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

vanishing viscosity solutions of nonlinear hyperbolic systems we consider the cauchy problem for a strictly hyperbolic n n system in one space dimension ut a u ux 0 assuming that the initial data have small total variation we show that the solutions of the viscous approximations ut a u ux euxx are defined globally in time and satisfy uniform bv estimates independent of e moreover they depend continuously on the initial data in the l 1 distance with a lipschitz constant independent of t e letting e 0 these viscous solutions converge to a unique limit depending lipschitz continuously on the initial data in the conservative case where a df is the jacobian

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

invertible preservers and algebraic groups abstract we consider groups of invertible linear transformations on matrices preserving some property let f be an infinite field our main result is that if an invertible transformation of m n f preserves a finite union of similarity classes then the transformation is essentially conjugation this was proved for f algebraically closed of characteristic zero by li and pierce our method relies heavily on results about maximal subgroups of algebraic groups these results were obtained by dynkin in characteristic zero and seitz in positive characteristic

a numerical scheme for singular shock solutions and a study of its consistence in the sense of distributions in this paper we present a numerical scheme for the approximation of singular shocks as long as some properties such as boundedness of the velocity are verified when the space step h tends to 0 we prove that the scheme provides approximate solutions that tend to satisfy the equations more precisely when the approximate solutions are plugged into the equations the result tends to 0 when h 0 in the familiar definition of weak solutions with the requirement of a smooth test function these properties can be fully proved for general classes of systems extending the korchinski system that do not have distribution solutions in the usual sense in other cases such as the keyfitz kranzer singular shocks these properties have been checked up to very small values of h these results explain numerical observations on very different systems

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

a musta scheme for a nonconservative two fluid model we present a multistage centered scheme of the kind proposed by toro appl numer math 56 2006 pp 1464 1479 for numerically resolving the simultaneous flow of two fluids through a transport pipeline this model contains nonconservative terms in both the temporal and spatial derivatives and an extension of the standard numerical framework for conservation laws is needed in this paper we rewrite the model in an equivalent mathematical form eliminating the nonconservative time derivatives this allows us to use the framework described by pares siam j numer anal 44 2006 pp 300 321 we develop force and musta type schemes which are consistent with pares formalism numerical simulations demonstrate a high degree of stability of our proposed schemes comparisons with the roe and rusanov schemes indicate that convergence to near identical solutions is obtained when the nonconservative terms are discretized with respect to the same evaluation of the path dependent integrals however if the schemes are not mutually formally path consistent in the sense of pares different converged solutions are obtained

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

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

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

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

a robust and accurate approach to computing compressible multiphase flow stratified flow model and ausm up scheme in this paper we propose a new approach to compute compressible multifluid equations firstly a single pressure compressible multifluid model based on the stratified flow model is proposed the stratified flow model which defines different fluids in separated regions is shown to be amenable to the finite volume method we can apply the conservation law to each subregion and obtain a set of balance equations secondly the ausm scheme which is originally designed for the compressible gas flow is extended to solve compressible liquid flows by introducing additional dissipation terms into the numerical flux the new scheme called ausm up can be applied to both liquid and gas flows thirdly the contribution to the numerical flux due to interactions between different phases is taken into account and solved by the exact riemann solver we will show that the proposed approach yields an accurate and robust method for computing compressible multiphase flows involving discontinuities such as shock waves and fluid interfaces several one dimensional test problems are used to demonstrate the capability of our method including the ransom s water faucet problem and the air water shock tube problem finally several two dimensional problems will show the capability to capture enormous details and complicated wave patterns in flows having large disparities in the fluid density and velocities such as interactions between water shock wave and air bubble between air shock wave and water column s and underwater explosion

continuous time analysis eigenstructure assignment and h sub 2 synthesis with enhanced linear matrix inequalities lmi characterizations this note describes a new framework for the analysis and synthesis of control systems which constitutes a genuine continuous time extension of results that are only available in discrete time in contrast to earlier results the proposed methods involve a specific transformation on the lyapunov variables and a reciprocal variant of the projection lemma in addition to the classical linearizing transformations on the controller data for a wide range of problems including robust analysis and synthesis multichannel h sub 2 stateand output feedback syntheses the approach leads to potentially less conservative linear matrix inequality lmi characterizations this comes from the fact that the technical restriction of using a single lyapunov function is to some extent ruled out in this new approach moreover the approach offers new potentials for problems that cannot be handled using earlier techniques an important instance is the eigenstructure assignment problem blended with lyapunov type constraints which is given a simple and tractable formulation

