a control theory for cartesian flexible robot arms in this article we first use a fourth order partial differential equation with boundary conditions to model a flexible robot arm on a moving base with a payload at the tip end through the state space formulation we show that such a system is both controllable and observable in an infinite dimensional hilbert space we also show that the system is stabilizable via a feedback control

computational methods for risk averse undiscounted transient markov models the total cost problem for discrete time controlled transient markov models is considered the objective functional is a markov dynamic risk measure of the total cost two solution methods value and policy iteration are proposed and their convergence is analyzed in the policy iteration method we propose two algorithms for policy evaluation the nonsmooth newton method and convex programming and we prove their convergence the results are illustrated on a credit limit control problem

automorphisms of b h with respect to minus partial order abstract let h be an infinite dimensional hilbert space and b h the algebra of all bounded linear operators on h we discuss possible extensions of the concept of the minus partial order from matrix to operator algebras in particular we show that mitra s unified theory of matrix partial orders based on generalized inverses can be modified in such a way that we get a unified approach to partial orders on b h or even more general algebras and rings then we choose the most natural among possible definitions of minus partial order on b h and describe the structure of corresponding automorphisms

orthogonality preservers in c algebras jb algebras and jb triples abstract we study orthogonality preserving operators between c algebras jb algebras and jb triples let t a e be an orthogonality preserving bounded linear operator from a c algebra to a jb triple satisfying that t 1 d is a von neumann regular element then t a e 2 r d every element in t a and d operator commute in the jb algebra e 2 r d and there exists a triple homomorphism s a e 2 r d such that t l d r d s where r d denotes the range tripotent of d in e an analogous result for a being a jb algebra is also obtained when t a b is an operator between two c algebras we show that denoting h t 1 then t orthogonality preserving if and only if there exists a triple homomorphism s a b satisfying h s z s z h h s z s z h and t z l h r h s z 1 2 h r h s z s z r h h this allows us to prove that a bounded linear operator between two c algebras is orthogonality preserving if and only if it preserves zero triple products

beam search heuristic to solve stochastic integer problems under probabilistic constraints abstract this paper proposes a beam search heuristic strategy to solve stochastic integer programming problems under probabilistic constraints beam search is an adaptation of the classical branch and bound method in which at any level of the search tree only the most promising nodes are kept for further exploration whereas the remaining are pruned out permanently the proposed algorithm has been compared with the branch and bound method the numerical results collected on the probabilistic set covering problem show that the beam search technique is very efficient and appears to be a promising tool to solve difficult stochastic integer problems under probabilistic constraints

a further algebraic version of cochran s theorem and matrix partial orderings abstract a new version of cochran s theorem for rectangular matrices is established being oriented toward partial isometries the new version parallels corresponding results concerned with arbitrary tripotent matrices and covers results concerned with hermitian tripotent matrices a discussion of a related new matrix partial ordering is also given

left star and right star partial orderings abstract two partial orderings in the set of complex matrices are introduced by combining each of the conditions a a a b and aa ba which define the star partial ordering with one of the conditions m a m b and m a m b which define the space preordering several properties of these orderings are examined with main emphasis on comparing the new orderings with the star ordering the minus ordering and other related partial orderings moreover some further characterizations of partial orderings in terms of inclusions of appropriate classes of generalized inverses are derived with the main emphasis on characterizations involving reflexive generalized inverses

on consistency of stochastic dominance and mean semideviation models we analyze relations between two methods frequently used for modeling the choice among uncertain outcomes stochastic dominance and mean risk approaches new necessary conditions for stochastic dominance are developed these conditions compare values of a certain functional which contains two components the expected value of a random outcome and a risk term represented by the central semideviation of the corresponding degree if the weight of the semideviation in the composite objective does not exceed the weight of the expected value maximization of such a functional yields solutions which are efficient in terms of stochastic dominance the results are illustrated graphically

star partial order on b h abstract let h be an infinite dimensional complex hilbert space and let b h be the algebra of all bounded linear operators on h in the paper the equivalent definition of the star partial order on b h using selfadjoint idempotent operators is introduced also some properties of the generalized concept of order relations on b h defined with the help of idempotent operators are investigated

