

a note on unitary similarity preserving linear mappings on b h let h be an infinite dimensional complex hilbert space we give the characterization of surjective mappings on b h that preserve unitary similarity in both directions

completely rank nonincreasing linear maps on spaces of operators we discuss some results and conjectures concerning rank nonincreasing rank preserving completely rank preserving and completely rank nonincreasing linear maps on spaces of operators we show that the main conjectures are equivalent to a statement about closures of joint similarity orbits of k tuples of matrices

local spectrum linear preservers at non fixed vectors abstract for a complex n n matrix t and a vector x c n we denote by t x respectively by r t x the local spectrum respectively the local spectral radius of t at x we prove that m n m n linear has the property that for each t m n there exists a nonzero x t c n such that t x t t x t if and only if there exists a m n invertible such that either t a t a 1 for each t m n or t a t t a 1 for each t m n modulo a multiplication by a unimodular complex number we arrive at the same conclusion by supposing that for each t m n there exists a nonzero x t c n such that r t x t r t x t

similarity preserving linear maps on b h we determine kernels of similarity preserving bounded linear maps on b h and give characterizations for elementary operators of length 1 to be similarity preserving

parallel search algorithms in global optimization a number of parallel search algorithms are proposed and analyzed for constrained global optimization problems algorithms for such problems involve a large number of iterations and function evaluations and a large number of independent local searches concurrent function evaluations are well suited for multiprocessing similarly concurrent iterations used for local minimizers can be implemented using multiprocessors in this paper we consider the global minimization of nonconvex quadratic problems the proposed algorithms are based on the used of linear programming and local search techniques specifically we solve multiple cost row linear programs and closely related nonlinear programs local searches in this approach because the constraint set is unchanged and only the objective function changes the subproblems can be solved independently of each other multitasking and vectorization techniques can be used effectively to exploit the parallelism inherent in these problems

sensor selection for estimation with correlated measurement noise in this paper we consider the problem of sensor selection for parameter estimation with correlated measurement noise we seek optimal sensor activations by formulating an optimization problem in which the estimation error given by the trace of the inverse of the bayesian fisher information matrix is minimized subject to energy constraints fisher information has been widely used as an effective sensor selection criterion however existing information based sensor selection methods are limited to the case of uncorrelated noise or weakly correlated noise due to the use of approximate metrics by contrast here we derive the closed form of the fisher information matrix with respect to sensor selection variables that is valid for any arbitrary noise correlation regime and develop both a convex relaxation approach and a greedy algorithm to find near optimal solutions we further extend our framework of sensor selection to solve the problem of sensor scheduling where a greedy algorithm is proposed to determine non myopic multi time step ahead sensor schedules lastly numerical results are provided to illustrate the effectiveness of our approach and to reveal the effect of noise correlation on estimation performance

on the convergence of cutting plane algorithms for a class of nonconvex mathematical programs we discuss the convergence of cutting plane algorithms for a class of nonconvex programs called the generalized lattice point problems glpp a set of sufficient conditions which guarantee finite convergence are presented although these conditions are usually difficult to enforce in a practical implementation they do illustrate the various factors that must be involved in a convergent rudimentary cutting plane algorithm a striking example of nonconvergence in which no subsequence converges to a feasible solution even when seemingly strong cutting planes are used is presented to show the effect of neglecting one such factor we give an application of our analysis to problems with multiple choice constraints and finally discuss a modification of cutting plane algorithms so as to make finite convergence more readily implementable

nonlinear maps preserving similarity on b h abstract let x be a real or complex banach space with dimension at least 3 n 1 x be the family of all rank one nilpotent operators we give the concrete form of every bijective map n 1 x n 1 x such that t s n 1 x t s n 1 x based on this result we characterize the surjective map b h b h witht s r t s r for all t s r b h where h is a hilbert space real or complex with dimension at least 3

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

spectral preservers and approximate spectral preservers on operator algebras abstract let a and b be unital primitive banach algebras with minimal idempotents we prove that every surjective spectral isometry from a onto b is of the form where c with 1 and is either an isomorphism or an anti isomorphism from a onto b as an application we show that for all banach spaces x and y the spectral nearisometries and the approximate spectrum preserving maps from l x onto l y are perturbations of actual spectral isometries and spectrum preserving maps respectively

