uncertainty principles for kac algebras in this paper we introduce the notation of bi shift of biprojections in subfactor theory to unimodular kac algebras we characterize the minimizers of the hirschman beckner uncertainty principle and the donoho stark uncertainty principle for unimodular kac algebras with biprojections and prove hardy s uncertainty principle in terms of the minimizers

polynomial embedding algorithms for controllers in a behavioral framework in this correspondence we will establish polynomial algorithms for computation of controllers in the behavioral approach to control in particular for the computation of controllers that regularly implement a given desired behavior and for controllers that achieve pole placement and stabilization by behavioral full interconnection and partial interconnection these synthesis problems were studied before in articles by belur and trentelman rocha and wood and willems in the reference section in the algorithms we will apply ideas around the unimodular and stable embedding problems the algorithms that are presented in this correspondence can be implemented by means of the polynomial toolbox of matlab

minimizers of the entropic uncertainty principle for locally compact quantum groups in this paper we give an alternative proof of the hirschman beckner uncertainty principle for locally compact quantum groups and characterize the minimizers of the uncertainty principles in this paper we give an alternative proof of the hirschman beckner uncertainty principle for locally compact quantum groups and characterize the minimizers of the uncertainty principles

constrained kaczmarz extended algorithm for image reconstruction abstract in this paper we present a constrained version of kaczmarz extended algorithm for improving image reconstruction from projections in computerized tomography we prove convergence of our algorithm in the general inconsistent case to a constrained least squares solution of the reconstruction problem under weaker hypothesis than those proposed in a previous paper by koltracht and lancaster for classical kaczmarz s projection method numerical experiments and comparisons are also presented on some model problems from the field of electromagnetic geotomography

nested bounds for the perron root of a nonnegative matrix abstract it is well known that for a nonnegative matrix a the smallest row sum r a and the largest row sum r a provide lower and upper bounds respectively for the perron root of a these bounds are generalized for a partitioned nonnegative matrix a the new bounds are better than r a and r a and they can be further improved by a refinement of the partition known monotonicity and convergence properties of r a and r a are generalized for the new bounds

upper bounds on the maximum modulus of subdominant eigenvalues of nonnegative matrices abstract upper bounds for the maximum modulus of the subdominant roots of square nonnegative matrices are obtained we provide a unified approach that yields or improves upon most of the bounds that have been obtained so far

on the rate of convergence of the alternating projection method in finite dimensional spaces abstract using the results of smith solmon and wagner k smith d solomon s wagner practical and mathematical aspects of the problem of reconstructing objects from radiographs bull amer math soc 83 1977 1227 1270 and nelson and neumann s nelson m neumann generalizations of the projection method with application to sor theory for hermitian positive semidefinite linear systems numer math 51 1987 123 141 we derive new estimates for the speed of the alternating projection method and its relaxed version in r m these estimates can be computed in at most o m 3 arithmetic operations unlike the estimates in papers mentioned above that require spectral information the new and old estimates are equivalent in many practical cases in cases when the new estimates are weaker the numerical testing indicates that they approximate the original bounds in papers mentioned above quite well

an uncertainty principle for unimodular quantum groups we present a generalization of hirschman s entropic uncertainty principle for locally compact abelian groups to unimodular locally compact quantum groups as a corollary we strengthen a well known uncertainty principle for compact groups and generalize the relation to compact quantum groups of kac type we also establish the complementarity of finite dimensional quantum group algebras in the non unimodular setting we obtain an uncertainty relation for arbitrary locally compact groups using the relative entropy with respect to the haar weight as the measure of uncertainty we also show that when restricted to q traces of discrete quantum groups the relative entropy with respect to the haar weight reduces to the canonical entropy of the random walk generated by the state

achievable behavior of general systems a basic question in systems and control theory concerns the characterization of the set of all achievable closed loop systems for a given plant system and a controller system to be designed this problem is addressed in a general behavioral context sufficient and often necessary conditions for a behavior to be achievable are given and for any achievable behavior a canonical controller is defined the results generalize previously obtained results obtained for finite dimensional linear systems the application to nonlinear differential systems is outlined

synchronization reachable topology and synchronization of discrete time linear multi agent systems in this note we consider the synchronization problem for discrete time linear multi agent systems with time varying network topology to describe a new joint connectivity condition for synchronization the concept of synchronization reachable topology is introduced under the conditions that agent dynamics is neutrally stable and network topology is synchronization reachable a synchronization and an exponential synchronization result are obtained using paracontraction theory the two results generalize in a natural way the classical results for the consensus of first order discrete time multi agent systems finally the effectiveness of the results is illustrated by a simulation example

an entropy based uncertainty principle for a locally compact abelian group abstract we classify all functions on a locally compact abelian group giving equality in an entropy inequality generalizing the heisenberg uncertainty principle in particular for functions on a real line we proof a conjecture of hirschman published in 1957