symmetries of the car algebra a automorphism of period two of the uhf c algebra of type 2 is constructed for which the fixed point algebra is not approximately finite dimensional the construction also yields a diagonal maximal commutative c subalgebra whose spectrum is not totally disconnected variations and consequences of the construction are discussed

a multiproduct risk averse newsvendor with law invariant coherent measures of risk we consider a multiproduct risk averse newsvendor under the law invariant coherent measures of risk we first establish several fundamental properties of the model regarding the convexity of the problem the symmetry of the solution and the impact of risk aversion specifically we show that for identical products with independent demands increased risk aversion leads to decreased orders for a large but finite number of heterogeneous products with independent demands we derive closed form approximations for the optimal order quantities the approximations are as simple to compute as the classical risk neutral solutions we also show that the risk neutral solution is asymptotically optimal as the number of products tends to be infinity and thus risk aversion has no impact in the limit for a risk averse newsvendor with dependent demands we show that positively negatively dependent demands lead to lower higher optimal order quantities than independent demands using a numerical study we examine the convergence rates of the approximations and develop additional insights into the interplay between dependent demands and risk aversion

convexity and decomposition of mean risk stochastic programs traditional stochastic programming is risk neutral in the sense that it is concerned with the optimization of an expectation criterion a common approach to addressing risk in decision making problems is to consider a weighted mean risk objective where some dispersion statistic is used as a measure of risk we investigate the computational suitability of various mean risk objective functions in addressing risk in stochastic programming models we prove that the classical mean variance criterion leads to computational intractability even in the simplest stochastic programs on the other hand a number of alternative mean risk functions are shown to be computationally tractable using slight variants of existing stochastic programming decomposition algorithms we propose decomposition based parametric cutting plane algorithms to generate mean risk efficient frontiers for two particular classes of mean risk objectives

optimization of convex risk functions we consider optimization problems involving convex risk functions by employing techniques of convex analysis and optimization theory in vector spaces of measurable functions we develop new representation theorems for risk models and optimality and duality theory for problems with convex risk functions

riesz basis approach to the stabilization of a flexible beam with a tip mass using an abstract condition of riesz basis generation of discrete operators in the hilbert spaces we show in this paper that a sequence of generalized eigenfunctions of an euler bernoulli beam equation with a tip mass under boundary linear feedback control forms a riesz basis for the state hilbert space in the meanwhile an asymptotic expression of eigenvalues and the exponential stability are readily obtained the main results of siam j control optim 36 1998 pp 1962 1986 are concluded as a special case and the additional conditions imposed there are removed

risk optimization with p order conic constraints a linear programming approach the paper considers solving of linear programming problems with p order conic constraints that are related to a certain class of stochastic optimization models with risk objective or constraints the proposed approach is based on construction of polyhedral approximations for p order cones and then invoking a benders decomposition scheme that allows for efficient solving of the approximating problems the conducted case study of portfolio optimization with p order conic constraints demonstrates that the developed computational techniques compare favorably against a number of benchmark methods including second order conic programming methods

on mappings preserving the sharp and star orders abstract the present paper is devoted to the study of linear maps preserving certain relations such as the sharp partial order and the star partial order in semisimple banach algebras and c algebras

minimal concave cost rebalance of a portfolio to the efficient frontier one usually constructs a portfolio on the efficient frontier but it may not be efficient after say three months since the efficient frontier will shift as the elapse of time we then have to rebalance the portfolio if the deviation is no longer acceptable the method to be proposed in this paper is to find a portfolio on the new efficient frontier such that the total transaction cost required for this rebalancing is minimal this problem results in a nonconvex minimization problem if we use mean variance model in this paper we will formulate this problem by using absolute deviation as the measure of risk and solve the resulting linearly constrained concave minimization problem by a branch and bound algorithm successfully applied to portfolio optimization problem under concave transaction costs it will be demonstrated that this method is efficient and that it leads to a significant reduction of transaction costs

risk averse control of undiscounted transient markov models we use markov risk measures to formulate a risk averse version of the undiscounted total cost problem for a transient controlled markov process using the new concept of a multikernel we derive conditions for a system to be risk transient that is to have finite risk over an infinite time horizon we derive risk averse dynamic programming equations satisfied by the optimal policy and we describe methods for solving these equations we illustrate the results on an optimal stopping problem and an organ transplantation problem

