a constructive representation for the fourier dual of the zadoff chu sequences in this paper a complex matrix c consisting of a set of perfect sequences is studied the matrix c is constructed by taking the inverse discrete fourier transform idft of a diagonal matrix in which the diagonal elements comprise an arbitrary periodically perfect sequence gamma properties of the matrix c are presented in addition the fourier dual e of the matrix c is investigated when gamma is a zadoff chu sequence for the case of n even m 1 and g 0 an explicit representation for the matrix e is derived

diameters and eigenvalues we derive a new upper bound for the diameter of a k regular graph g as a function of the eigenvalues of the adjacency matrix namely suppose the adjacency matrix of g has eigenvalues ai a2 a with ia i i vi21 ia i where ai k a ia21 then the diameter d g must satisfy d g we will consider families of graphs whose eigenvalues can be explicitly de termined these graphs are determined by sums or differences of vertex labels namely the pair i j being an edge depends only on the value i j or i j for directed graphs we will show that these graphs are expander graphs with small diameters by using an inequality on character sums which was recently proved by n m katz bell communications research 445 south street morristown new jersey 07960 this content downloaded from 207 46 13 111 on sat 21 may 2016 07 00 04 utc all use subject to http about jstor org terms

holomorphic quantization on the torus and finite quantum mechanics we explicitly construct the quantization of classical linear maps of on toroidal phase space of arbitrary modulus using the holomorphic chiral version of the metaplectic representation we show that finite quantum mechanics fqm on tori of arbitrary integer discretization is a consistent restriction of the holomorphic quantization of to the subgroup being the principal congruent subgroup on a finite dimensional hilbert space the generators of the rotation group for arbitrary values of l are determined as well as their quantum mechanical eigenvalues and eigenstates

eigenvalue assignment by minimal state feedback gain in lti multivariable systems in this article an improved method for eigenvalue assignment via state feedback in the linear time invariant multivariable systems is proposed this method is based on elementary similarity operations and involves mainly utilisation of vector companion forms and thus is very simple and easy to implement on a digital computer in addition to the controllable systems the proposed method can be applied for the stabilisable ones and also systems with linearly dependent inputs moreover two types of state feedback gain matrices can be achieved by this method 1 the numerical one which is unique and 2 the parametric one in which its parameters are determined in order to achieve a gain matrix with minimum frobenius norm the numerical examples are presented to demonstrate the advantages of the proposed method

finite analogues of euclidean space graphs are attached to fqn where fq is the field with q elements q odd using an analogue of the euclidean distance the graphs are shown to be asymptotically ramanujan for large q better than ramanujan in half the cases comparisons are made with finite upper half planes constructed in a similar way using an analogue of poincare s non euclidean distance the eigenvalues of the adjacency operators of the finite euclidean graphs are shown to be kloosterman sums

parametric output feedback controller design abstract a parameterization of fixed gain output feedback controllers which will assign a complete set of distinct eigenvalues to a given state space system is presented the main result is a compact parametric expression for the output feedback controller gain matrix explicitly characterized by two sets of free parameters the set of n closed loop system eigenvalues and a set of mr n design parameters for n state r input m output systems the free design parameters are determined by a sequential design procedure which automatically satisfies the basic orthogonality constraints on the left and right closed loop eigenvectors under the condition m r n the principal benefits of the explicit characterization of a parametric class of output feedback controllers lie in the ability to directly accommodate various different design criteria an illustration of the parametric output feedback design procedure is given by way of approximating the optimal full state regulator response of a fifth order pilot plant evaporator model

convex invariant means and a pathwise central limit theorem on etudie le probleme de choisir un point aleatoirement a partir de la ligne des reels on definit une notion de distribution d espace uniforme on considere trois sources supplementaires d uniformite l invariance d echelle convexe la consistance avec des methodes de moyennes et la linearite mesure de mokobodski

use of the design freedom of time optimal control abstract a method for synthesizing a state feedback time optimal controller for linear n state r input discrete time systems is developed the nonuniqueness of the solution is organized in such a way as to select the controller with the minimum value of the frobenius norm of the feedback gain matrix k it is shown that among the rn design parameters in the parametric form of k only r n rp r need to be considered in the search technique where p r is the order of the smallest jordan block in the jordan form of the closed loop system

a problem of time in the multiplicative scheme for the n site hopper quantum measure theory qmt is an approach to quantum mechanics based on the path integral in which quantum theory is conceived of as a generalised stochastic process one of the postulates of qmt is that events with zero quantum measure do not occur however this is not sufficient to give a full picture of the quantum world determining the other postulates is a work in progress and this paper investigates a proposal called the multiplicative scheme for qmt in which the physical world corresponds essentially to a set of histories from the path integral this scheme is applied to sorkin s n site hopper a discrete unitary model of a single particle on a ring of n sites motivated by free schrodinger propagation it is shown that the multiplicative scheme s global features lead to the conclusion that no non trivial time finite event can occur

author s reply to comments on eigenstructure assignment in linear multivariable systems a parametric solution by m m fahmy and j o reilly the authors reply that klein is correct in his observation that the approaches to eigenstructure assignment in earlier articles by b c moore 1976 g klein and moore 1977 are equivalent to those of the authors they assert however that their philosophies are quite different these differences are then described

dead beat control of linear discrete time systems the paper considers the problem of determining the various classes of state feed back dead beat controllers for linear multivariable discrete time systems unlike earlier work attention is not restricted to the special case of minimum time dead beat controllers a general dead beat control problem is posed and solved the solution is based principally on an approach of closed loop eigenstructure assignment the minimum of free parameters in each class are specified and used in an explicit parametric form for the feedback gain matrix the concept of the greatest minimum of free parameters is introduced finally the method is illustrated by a numerical example