uncertainty principles for locally compact quantum groups abstract in this paper we prove the donoho stark uncertainty principle for locally compact quantum groups and characterize the minimizer which are bi shifts of group like projections we also prove the hirschman beckner uncertainty principle for compact quantum groups and discrete quantum groups furthermore we show hardy s uncertainty principle for locally compact quantum groups in terms of bi shifts of group like projections

stabilization pole placement and regular implementability in this paper we study control by interconnection of linear differential systems we give necessary and sufficient conditions for regular implementability of a given linear differential system we formulate the problems of stabilization and pole placement as problems of finding a suitable regularly implementable sub behavior of the manifest plant behavior the problem formulations and their resolutions are completely representation free and specified only in terms of the system dynamics control is viewed as regular interconnection a controller is a system that constrains the plant behavior through a distinguished set of variables namely the control variables the issue of implementation of a controller in the feedback configuration and its relation to regularity of interconnection is addressed freedom of disturbances in a plant and regular interconnection with a controller also turn out to be inter related

on the parametrization of all regularly implementing and stabilizing controllers in this paper we deal with problems of controller parametrization in the context of behavioral systems given a full plant behavior a subbehavior of the manifest plant behavior is called regularly implementable if it can be achieved as the controlled behavior resulting from the interconnection of the full plant behavior with a suitable controller behavior in such a way that the controller does not impose restrictions that are already present in the plant we establish a parametrization of all controllers that regularly implement a given behavior we also obtain a parametrization of all stabilizing controllers

the uncertainty principle on groups the classical uncertainty principle asserts that both a function and its fourier transform cannot be largely concentrated on intervals of small measure donoho and stark siam j app math 49 1989 pp 906 931 have shown recently that both cannot be largely concentrated on any sets of small measure in the case of functions on the line or functions on finite cyclic groups and with concentrations measured in l 2 the purpose of this note is to extend these results to functions on sigma finite locally compact abelian groups with concentrations measured in l p 1 leqq p leqq 2 the first uncertainty principle on groups due to matolcsi and szucs d r acad sci paris 277 1973 pp 841 843 deals with full rather than large concentration asserting that if a function and its fourier transform are supported by sets t and w then the product of the haar measures of t and w must be at least 1 for the case of full concentration in r n benedicks j math anal appl 106 1985 pp 1

the canonical controllers and regular interconnection we study the control problem from the point of view of the behavioral systems theory two controller constructions called canonical controllers are introduced we prove that for linear time invariant behaviors the canonical controllers implement the desired behavior if and only if there exists a controller that implements it we also investigate the regularity of the canonical controllers and establish the fact that they are maximally irregular this means a canonical controller is regular if and only if every other controller that implements the desired behavior is regular

strong underrelaxation in kaczmarz s method for inconsistent systems we investigate the behavior of kaczmarz s method with relaxation for inconsistent systems we show that when the relaxation parameter goes to zero the limits of the cyclic subsequences generated by the method approach a weighted least squares solution of the system this point minimizes the sum of the squares of the euclidean distances to the hyperplanes of the system if the starting point is chosen properly then the limits approach the minimum norm weighted least squares solution the proof is given for a block kaczmarz method

generalizations of the projection methods with application to sor theory for hermitian positive semidefinite linear systems ann n complex matrixb is calledparacontracting if b 2 1 and 0 x n i b bx 2 x 2 we show that a productb b k b k 1 b1 ofk paracontracting matrices is semiconvergent and give upper bounds on the subdominant eigenvalue ofb in terms of the subdominant singular values of theb i s and in terms of the angles between certain subspaces our results here extend earlier results due to halperin and due to smith solomon and wagner we also determine necessary and sufficient conditions forn numbers in the interval 0 1 to form the spectrum of a product of two orthogonal projections and hence characterize the subdominant eigenvalue of such a product in the final part of the paper we apply the upper bounds mentioned earlier to provide an estimate on the subdominant eigenvalue of the sor iteration matrix associated with ann n hermitian positive semidefinite matrixa none of whose diagonal entries vanish

iterative algorithms for large partitioned linear systems with applications to image reconstruction abstract we present a unifying framework for a wide class of iterative methods in numerical linear algebra in particular the class of algorithms contains kaczmarz s and richardson s methods for the regularized weighted least squares problem with weighted norm the convergence theory for this class of algorithms yields as corollaries the usual convergence conditions for kaczmarz s and richardson s methods the algorithms in the class may be characterized as being group iterative and incorporate relaxation matrices as opposed to a single relaxation parameter we show that some well known iterative methods of image reconstruction fall into the class of algorithms under consideration and are thus covered by the convergence theory we also describe a novel application to truly three dimensional image reconstruction

convergence properties of art and sor algorithms art algorithms with relaxation parameters are studied for general consistent or inconsistent linear algebraic systemsrx f and a general convergence theorem is formulated the advantage of severe underrelaxation is reexamined and clarified the relationship to solutions obtained by applying sor methods to the equationrr t y f is investigated