diagonality inc algebras soit a une c algebre et a sa les elements hermitiens soit i un ideal ferme separable dans une c algebre a et on suppose que les elements de a sa de spectres finis sont denses dans a sa si a a sa et e 0 alors il existe b a sa diagonal relativement a i et il existe x i sa tel que x e et a b x

insdecm an interactive procedure for stochastic multicriteria decision problems abstract a new interactive technique for a discrete stochastic multiattribute decision making problem is proposed in this paper it is assumed that performance probability distribution for each action on each attribute is known two concepts are combined in the procedure stochastic dominance and interactive approach the first one is employed for generating efficient actions and constructing rankings of actions with respect to attributes the second concept is used when the communication between the dm and the model is conducted it is assumed that decision maker s restrictions are defined by specifying minimal or maximal values of scalar criteria measuring either expected outcome or variability of outcomes as such restrictions are in general not consistent with stochastic dominance rules we suggest verifying this consistency and asking the decision maker to redefine inconsistent restrictions

maps preserving the diamond partial order the present paper is devoted to the study of the diamond partial order in c algebras we characterize linear maps preserving this partial order

conditional risk mappings we introduce an axiomatic definition of a conditional convex risk mapping and we derive its properties in particular we prove a representation theorem for conditional risk mappings in terms of conditional expectations we also develop dynamic programming relations for multistage optimization problems involving conditional risk mappings

frontiers of stochastically nondominated portfolios we consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution we propose mean risk models that are solvable by linear programming and generate portfolios whose returns are nondomi nated in the sense of second order stochastic dominance next we develop a specialized parametric method for recovering the entire mean risk efficient frontiers of these models and we illustrate its operation on a large data set involving thousands of assets and real izations the problem of optimizing a portfolio of finitely many assets is a classical problem in theoretical and computational finance since the seminal work of markowitz 1952 it is generally agreed that portfolio performance should be measured in two distinct dimen sions the mean describing the expected return and the risk which measures the uncer tainty of the return in the mean risk approach we select from the universe of all possible portfolios those that are efficient for a given value of the mean they minimize the risk or equivalently for a given value of risk they maximize the mean such an approach has many advantages it allows one to formulate the problem as a parametric optimization problem and it facilitates the trade off analysis between mean and risk markowitz used the variance of the return as the measure of the risk it is easy to compute and it reduces the portfolio selection problem to a parametric quadratic pro gramming problem one can however construct simple counterexamples that show the imperfection of the variance as the risk measure it treats over performance equally as under performance and more importantly its use may suggest a portfolio that is always outperformed by another portfolio the use of the semivariance rather than the variance was already recommended by markowitz 1959 but even in this case significant deficien cies remain as we shall explain another theoretical approach to the portfolio selection problem is that of stochastic dominance see whitmore and findlay 1978 levy 1992 the usual first order defi nition of stochastic dominance gives a partial order in the space of real random variables more important from the portfolio point of view is the notion of second order dominance which is also defined as a partial order but which is equivalent to this statement a random variable y dominates the random variable z if e u y e u z for all nondecreasing concave functions u for which these expected values are finite thus no risk averse decision marker will prefer a portfolio with return z over a portfolio with return y while

a feedback control and a simulation of a torsional elastic robot arm a feedback control is designed for a torsional elastic robot arm to be exponentially stable and to arrive at any designated position an eigenvalue problem is discussed and a finite dimensional approximation theorem is proposed and proved based on the numerical analysis and the approximation theorem we can simulate the system and show that the bending vibration the torsional vibration the rigid turning angle and the bending moment of the robot arm can be controlled in a short period of time

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

stabilization of beams by pointwise feedback control a flexible structure consisting of serially connected euler bernoulli beams with co located sensors and actuators is considered controls are point forces and point bending moments applied at the nodes it is known that uniform exponential stability can be achieved with linear velocity feedback a sensitivity analysis of the system s spectrum with respect to feedback coefficients is set up it is also proved that in a particular case exponential decay rate can be obtained from the spectrum of the system