fixed order h controller design for systems with ellipsoidal parametric uncertainty in this article fixed order robust h controller design for systems with ellipsoidal parametric uncertainty based on parameter dependent lyapunov functions is studied using the concept of strictly positive realness sprness of transfer functions a fixed order robust control design method in terms of solution to a set of linear matrix inequalities lmis is proposed since controller parameters are decision variables any controller structure such as pid can be considered the weighted infinity norm of closed loop sensitivity functions are considered as performance specification in the synthesis problem the simulation results show the effectiveness of the proposed method

fixed order controller design for polytopic systems using lmis convex parameterization of fixed order robust stabilizing controllers for systems with polytopic uncertainty is represented as a linear matrix inequality lmi using the kalman yakubovich popov kyp lemma this parameterization is a convex inner approximation of the whole nonconvex set of stabilizing controllers and depends on the choice of a central polynomial it is shown that with an appropriate choice of the central polynomial the set of all stabilizing fixed order controllers that place the closed loop poles of a polytopic system in a disk centered on the real axis can be outbounded with some lmis these lmis can be used for robust pole placement of polytopic systems

the representation and characterization of drazin inverses of operators on a hilbert space in this note the representation and characterization of drazin inverses of operators on a hilbert space are established

c algebras of real rank zero abstract the concept of real rank of a c algebra is introduced as a non commutative analogue of dimension it is shown that real rank zero is equivalent to the previously defined conditions fs and hp and that it is invariant under strong morita equivalence in particular under stable isomorphism real rank zero is also invariant under inductive limits and split extensions and the class may well be regarded as the conceptual completion of the af algebras in some cases notably when the algebra is matroid it is shown that the multiplier algebra also has real rank zero although that is not true in general by a result of g j murphy this implies a weyl von neumann type result for self adjoint multiplier elements in these cases

linear preservers of controllability and or observability abstract consider a linear control differential equations system x ax bu y cx du where x c n u c m y c p and a b c d are matrices of appropriate sizes with entries in c this system or the matrix pair a b or the matrix 4 tuple a b c d is called controllable if rank a i b n for all 0 let be a linear transformation on c n n m the linear space of all matrix pairs a b then is said to preserve controllability if it maps controllable matrix pairs to controllable matrix pairs we prove that preserves controllability if and only if a b sas 1 sbf sbr f a b i 0 where is a nonzero scalar s r are nonsingular and f is a linear functional based on this result we also find all linear mappings on the linear space of all matrix 4 tuples a b c d which preserve controllability characterizations of linear preservers of observability a concept dual to controllability hence follow some variations of the above problems are also discussed

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

multiplier design for extended strict positive realness and its applications given a stable square plant g 1 s based on linear matrix inequality lmi method necessary and sufficient conditions are presented for the existence of a stable multiplier g 2 s such that g 1 s g 2 s is extended strictly positive real espr furthemore for uncertain plants the corresponding problems are considered and solved an application to the study of dichotomy for pendulum like systems is also presented examples are given to illustrate the results

a generalization of the motzkin taussky theorem abstract in this paper we generalize the motzkin taussky theorem to matrices with polynomial entries

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

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

h_ infty controller design using an alternative to youla parameterization all h controllers of a siso lti system are parameterized thanks to the relation between bounded real lemma and positive real lemma this new parameterization shares the same features with youla parameterization namely on the convexity of h norm constraints for the closed loop transfer functions however it can deal with low order controllers and can be extended easily for the systems with polytopic uncertainty the effectiveness of the proposed method is shown via an academic example