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

induced operators on symmetry classes of tensors let v be an n dimensional hilbert space suppose h is a subgroup of the symmetric group of degree m and x h c is a character of degree 1 on h consider the symmetrizer on the tensor space m v s v 1 v m 1 h v 1 1 x v 1 m defined by h and x the vector space m v m x h s v is a subspace of m v called the symmetry class of tensors over v associated with h and x the elements in v m x h of the form s v 1 v m are called decomposable tensors and are denoted by v 1 v m for any linear operator t acting on v there is a unique induced operator k t acting on v m x h satisfying k t v 1 v m tv 1 tv m in this paper several basic problems on induced operators are studied

asymptotic similarity preserving additive maps on b x abstract let x be an infinite dimensional complex banach space and denote b x the algebra of all bounded linear operators acting on x we show that an additive surjective map on b x preserves asymptotic similarity in both directions if and only if there exist a nonzero scalar c an invertible bounded linear or conjugate linear operator a and an asymptotic similarity invariant additive functional on b x such that either t cata 1 t i for all t or t cat a 1 t i for all t in the case that x has infinite multiplicity especially if x is an infinite dimensional hilbert space above asymptotic similarity invariant additive functional is always zero

linear maps preserving products of positive or hermitian matrices abstract in this note we consider linear maps on the complex n n matrix algebra m n preserving products of either two positive matrices a positive matrix and a hermitian matrix or two hermitian matrices we give characterizations of all those injections

the linear preservers of non singularity in a large space of matrices let k be an arbitrary field and v a linear subspace of mn k such that codimv n 1 using a recent generalization of a theorem of atkinson and lloyd 11 we show that every linear embedding of v into mn k which preserves non singularity must be m pmq or m pm t q for some pair p q of non singular matrices of mn k unless n 3 codimv 1

linear maps preserving commutativity abstract commutativity preserving maps on the real space of all real symmetric or complex self adjoint matrices are characterized related results are given for adjoint preserving maps defined on all n n matrices these results are extended to infinite dimensions in the case of invertible maps

analysis of spectral variation and some inequalities a geometric method based on a decomposition of the space of complex matrices is employed to study the variation of the spectrum of a matrix when adapted to special cases this leads to some classical inequalities as well as some new ones as an example of the latter we show that if u v are unitary matrices and k is a skew hermitian matrix such that uv exp k then for every unitary invariant norm the distance between the eigenvalues of v and those of vis bounded by k this generalises two earlier results which used particular unitary invariant norms

similarity preserving linear maps on upper triangular matrix algebras in this note we consider similarity preserving linear maps on the algebra of all n n complex upper triangular matrices tn we give characterizations of similarity invariant subspaces in tn and similarity preserving linear injections on tn furthermore we considered linear injections on tn preserving similarity in mn as well

linear maps preserving zero products on nest subalgebras of von neumann algebras in this paper it is proved that every surjective linear map preserving identity and zero products in both directions between two nest subalgebras with non trivial nests of any factor von neumann algebra is an isomorphism and that every surjective weakly continuous linear map preserving identity and zero jordan products in both directions between two nest subalgebras with non trivial nests of any factor von neumann algebra is either an isomorphism or an anti isomorphism

a note on spectrum preserving maps abstract let a and b be unital semisimple banach algebras if m 2 a b is a bijective spectrum preserving linear map then is a jordan homomorphism

similarity preserving linear maps on matrices abstract we determine all similarity preserving linear maps on the space of n x n complex matrices and all unitary equivalence preserving linear maps on the space of n x n hermitian matrices sub majorization preserving linear maps on hermitian matrices are also determined

global optimization of mixed integer quadratically constrained quadratic programs miqcqp through piecewise linear and edge concave relaxations we propose a deterministic global optimization approach whose novel contributions are rooted in the edge concave and piecewise linear underestimators to address nonconvex mixed integer quadratically constrained quadratic programs miqcqp to epsilon global optimality the facets of low dimensional n 3 edge concave aggregations dominating the termwise relaxation of miqcqp are introduced at every node of a branch and bound tree concave multivariable terms and sparsely distributed bilinear terms that do not participate in connected edge concave aggregations are addressed through piecewise linear relaxations extensive computational studies are presented for point packing problems standard and generalized pooling problems and examples from globallib meeraus globallib http www gamsworld org global globallib htm