from stochastic dominance to mean risk models semideviations as risk measures abstract two methods are frequently used for modeling the choice among uncertain outcomes stochastic dominance and mean risk approaches the former is based on an axiomatic model of risk averse preferences but does not provide a convenient computational recipe the latter quantifies the problem in a lucid form of two criteria with possible trade off analysis but cannot model all risk averse preferences in particular if variance is used as a measure of risk the resulting mean variance markowitz model is in general not consistent with stochastic dominance rules this paper shows that the standard semideviation square root of the semivariance as the risk measure makes the mean risk model consistent with the second degree stochastic dominance provided that the trade off coefficient is bounded by a certain constant similar results are obtained for the absolute semideviation and for the absolute and standard deviations in the case of symmetric or bounded distributions in the analysis we use a new tool the outcome risk o r diagram which appears to be particularly useful for comparing uncertain outcomes

on the structure of simple c algebras tensored with a uhf algebra ii let d be a simple unital c algebra let b be a uhf algebra and put a b d it is proved that if p q a are projections and p q for all quasitraces on a then p q in the sense of murray and von neumann a more general result involving positive operators in a is also proved if d has finitely many extremal quasi traces and the projections in d k separate these then it is proved that a has real rank zero finally it is proved that provided d is stably finite then each positive state on k0 d lifts to a quasi trace

abelian strict approximation in aw algebras and weyl von neumann type theorems in this paper for a c algebra a with m m a an aw algebra or equivalently for an essential norm closed two sided ideal a of an aw algebra m we investigate the strict approximability of the elements of m from commutative c subalgebras of a in the relevant case of the norm closed linear span a of all finite projections in a semi finite aw algebra m we shall give a complete description of the strict closure in m of any maximal abelian self adjoint subalgebra masa of a we shall see that the situation is completely different for discrete respectively continuous m in the discrete case for any masa c of a the strict closure of c is equal to the relative commutant c m while in the continuous case under certain conditions concerning the center valued quasitrace of the finite reduced algebras of m satisfied by all von neumann algebras c is already strictly closed thus in the continu ous case no elements of m which are not already belonging to a can be strictly approximated from commutative c subalgebras of a in spite of this pathology of the strict topology in the case of the norm closed linear span of all finite projections of a continuous semi finite aw algebra we shall prove that in general situations including also this case any normal y 2 m is equal modulo a to some x 2 m which belongs to an order theoretical closure of an appropriate commutative c subalgebra of a in other words if we replace the strict topology with order theoretical approximation weyl von neumann berg sikonia type theo rems will hold in substantially greater generality

dimension and stable rank in the k theory of c algebras in topological k theory which can be viewed as the algebraic side of the theory of vector bundles some of the interesting properties which one investigates are for example the conditions under which bundles must possess trivial direct summands or the extent to which the cancellation property for direct whitney sums of bundles holds such properties turn out to be controlled in part by the dimension of the base space and results describing the nature of this control are among what are frequently called stability results 17 during the past few years there has been a sudden flowering of a theory for c algebras see surveys 35 36 37 since c algebras are profitably thought of as non commutative locally compact spaces with the finitely generated projective modules being the appropriate generalization of vector bundles according to swan s theorem 40 it would be natural to look for stability results for c algebras but until now the theory has been focussed on the c groups of c algebras and there has been little discussion of stability properties presumably in part for lack of an appropriate concept of dimension for c algebras one of the main objectives of this paper is to introduce a concept of dimension for c algebras which directly generalizes the classical concept of dimension for compact spaces 16 20 22 and to develop some techniques for calculating it notably for c algebras which are obtained as crossed product algebras for an action of the group of integers in algebraic k theory which is the generalization of topological c theory to rings a substantial number of stability properties have been discovered 2 39 42 48 within that theory the concept which has played a role most analogous to that of dimension is the bass stable rank but despite its many successes the bass stable rank has often been difficult to calculate even for relatively uncomplicated rings another main objective of the present paper is to make accessible for application to c algebras some of the stability results from algebraic c theory this comes about from the fact that the concept of dimension which we introduce dominates the bass stable rank i was led to seek stability results for c algebras by my desire to determine whether the cancellation property for projective modules holds for the irrational rotation c algebras discussed in 30 which as elliott 11 has suggested can appropriately be called 2 dimensional non commutative tori in more concrete terms the question is whether two projections in such an algebra which have the same trace must be unitarily equivalent the present paper provides the general theory which is needed for the affirmative answer which i obtained in a subsequent paper i will derive the