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

why many theories of shock waves are necessary convergence error in formally path consistent schemes we are interested in nonlinear hyperbolic systems in nonconservative form arising in fluid dynamics and for solutions containing shock waves we investigate the convergence of finite difference schemes applied to such systems according to dal maso lefloch and murat s theory a shock wave theory for a given nonconservative system requires prescribing a priori a family of paths in the phase space in the present paper we consider schemes that are formally consistent with a given family of paths and we investigate their limiting behavior as the mesh is refined we first generalize to systems a property established earlier by hou and lefloch for scalar conservation laws and we prove that nonconservative schemes generate at the level of the limiting hyperbolic system an convergence error source term which provided the total variation of the approximations remains uniformly bounded is a locally bounded measure this convergence error measure is supported on the shock trajectories and as we demonstrate here is usually small in the special case that the scheme converges in the sense of graphs a rather strong convergence property often violated in practice then this measure source term vanishes we also discuss the role of the equivalent equation associated with a difference scheme here the distinction between scalar equations and systems appears most clearly since for systems the equivalent equation of a scheme that is formally path consistent depends upon the prescribed family of paths the core of this paper is devoted to investigate numerically the approximation of several simplified or full hyperbolic models arising in fluid dynamics this leads us to the conclusion that for systems having nonconservative products associated with linearly degenerate characteristic fields the convergence error vanishes for more general models this measure is evaluated very accurately especially by plotting the shock curves associated with each scheme under consideration as we demonstrate plotting the shock curves provide a convenient approach for evaluating the range of validity of a given scheme

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

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

nonlinear generalized functions and jump conditions for a standard one pressure liquid gas model abstract the mixture of a liquid and a gas is classically represented by one pressure models these models are a system of pdes in nonconservative form and shock wave solutions do not make sense within the theory of distributions they give rise to products of distributions that are not defined within distribution theory but they make sense by applying a theory of nonlinear generalized functions to these equations in contrast to the familiar case of conservative systems the jump conditions cannot be calculated a priori jump conditions for these nonconservative systems can be obtained using the theory of nonlinear generalized functions by inserting some adequate physical information into the equations the physical information that we propose to insert for the one pressure models of a mixture of a liquid and a gas is a natural mathematical expression in the theory of nonlinear generalized functions of the fact that liquids are practically incompressible while gases are very compressible and so they do not satisfy equally well their respective state laws on the shock waves this modelization gives well defined explicit jump conditions the great numerical difficulty for solving numerically nonconservative systems is due to the fact that slightly different numerical schemes can give significantly different results the jump conditions obtained above permit to select the numerical schemes and validate those that give numerical solutions that satisfy these jump conditions which can be an important piece of information in the absence of other explicit discontinuous solutions and of precise observational results we expose with care the mathematical originality of the theory of nonlinear generalized functions an original abstract analysis issued by the leopoldo nachbin team on infinite dimensional holomorphy that permits to state mathematically physical facts that cannot be formulated within distribution theory and are the key for the removal of ambiguities that classically appear when one tries to calculate on multiplications of distributions that occur in the differential equations of physics

how to prevent pressure oscillations in multicomponent flow calculations a new numerical scheme for computing multicomponent flows is presented it is able to handle strong shocks is pressure oscillation free through the contact discontinuities and guarantees the posi tivity of mass fractions some numerical experiments on shock tubes indicate the convergence to the correct weak solution comparisons with classical finite volume schemes are also proposed

limits of nonlinear weak asymptotic methods we propose a mathematical limit of l1 stable weak asymptotic methods a family of l1 stable approximate solutions is transformed into a normal family of holomorphic functions defined in a complex domain having the real space on its boundary this provides a holomorphic function which is the same mathematical object as the solutions from explicit calculations the weak limit of the approximate solutions from weak asymptotic methods in the space of bounded radon measures is recovered as a boundary value of this holomorphic function

a new robust d stability condition for real convex polytopic uncertainty abstract the problem of robust d stability analysis with respect to real convex polytopic uncertainties is tackled a new lmi based sufficient condition for the existence of parameter dependent lyapunov functions is proposed this condition generalises previously published conditions numerical comparisons with quadratic stability results as well as previous results based on parameter dependent lyapunov functions illustrate the relevance of this new condition finally this result appears to be promising for robust multi objective performance analysis and control synthesis purposes

zero product preserving additive maps on symmetric operator spaces and self adjoint operator spaces in this note we characterize the additive maps on the space of symmetric operators and the space of self adjoint operators which preserve zero products in both directions and the additive maps on the space of self adjoint operators which preserve jordan zero products in both directions we also give a complete classification of additive maps on the von neumann algebra of all bounded linear operators acting on a hilbert space which preserve square zero in both directions or preserve operators annihilated by a polynomial in both directions