on interconnections control and feedback the purpose of this paper is to study interconnections and control of dynamical systems in a behavioral context we start with an extensive physical example which serves to illustrate that the familiar input output feedback loop structure is not as universal as we have been taught to believe this leads to a formulation of control problems in terms of interconnections subsequently we study interconnections of linear time invariant systems from this vantage point let us mention two of the results obtained the first one states that any polynomial can be achieved as the characteristic polynomial of the interconnection with a given plant provided the plant is not autonomous the second result states that any subsystem of a controllable system can be implemented by means of a singular feedback control law these results yield pole placement and stabilization of controllable plants as a special case these ideas are finally applied to the stabilization of a nonlinear system around an operating point

on the convergence of asynchronous paracontractions with application to tomographic reconstruction from incomplete data abstract convergence of iterative processes in c k of the form x i r i j i x 1 r i 1 1 p j i x i where j i 1 2 n i 1 2 is analyzed it is shown that if the matrices p 1 p n are paracontracting in the same smooth strictly convex norm and if the sequence j i i 1 has certain regularity properties then the above iterates converge this result implies the convergence of a parallel asynchronous implementation of the algebraic reconstruction technique art algorithm often used in tomographic reconstruction from incomplete data

rational representations and controller synthesis of l2 behaviors this paper considers linear dynamical systems restricted to square integrable trajectories following the behavioral formalism a number of relevant classes of linear and shift invariant l 2 systems are defined it is shown that rational functions analytic in specific half spaces of the complex plane prove most useful for representing such systems for various classes of l 2 systems this paper provides a complete characterization of system equivalence in terms of rational kernel representations of l 2 systems in addition a complete solution is given for the problem when selected non manifest variables of an l 2 system can be completely eliminated from their behavior this elimination theorem has considerable independent interest in general modeling problems it is shown that the elimination result is key in the solution of the problem for realizing an arbitrary l 2 system as the interconnection of a given l 2 system and a to be synthesized l 2 system in the context of control this problem amounts to characterizing the existence and parameterization of all controllers that after interconnection with a given plant constitute a desired controlled system

synthesis of dissipative systems using quadratic differential forms part ii the problem discussed is that of designing a controller for a linear system that renders a quadratic functional nonnegative our formulation and solution of this problem is completely representation free the system dynamics are specified by a differential behavior and the performance is specified through a quadratic differential form we view control as interconnection a controller constrains a distinguished set of system variables the control variables the resulting behavior of the to be controlled variables is called the controlled behavior the constraint that the controller acts through the control variables only can be succinctly expressed by requiring that the controlled behavior should be wedged in between the hidden behavior obtained by setting the control variables equal to zero and the plant behavior obtained by leaving the control variables unconstrained the main result is a set of necessary and sufficient conditions for the existence of a controlled behavior that meets the performance specifications the essential requirement is a coupling condition an inequality that combines the storage functions of the hidden behavior and the orthogonal complement of the plant behavior

on the spectrum of the sor operator for symmetric positive definite matrices one attractive feature of the classical successive overrelaxation sor iterative method is its algorithmic simplicity whereas for linear systems with symmetric positive definite matrices a the theorem of ostrowski guarantees convergence as long as the relaxation parameter 0 2 results on the optimal choice of can only be obtained under certain additional assumtions on a here for positive definite systems with coefficient matrices a i l lt in which l is not necessarily strictly lower triangular we study the behavior of the spectrum of the sor operator l as 0 and 2 and describe enclosure sets which may be used to estimate the spectral radius of l for 0 2 numerical experiments show why results on the optimal relaxation parameter are difficult to obtain in the general case of positive definite systems

the structure of some matrices arising in tomography linear algebraic systems rx y are considered which are generated by typical limited angle tomographic problems a detailed examination is made of vectors x for which rx 0 and which are responsible for ghost images frequently referred to in the literature in particular the construction of an orthogonal basis for the subspace of all such vectors x is investigated and is complete in some special cases it is shown how advantage can be taken of this information

trajectory control and interconnection of 1d and nd systems in this paper we examine the relationship between control viewed as concatenation of trajectories and control viewed as interconnection of systems we show that for one dimensional linear time invariant systems the ability to obtain a given subsystem by regular interconnection a prerequisite for any feedback type structure is equivalent to the ability to drive any trajectory into that subsystem however in the case of multidimensional systems the former is a stronger property than the latter trajectory controllability can however be expressed as a regular interconnection of behaviors in an extended variable space by introducing latent or auxiliary variables this leads as a by product to the notion of controlling a system by means of latent variables

on the acceleration of kaczmarz s method for inconsistent linear systems abstract let the linear system ax b be rectangular but solvable if a is a large sparse matrix then one possibility to solve the system is to use the iterative method of kaczmarz even in the case when the system is unsolvable this method is applicable if the relaxation parameters are kept fixed in a certain interval to get a meaningful result however one has to apply strong underrelaxation we give an interpretation of the limit in terms of a generalized inverse of a and derive bounds with respect to the least squares solution using a result of buoni and varga we estimate the speed of convergence it is further shown that the eigenvalues of the iteration matrix are nearly real numbers and we propose to use chebyshev acceleration this results in a significant speedup