mean absolute deviation portfolio optimization model and its applications to tokyo stock market the purpose of this paper is to demonstrate that a portfolio optimization model using the l1 risk mean absolute deviation risk function can remove most of the difficulties associated with the classical markowitz s model while maintaining its advantages over equilibrium models in particular the l1 risk model leads to a linear program instead of a quadratic program so that a large scale optimization problem consisting of more than 1 000 stocks may be solved on a real time basis numerical experiments using the historical data of nikkei 225 stocks show that the l1 risk model generates a portfolio quite similar to that of the markowitz s model within a fraction of time required to solve the latter

solving non linear portfolio optimization problems with the primal dual interior point method stochastic programming is recognized as a powerful tool to help decision making under uncertainty in financial planning the deterministic equivalent formulations of these stochastic programs have huge dimensions even for moderate numbers of assets time stages and scenarios per time stage so far models treated by mathematical programming approaches have been limited to simple linear or quadratic models due to the inability of currently available solvers to solve nlp problems of typical sizes however stochastic programming problems are highly structured the key to the efficient solution of such problems is therefore the ability to exploit their structure interior point methods are well suited to the solution of very large non linear optimization problems in this paper we exploit this feature and show how portfolio optimization problems with sizes measured in millions of constraints and decision variables featuring constraints on semi variance skewness or non linear utility functions in the objective can be solved with the state of the art solver

on some characterizations of the star partial ordering for matrices and rank subtractivity abstract the main result is that drazin s star partial ordering a b holds if and only if a b and b a b a where a b is defined by a a a b and aa ba and where a b denotes rank subtractivity here a and b are m n complex matrices and the superscript denotes the moore penrose inverse several other characterizations of a b are given with particular emphasis on what extra condition must be added in order that rank subtractivity becomes the stronger star order a key tool is a new canonical form for rank subtractivity connections with simultaneous singular value decompositions schur complements and idempotent matrices are also mentioned

some orders for operators on hilbert spaces in this paper we present some interesting properties of the diamond left right star and sharp orders for operators on hilbert spaces

direct strain feedback control of flexible robot arms new theoretical and experimental results this paper addresses control problems for flexible robot arms by using direct strain feedback the purpose is to make clear why direct strain feedback can damp out vibration of flexible arms satisfactorily we concentrate on one link flexible robot arms whose dynamic models can be represented by linear partial differential equations with appropriate boundary conditions which have been well examined in a number of papers a key contribution of this paper is the introduction of the concept of strict a dependent operators which allows us to prove rigorously the closed loop stability of direct strain feedback and the existence and uniqueness of nonstandard second order abstract differential equations in hilbert spaces several control experiments are performed verifying the main theoretical points of this paper demonstrating satisfactory control results of direct strain feedback and leading to potential application of this simple control method for flexible robot control

random variables monotone relations and convex analysis random variables can be described by their cumulative distribution functions a class of nondecreasing functions on the real line those functions can in turn be identified after the possible vertical gaps in their graphs are filled in with maximal monotone relations such relations are known to be the subdifferentials of convex functions analysis of these connections yields new insights the generalized inversion operation between distribution functions and quantile functions corresponds to graphical inversion of monotone relations in subdifferential terms it corresponds to passing to conjugate convex functions under the legendre fenchel transform among other things this shows that convergence in distribution for sequences of random variables is equivalent to graphical convergence of the monotone relations and epigraphical convergence of the associated convex functions measures of risk that employ quantiles var and superquantiles cvar either individually or in mixtures are illuminated in this way formulas for their calculation are seen from a perspective that reveals how they were discovered the approach leads further to developments in which the superquantiles for a given distribution are interpreted as the quantiles for an overlying superdistribution in this way a generalization of koenker basset error is derived which lays a foundation for superquantile regression as a higher order extension of quantile regression

matrix partial orders through generalized inverses unified theory the unified theory presented here covers as special cases the star order of drazin the minus order of hartwig and nambooripad the sharp order and other partial orders introduced by the author

risk averse two stage stochastic linear programming modeling and decomposition we formulate a risk averse two stage stochastic linear programming problem in which unresolved uncertainty remains after the second stage the objective function is formulated as a composition of conditional risk measures we analyze properties of the problem and derive necessary and sufficient optimality conditions next we construct a new decomposition method for solving the problem that exploits the composite structure of the objective function we illustrate its performance on a portfolio optimization problem