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

a nearly implicit hydrodynamic numerical scheme for two phase flows this article presents an extension of the semi implicit numerical scheme for two phase flow simulation the extension uses an implicit evaluation of the convective fluxes and thus eliminates the material courant stability restriction the new algorithm involves a two step approach for the mass and energy equations and a single fully implicit step for the momentum evaluations some analysis and accuracy considerations for the scheme are also presented

the drazin inverse in multibody system dynamics the numerical analysis of multibody system dynamics is based on the equations of motion as differential algebraic systems a thorough analysis of the linearized equations and their solution theory leads to an equivalent system of ordinary differential equations which gives deeper insight into the derivation of integration schemes and into the stabilization approaches the main tool is the drazin inverse a generalized matrix inverse which preserves the eigenvalues the results are illustrated by a realistic truck model finally the approach is extended to the nonlinear index 2 formulation

global well posedness and decay rates of strong solutions to a non conservative compressible two fluid model in this paper we consider a compressible two fluid model with constant viscosity coefficients and unequal pressure functions p neq p as mentioned in the seminal work by bresch desjardins et al arch rational mech anal 196 599 629 2010 for the compressible two fluid model where p p common pressure is used and capillarity effects are accounted for in terms of a third order derivative of density the case of constant viscosity coefficients cannot be handled in their settings besides their analysis relies on a special choice for the density dependent viscosity refer also to another reference commun math phys 309 737 755 2012 by bresch huang and li for a study of the same model in one dimension but without capillarity effects in this work we obtain the global solution and its optimal decay rate in time with constant viscosity coefficients and some smallness assumptions in particular capillary pressure is taken into account in the sense that delta p p p f neq 0 where the difference function f is assumed to be a strictly decreasing function near the equilibrium relative to the fluid corresponding to p this assumption plays an key role in the analysis and appears to have an essential stabilization effect on the model in question

on solutions to equilibrium problems for systems of stiffened gases we consider an isolated system of n immiscible fluids each following a stiffened gas equation of state we consider the problem of calculating equilibrium states from the conserved fluid mechanical properties i e the partial densities and internal energies we consider two cases in each case mechanical equilibrium is assumed but the fluids may or may not be in thermal equilibrium for both cases we address the issues of existence uniqueness and physical validity of equilibrium solutions we derive necessary and sufficient conditions for physically valid solutions to exist and prove that such solutions are unique we show that for both cases physically valid solutions can be expressed as the root of a monotonic function in one variable we then formulate efficient algorithms which unconditionally guarantee global and quadratic convergence toward the physically valid solution

low order controller design for siso systems using coprime factors and lmi this paper develops a low order controller design method for linear continuous time invariant single input single output systems requiring only the solution of a convex optimization problem the technique integrates several well known results in control theory an important step is the use of coprime factors so that based on strictly positive real functions feedback stabilization using low order controllers becomes a zero placement problem which is convex from this result we develop algorithms to solve two optimal control problems

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

positive polynomials and robust stabilization with fixed order controllers recent results on positive polynomials are used to obtain a convex inner approximation of the stability domain in the space of coefficients of a polynomial an application to the design of fixed order controllers robustly stabilizing a linear system subject to polytopic uncertainty is then proposed based on linear matrix inequality optimization the key ingredient in the design procedure resides in the choice of the central polynomial several numerical examples illustrate the relevance of the approach

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

weakly implicit numerical schemes for a two fluid model the aim of this paper is to construct semi implicit numerical schemes for a two phase two fluid flow model allowing for violation of the cfl criterion for sonic waves while maintaining a high level of accuracy and stability on volume fraction waves by using an appropriate hybridization of a robust implicit flux and an upwind explicit flux we obtain a class of first order schemes which we refer to as weakly implicit mixture flux wimf methods in particular by using an advection upstream splitting method ausmd type of upwind flux s evje and t flatten j comput phys 192 2003 pp 175 210 we obtain a scheme denoted as wimf ausmd we present several numerical simulations all of them indicating that the cfl stability of the wimf ausmd scheme is governed by the velocity of the volume fraction waves and not the rapid sonic waves comparisons with an explicit roe scheme indicate that the scheme presented in this paper is highly efficient robust and accurate on slow transients by exploiting the possibility to take much larger time steps it outperforms the roe scheme in the resolution of the volume fraction wave for the classical water faucet problem on the other hand it is more diffusive on pressure waves although conservation of positivity for the masses is not proved we demonstrate that a fix may be applied making the scheme able to handle the transition to one phase flow while maintaining a high level of accuracy on volume fraction fronts