non equilibrium dynamics of the ising model for t less than equal totc the growth of order in ising models with nonconserved order parameter is considered for quenches to final temperatures tf 0 and tf tc the results of numerical simulations in spatial dimension d 2 are presented in all cases a scaling regime is entered for sufficiently long times where the characteristic length scale is the domain size l t approximately t12 for tf 0 and the nonequilibrium correlation length xi t approximately t1z for tf tc the equal time correlation function has the expected scaling forms f r l t and r d 2 eta fc r xi t for tf 0 and tc respectively the scaling function fc x has interesting short distance behaviour which is elucidated using scaling arguments and by in and 1 n expansions the t 0 scaling function f x depends on whether the spin correlations present in the initial conditions are of long or short range as does the exponent which describes the decay of the autocorrelation function a t si t si o approximately l t results for a quench from the equilibrium critical state to tf 0 are consistent with theoretical predictions

characterizations of automorphisms of operator algebras on banach spaces abstract let x be a complex banach space of dimension greater than one and denote by b x the algebra of all the bounded linear operators on x it is shown that if b x b x is a multiplicative map not assumed linear and if is sufficiently close to a linear automorphism of b x in some uniform sense then it is actually an automorphism

invertibility preserving linear maps on j subspace lattice algebras it is shown that every unital surjective linear map between j subspace lattice algebras which preserves invertibility in both directions is a jordan isomorphism this result can apply to atomic boolean subspace lattice algebras and pentagon subspace lattice algebras

unital and multiplicatively spectrum preserving surjections between semi simple commutative banach algebras are linear and multiplicative abstract let t be a surjective map from a unital semi simple commutative banach algebra a onto a unital commutative banach algebra b suppose that t preserves the unit element and the spectrum f g of the product of any two elements f and g in a coincides with the spectrum t f t g then b is semi simple and t is an isomorphism the condition that t is surjective is essential an example of a non linear and non multiplicative unital map from a commutative c algebra into itself such that t f t g f g holds for every f g are given we also show an example of a surjective unital map from a commutative c algebra onto itself which is neither linear nor multiplicative such that t f t g f g holds for every f g

on grassmannians associated with jb triples then is a complex lie group that has precisely n 1 orbits e0 en in e each er is the locally closed complex submanifold of all matrices of rank r clearly er 1 is in the closure of er for every 1 r n and en is the unique open orbit for every pair of integers p q 0 let gp q be the grassmannian of all p planes in cp q then gp q is a compact symmetric hermitian manifold of dimension pq holomorphically equivalent to gq p every er is in a canonical way a equivariant holomorphic fibre bundle

jointly constrained biconvex programming this paper presents a branch and bound algorithm for minimizing the sum of a convex function in x a convex function in y and a bilinear term in x and y over a closed set such an objective function is called biconvex with biconcave functions similarly defined the feasible region of this model permits joint constraints in x and y to be expressed the bilinear programming problem becomes a special case of the problem addressed in this paper we prove that the minimum of a biconcave function over a nonempty compact set occurs at a boundary point of the set and not necessarily an extreme point the algorithm is proven to converge to a global solution of the nonconvex program we discuss extensions of the general model and computational experience in solving jointly constrained bilinear programs for which the algorithm has been implemented

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

a finite branch and bound algorithm for nonconvex quadratic programming via semidefinite relaxations existing global optimization techniques for nonconvex quadratic programming qp branch by recursively partitioning the convex feasible set and thus generate an infinite number of branch and bound nodes an open question of theoretical interest is how to develop a finite branch and bound algorithm for nonconvex qp one idea which guarantees a finite number of branching decisions is to enforce the first order karush kuhn tucker kkt conditions through branching in addition such an approach naturally yields linear programming lp relaxations at each node however the lp relaxations are unbounded a fact that precludes their use in this paper we propose and study semidefinite programming relaxations which are bounded and hence suitable for use with finite kkt branching computational results demonstrate the practical effectiveness of the method with a particular highlight being that only a small number of nodes are required