a unified approach to uncertain optimization abstract in this paper we consider uncertain scalar optimization problems with infinite scenario sets we apply methods from vector optimization in general spaces set valued optimization and scalarization techniques to develop a unified characterization of different concepts of robust optimization and stochastic programming these methods provide new insights on the interrelation between different concepts for handling uncertainties and naturally lead to new concepts of robustness

analysis and control of a two link and three joint elastic robot arm a robot system composed of two link arm and three joint is considered in this paper an evolution equation corresponding to the robot system formulated by partial differential equations with initial and boundary conditions is established in an appropriate hilbert space the spectral properties of the main operator of the evolution equation is first discussed and then its semigroup generation is presented based on the resulting spectral properties of finally an asymptotical behavior of the robot system under a designed feedback control is shown in terms of semigroup approach

second order stochastic dominance constrained portfolio optimization theory and computational tests abstract due to the definition of second order stochastic dominance ssd in terms of utility theory portfolio optimization with ssd constraints is of major practical interest we contribute to the field in two ways first we present a self contained theory with some new results and new proofs of known results second we perform a set of tests for computational efficiency we provide new and simple arguments for the formulation of ssd constraints in a mathematical programming framework for many individuals an ssd constraint may seem too severe wherefore various relaxations assd have been proposed we introduce yet another relaxation directional ssd where a candidate portfolio is admissible if a step from the benchmark in the direction of the candidate yields a dominating portfolio optimal step size depends on individual preferences reflected by the objective function we compare computational efficiency of seven approaches for sd constrained portfolio problems including ssd and assd constrained cases

process based risk measures and risk averse control of discrete time systems for controlled discrete time stochastic processes we introduce a new class of dynamic risk measures which we call process based their main feature is that they measure risk of processes that are functions of the history of a base process we introduce a new concept of conditional stochastic time consistency and we derive the structure of process based risk measures enjoying this property we show that they can be equivalently represented by a collection of static law invariant risk measures on the space of functions of the state of the base process we apply this result to controlled markov processes and we derive dynamic programming equations we also derive dynamic programming equations for multistage stochastic programming with decision dependent distributions

stochastically weighted stochastic dominance concepts with an application in capital budgeting abstract the problem of comparing random vectors arises in many applications we propose three new concepts of stochastically weighted dominance for comparing random vectors x and y the main idea is to use a random vector v to scalarize x and y as v t x and v t y and subsequently use available concepts from stochastic dominance and stochastic optimization for comparison for the case where the distributions of x y and v have finite support we give mixed integer linear inequalities that can be used for random vector comparison as well as for modeling of optimization problems where one of the random vectors depends on decisions to be optimized some advantages of the proposed new concepts are illustrated with the help of a capital budgeting example

orthogonality preserving linear maps on c algebras with non zero socles abstract we study orthogonality preserving surjective linear maps from a unital c algebra with non zero socle a to a c algebra in particular we prove that when a has essential socle every biorthogonality preserving surjective linear map t a b is automatically bounded and a jordan isomorphism multiplied by an invertible element

risk adjusted probability measures in portfolio optimization with coherent measures of risk abstract we consider the problem of optimizing a portfolio of n assets whose returns are described by a joint discrete distribution we formulate the mean risk model using as risk functionals the semideviation deviation from quantile and spectral risk measures using the modern theory of measures of risk we derive an equivalent representation of the portfolio problem as a zero sum matrix game and we provide ways to solve it by convex optimization techniques in this way we reconstruct new probability measures which constitute part of the saddle point of the game these risk adjusted measures always exist irrespective of the completeness of the market we provide an illustrative example in which we derive these measures in a universe of 200 assets and we use them to evaluate the market portfolio and optimal risk averse portfolios

on group inverses and the sharp order abstract in this work the group inverse of a matrix is used to define the order on square matrices of index 1 the order is similar to the order of drazin 2 and the minus order of hartwig 6 10 and nambooripad 17 the order and the order are compared and contrasted many conditions are given which assure the equivalence of the various partial orders studied