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

rank 1 nilpotency linear preservers on nest algebras abstract let n and m be two nests on banach spaces x and y respectively and let be a linear map between nest algebras alg n and alg m of which the range contains all rank 1 nilpotent operators in alg m we give some structure theorems for to be rank 1 nilpotency preserving in both directions and obtain particularly a characterization of such if it is bounded and x and y are hilbert spaces with dimx 6

linear maps and additive maps that preserve operators annihilated by a polynomial abstract let h k be infinite dimensional complex hilbert spaces and let p t be a complex polynomial with deg p 2 in this paper we give a sufficient and necessary condition for a surjective linear or additive map b h b k to preserve operators annihilated by p in both directions and answer a question raised by semrl affirmatively

a convex parameterization of robustly stabilizing controllers this paper treats synthesis of robust controllers for linear time invariant systems uncertain real parameters are assumed to appear linearly in the closed loop characteristic polynomial the main contribution is to give a convex parameterization of all controllers that simultaneously stabilize the system for all possible parameter combinations with the new parameterization certain robust performance problems can be stated in terms of quasi convex optimization

an approximate linearized riemann solver for a two fluid model an approximate linearized riemann solver is presented for the numerical simulation of two phase flows this new solver is based on a linearization of nonconservative products and uses an extension of roe s approximate riemann solver the scheme is applied to shock tube problem and to a standard test for two fluid codes

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

analysis and synthesis of robust control systems via parameter dependent lyapunov functions in this paper the problem of robust stability of systems subject to parametric uncertainties is considered sufficient conditions for the existence of parameter dependent lyapunov functions are given in terms of a criterion which is reminiscent of but less conservative than popov s stability criterion an equivalent frequency domain criterion is demonstrated the relative sharpness of the proposed test and existing stability criteria is then discussed the use of parameter dependent lyapunov functions for robust controller synthesis is then considered it is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant a possible synthesis procedure and a numerical example are then discussed

fixed order robust h_ infty controller design with regional pole assignment in this technical note the problem of designing fixed order robust hinfin controllers is considered for linear systems affected by polytopic uncertainty a polynomial method is employed to design a fixed order controller that guarantees that all the closed loop poles reside within a given region of the complex plane in order to utilize the freedom of the controller design an hinfin performance specification is also enforced by using the equivalence between robust stability and hinfin norm constraint the design problem is formulated as a linear matrix inequality lmi constraint whose decision variables are controller parameters an illustrative example demonstrates the feasibility of the proposed design methods

on the wave structure of two phase flow models we explore the relationship between two common two phase flow models usually denoted as the two fluid and drift flux models they differ in their mathematical description of momentum transfer between the phases in this paper we provide a framework in which these two model formulations are unified the drift flux model employs a mixture momentum equation and treats interphasic momentum exchange indirectly through the slip relation which gives the relative velocity between the phases as a function of the flow parameters this closure law is in general highly complex which makes it difficult to analyze the model algebraically to facilitate the analysis we express the quasi linear formulation of the drift flux model as a function of three parameters the derivatives of the slip with respect to the vector of unknown variables the wave structure of this model is investigated using a perturbation technique then we rewrite the drift flux model with a general slip relation such that it is expressed in term

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

asymptotic study of the initial value problem to a standard one pressure model of multifluid flows in nondivergence form abstract we construct families of approximate solutions to the initial value problem and provide complete mathematical proofs that they tend to satisfy the standard system of isothermal one pressure two fluid flows in 1 d when the data are l 1 in densities and l in velocities to this end we use a method that reduces this system of pdes to a family of systems of four odes in banach spaces whose smooth solutions are these approximate solutions this method is constructive using standard numerical methods for odes one can easily and accurately compute these approximate solutions which therefore from the mathematical proof can serve for comparison with numerical schemes one observes agreement with previously known solutions from scientific computing evje and flatten 2003 16 we show that one recovers the solutions of these authors exactly in one case with a slight difference in another case then we propose an efficient numerical scheme for the original system of two fluid flows and show it gives back exactly the same results as the theoretical solutions obtained above

on the rank minimization problem over a positive semidefinite linear matrix inequality we consider the problem of minimizing the rank of a positive semidefinite matrix subject to the constraint that an affine transformation of it is also positive semidefinite our method for solving this problem employs ideas from the ordered linear complementarity theory and the notion of the least element in a vector lattice this problem is of importance in many contexts for example in feedback synthesis problems and such an example is also provided

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