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

methods for global concave minimization a bibliographic survey the global concave minimization problem is to find the constrained global minimum of a concave function since such a function may have many local minima finding the global minimum is a computationally difficult problem in this bibliographic survey which includes most of the recent papers on constrained global concave minimization we have attempted to briefly summarize the main ideas in each paper these recent papers include those concerned with large scale global concave minimization and bilinear programming

additive mappings on operator algebras preserving absolute values abstract it is shown that an additive map b h b k is the sum of two homomorphisms one of which is c linear and the other is c antilinear provided that 1 a a a for all a b h 2 b i is an orthogonal projection and 3 c i i k i k the structure of is more refined when it is injective the paper also studies the properties of in the absence of condition b here b h and b k denote the algebras of all bounded linear operators on hilbert spaces h and k respectively these extend a result of l molnar bull austral math soc 53 1996 391 saying an additive map b h b h is a constant multiple of an either c linear or c antilinear homomorphism provided that 1 a a a for all a b h and 2 b b h contains all finite rank operators

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

similarity invariant real linear subspaces and similarity preserving additive maps let h be a separable complex infinite dimensional hilbert space all similarity invariant real linear subspaces of b h the banach algebra of all bounded linear operators on h are characterized as an application all continuous additive surjective maps on b h which preserving similarity in both directions are completely classified

front migration in the nonlinear cahn hilliard equation the method of matched asymptotic expansions is used to describe solutions of the nonlinear cahn hilliard equation for phase separation in n 1 space dimensions the expansion is formally valid when the thickness of internal transition layers is small compared with the distance separating layers and with their radii of curvature on the dominant slowest timescale the interface velocity is determined by the mean curvature of the interface by a non local relation which is identical to that in a well known quasi static model of solidification which exhibits a shape instability discovered by mullins sekerka j appl phys 34 323 329 1963 on a faster timescale the cahn hilliard equation regularizes a classic two phase stefan problem similarity solutions of the two phase stefan problem should describe boundary layers existence and uniqueness of such similarity solutions which admit metastable states is proved rigorously in an appendix

on a class of quadratic programs abstract this paper considers a class of quadratic programs where the constraints ae linear and the objective is a product of two linear functions assuming the two linear factors to be non negative maximization and minimization cases are considered each case is analyzed with the help of a bicriteria linear program obtained by replacing the quadratic objective with the two linear functions global minimum maximum is attained at an efficient extreme point efficient point of the feasible set in the solution space and corresponds to an efficient extreme point efficient point of the feasible set in the bicriteria space utilizing this fact and certain other properties two finite algorithms including validations are given for solving the respective problems each of these essentially consists of solving a sequence of linear programs finally a method is provided for relaxing the non negativity assumption on the two linear factors of the objective function

global optimization algorithms for linearly constrained indefinite quadratic problems abstract in this paper we consider the problem of finding the constrained global optimum of an indefinite quadratic function since such a function may have many local optima finding the global optimum is a computationally difficult problem we give an overview of the most important methods used which include benders decomposition concave programming approaches enumerative techniques and bilinear programming

on operators preserving commutativity abstract let l x be the algebra of all bounded operators on a non trivial complex banach space x and f l x l x a bijective linear operator such that f and f 1 both send commuting pairs of operators into commuting pairs then either f a uau 1 p a i or f a ua u 1 p a i where p is a linear functional on l x u is a bounded linear bijective operator between the appropriate two spaces is a complex constant and a is the adjoint of a the form of an operator f for which f and f 1 both send projections of rank one into projections of rank one is also determined

approximately spectrum preserving maps let x and y be superreflexive complex banach spaces and let b x and b y be the banach algebras of all bounded linear operators on x and y respectively if a bijective linear map b x b y almost preserves the spectra then it is almost multiplicative or anti multiplicative furthermore in the case where x y is a separable complex hilbert space such a map is a small perturbation of an automorphism or an anti automorphism