portfolio construction based on stochastic dominance and target return distributions mean risk models have been widely used in portfolio optimization however such models may produce portfolios that are dominated with respect to second order stochastic dominance and therefore not optimal for rational and risk averse investors this paper considers the problem of constructing a portfolio which is non dominated with respect to second order stochastic dominance and whose return distribution has specified desirable properties the problem is multi objective and is transformed into a single objective problem by using the reference point method in which target levels known as aspiration points are specified for the objective functions a model is proposed in which the aspiration points relate to ordered outcomes for the portfolio return this concept is extended by additionally specifying reservation points which act pre emptively in the optimization model the theoretical properties of the models are studied the performance of the models on real data drawn from the hang seng index is also investigated

automatic continuity of biorthogonality preservers between compact c algebras and von neumann algebras abstract we prove that every biorthogonality preserving linear surjection between two dual or compact c algebras or between two von neumann algebras is automatically continuous

automatic continuity of m norms on c algebras abstract elements a and b of a c algebra are called orthogonal a b if a b a b 0 we say that vectors x and y in a banach space x are semi m orthogonal x sm y if x y max x y we prove that every linear bijection t a x where x is a banach space a is either a von neumann algebra or a compact c algebra and t a sm t b whenever a b must be continuous consequently every complete semi m norm on a von neumann algebra or on a compact c algebra is automatically continuous

groups quasidiagonality and interpolation by multiplier projections we relate the following conditions on a a unital c algebra a with the fs property a k1 a 0 b every projection in m a a lifts c the general weyl von neumann theorem holds in m a any selfadjoint element h in m a can be written as h a lpi a for some selfadjoint element a in a some bounded real sequence ai and some mutually orthogonal projections pi in a with ez1 pi 1 d m a has fs and e interpolation by multiplier projections holds for any closed projections p and q in a with pq o there is a projection r in m a such that p b 4 a and that a x b if in addition a is stable combining the above results we obtain counterexamples to the conjecture of g k pedersen a has fs m a has fs for example the stabilized buncededdens algebras hence the generalized weyl von neumann theorem does not generally hold in l ha for a unital c algebras with fs

control and stability of a torsional elastic robot arm a mathematical model for a long elastic torsional robot beam is determined the above system can be expressed as an evolution equation on a hilbert space furthermore the system is shown to be stable and controllable and we design a controller for the system

exponential rank and exponential length of operators on hilbert c modules in this article we consider unitary operators on the hilbert c module ha associated with a large class of c algebras let l x denote the algebra consisting of all bounded linear operators on a separable hilbert space 7 and let k denote the algebra of all compact operators on r halmos and kakutani proved that every unitary operator on r is a product of four symmetries cf ha 143 haka for the case when x is a compact hausdorff space ringrose r recently considered the c algebra c x l q consisting of all norm continuous maps from x to l x and proved that every unitary element of c x l x can be written as a product of at most three exponentials in other words a norm continuous map u from x to the unitary group of l x forms a product of three norm continuous maps written as exp ihi exp ih2 exp ih3 where hl h2 and h3 are maps from x to the space of self adjoint operators in l x phillips and ringrose phr conjectured that every unitary of c x l x can even be approximated in the norm by products of two exponentials using techniques in the theory of c algebras but by a different approach we generalized ringrose s result to hilbert c modules associated with all a unital in particular all unital c algebras cf z8 we also proved in z8 similar results for the c algebra consisting of norm continuous maps from x to a purely infinite simple c algebra the purpose of this article is to settle the phillips ringrose conjecture in the affirmative and to prove a generalized version of the halmos kakutani theorem in haka we consider the group of unitary operators on hilbert c modules associated with the following two specific classes which together comprise the majority of interesting c algebras

risk averse dynamic programming for markov decision processes we introduce the concept of a markov risk measure and we use it to formulate risk averse control problems for two markov decision models a finite horizon model and a discounted infinite horizon model for both models we derive risk averse dynamic programming equations and a value iteration method for the infinite horizon problem we develop a risk averse policy iteration method and we prove its convergence we also propose a version of the newton method to solve a nonsmooth equation arising in the policy iteration method and we prove its global convergence finally we discuss relations to min max markov decision models

modeling stabilization and control of serially connected beams many flexible structures consist of a large number of components coupled end to end in the form of a chain in this paper we consider the simplest type of such structures which is formed by n seri

optimality and duality theory for stochastic optimization problems with nonlinear dominance constraints we consider a new class of optimization problems involving stochastic dominance constraints of second order we develop a new splitting approach to these models optimality conditions and duality theory these results are used to construct special decomposition methods

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