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

on the convexification of nonlinear programming problems an applications oriented survey abstract some important classes of decision models give rise to nonconvex minimization problems that by domain or range transformation are transformable into convex problems thus the powerful theoretical results and the efficiency of algorithms in convex programming can be exploited for a wide range of problems if no convexifying transformation is at hand one often requires to approximate a nonconvex objective by a convex one then a priori as well as post computational errorbounds are of interest the purpose of this paper is to outline briefly some of the ideas and results on convexification that may be useful in practice

global minimization of large scale constrained concave quadratic problems by separable programming the global minimization of a large scale linearly constrained concave quadratic problem is considered the concave quadratic part of the objective function is given in terms of the nonlinear variablesx r n while the linear part is in terms ofy r k for large scale problems we may havek much larger thann the original problem is reduced to an equivalent separable problem by solving a multiple cost row linear program with 2n cost rows the solution of one additional linear program gives an incumbent vertex which is a candidate for the global minimum and also gives a bound on the relative error in the function value of this incumbent ana priori bound on this relative error is obtained which is shown to be 0 25 in important cases if the incumbent is not a satisfactory approximation to the global minimum a guaranteede approximate solution is obtained by solving a single liner zero one mixed integer programming problem this integer problem is formulated by a simple piecewise linear underestimation of the separable problem

preservers of local spectra of matrix sums abstract let m n c be the set of n n complex matrices and for a nonzero vector e c n and t m n c let t e denote the local spectrum of t at e we characterize surjective maps on m n c which satisfy t s e t s e for all matrices t and s we arrive at the same conclusion by supposing that t s e t s e for all matrices t and s without the surjectivity assumption on continuous maps from m n c onto itself that preserve the local spectral radius of the sum of matrices at a nonzero fixed vector are also characterized

a note on similarity preserving linear maps on matrices abstract we give a simple proof of a result of hiai concerning similarity preserving linear maps on n n complex matrices as well as its extension to fields of characteristic zero

maps preserving the spectrum of generalized jordan product of operators abstract let a 1 a 2 be standard operator algebras on complex banach spaces x 1 x 2 respectively for k 2 let i 1 i m be a sequence with terms chosen from 1 k and define the generalized jordan product t 1 t k t i 1 t i m t i m t i 1 on elements in a i this includes the usual jordan product a 1 a 2 a 1 a 2 a 2 a 1 and the triple a 1 a 2 a 3 a 1 a 2 a 3 a 3 a 2 a 1 assume that at least one of the terms in i 1 i m appears exactly once let a map a 1 a 2 satisfy that a 1 a k a 1 a k whenever any one of a 1 a k has rank at most one it is shown in this paper that if the range of contains all operators of rank at most three then must be a jordan isomorphism multiplied by an m th root of unity similar results for maps between self adjoint operators acting on hilbert spaces are also obtained

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

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

the bounds of feasible space on constrained nonconvex quadratic programming this paper presents a method to estimate the bounds of the radius of the feasible space for a class of constrained nonconvex quadratic programmings results show that one may compute a bound of the radius of the feasible space by a linear programming which is known to be a p problem n karmarkar a new polynomial time algorithm for linear programming combinatorica 4 1984 373 395 it is proposed that one applies this method for using the canonical dual transformation d y gao canonical duality theory and solutions to constrained nonconvex quadratic programming j global optimization 29 2004 377 399 for solving a standard quadratic programming problem

isometries of a generalized numerical radius abstract for 0 q 1 the q numerical range is defined on the algebra m n of all n n complex matrices by w q a x ay x y c n x y 1 y x q the q numerical radius is defined by r q a max w q a we characterize isometries of the metric space m n r q i e the maps m n m n that satisfy r q a b r q a b we also characterize maps on m n that preserves the q numerical range the maps are not assumed to be linear

asymptotic similarity preserving linear maps on b h it is proved that a bounded linear surjective map on b h which is asymptotic similarity preserving is nonzero scalar multiple of either an automorphism or an anti automorphism

linear operators preserving t congruence on matrices abstract two complex or real square matrices a and b are said to be t congruent if there exists a nonsingular matrix s such that a sbs t if a and b are complex respectively real and s is unitary respectively real orthogonal we say that they are unitarily t congruent respectively real orthogonally congruent in this note we obtain characterizations of linear operators on various matrix spaces that preserve t congruence results and problems concerning unitary t congruence or orthogonal t congruence are discussed

some general techniques on linear preserver problems abstract several general techniques on linear preserver problems are described the first one is based on a transfer principle in model theoretic algebra that allows one to extend linear preserver results on complex matrices to matrices over other algebraically closed fields of characteristic 0 the second one concerns the use of some simple geometric technique to reduce linear preserver problems to standard types so that known results can be applied the third one is about solving linear preserver problems on more general operator algebras by reducing the problems to idempotent preservers numerous examples will be given to demonstrate the proposed techniques