parametric compensator design a parametrization of dynamical output feedback compensators that will assign a complete set of distinct eigenvalues to a given state space system is presented the main result is a compact parametric expression for the gain matrices of an output feedback compensator of dynamical order i n m r explicitly characterized by two sets of free parameters the set of n l closed loop system eigenvalues and a set of n mr n m r 1 effective free parameters for n state r input m output systems these latter n effective free parameters are determined by a sequential design procedure the principal benefits of the explicit characterization of a parametric class of dynamical output feedback compensators lie in the ability to directly accommodate various different design criteria

quantum mechanics on p adic fields a formulation of quantum mechanics on p adic number fields is presented quantum amplitudes are taken as complex functions of p adic variables and it is shown how the weyl approach to quantum mechanics can be generalized to the p adic case the p adic analogs of simple one dimensional systems free particle compact and noncompact oscillators are defined by a group of motion which is an abelian subgroup of sl 2 qp in each case the evolution operator is a unitary representation of the appropriate group its spectrum is given by characters and its eigenstates are calculated

minimum gain minimum time deadbeat controllers abstract this paper considers the design of minimum gain minimum time deadbeat controllers mgmtdc for linear discrete time systems a new direct method for constructing the mgmtdc of minimum frobenius norm is developed compared with many existing techniques the proposed method gives analytic expressions for the constructed mgmtdc requires less computational effort and does not require that the transition matrix be nonsingular

parametric eigenstructure assignment by output feedback control the case of multiple eigenvalues this paper deals with closed loop eigenstructure assignment by output feedback control in linear multivariable systems for the general case of multiple eigenvalues the approach is algebraic in nature and operates directly on the closed loop characteristic equation using fundamental properties of determinants and their derivatives a compact form for the controller gain matrix is derived and expressed in terms of a set of parameter vectors that specify the non uniqueness of the solution of the eigenvalue assignment problem some of these parameter vectors assume restricted forms while others are free a computational scheme is given in which the free parameter vectors are determined in such a way as to assign the corresponding eigenvectors and generalized eigenvectors in a weighted least square error sense an illustrative numerical example is included

output feedback pole placement in the design of suboptimal linear quadratic regulators a design oriented methodology is presented for the construction of low order suboptimal output feedback compensators the design is suboptimal in the sense that it retains an l dimensional eigenspace from a reference optimal state feedback linear quadratic regulator problem if r is the number of outputs then for fixed l r it is known that the design requires a dynamic compensator of dimension l r the parameters of the compensator are determined by the solution of an associated output feedback pole placement problem using iterative dyadic pole placement a procedure is given which determines the solution of this problem without a priori assumptions on the dimension of the compensator the design is also extended to the class of stabilizable systems and the resulting compensator is shown to possess a separation property

erdos distance problem in vector spaces over finite fields we study the erdos falconer distance problem in vector spaces over finite fields let be a finite field with elements and take we develop a fourier analytic machinery analogous to that developed by mattila in the continuous case for the study of distance sets in to provide estimates for minimum cardinality of the distance set in terms of the cardinality of bounds for gauss and kloosterman sums play an important role in the proof

graph spectra for finite upper half planes over rings abstract graphs attached for finite analogues of the poincare upper half plane over rings z p r z are introduced for p an odd prime the spectra of these graphs for r 2 are shown to be related to those for r 1 which were studied earlier in contrast to the case r 1 we find that the graphs are not ramanujan graphs when r 2 and p 5 histograms of the eigenvalues for r 1 and 2 are also compared the graphs over rings are of interest for connections with p adic upper half planes as well as fundamental domains for congruence subgroups of the modular group sl 2 z

eigenstructure assignment by decentralized output feedback a complete parametric approach the problem of eigenstructure assignment in multivariable linear systems by decentralized output feedback is considered by using a complete parametric solution of a generalized sylvester matrix equation parametric representations of both the left and right closed loop eigenvectors and generalized eigenvectors as well as the feedback gains with respect to the closed loop eigenvalues and two series of partially free parameter vectors are established the obtained result does not require any conditions on the closed loop eigenvalues and generalizes some previous results in this area an example shows the effect of the proposed approach

artin schreier curves exponential sums and coding theory abstract this is a survey of some results recently obtained on the distribution of the weights of some classical linear codes on the one hand such as the dual of the melas code and the geometric bch codes discovered by goppa subfield subcodes of goppa codes on the other hand these results depend upon the properties of certain algebraic curves defined over a finite field and the associated exponential sums such as the kloosterman sums

low correlation sequences from linear combinations of characters pairs of binary sequences formed using linear combinations of multiplicative characters of finite fields are exhibited that when compared with a random sequence pairs simultaneously achieve significantly lower mean square autocorrelation values for each sequence in the pair and significantly lower mean square crosscorrelation values if we define crosscorrelation merit factor analogously to the usual merit factor for autocorrelation and if we define demerit factor as the reciprocal of merit factor then randomly selected binary sequence pairs are known to have an average crosscorrelation demerit factor of 1 our constructions provide sequence pairs with a crosscorrelation demerit factor significantly less than 1 and at the same time the autocorrelation demerit factors of the individual sequences can also be made significantly less than 1 which also indicates better than average performance the sequence pairs studied here provide combinations of autocorrelation and crosscorrelation performance that are not achievable using sequences formed from single characters such as maximal linear recursive sequences m sequences and legendre sequences in this paper exact asymptotic formulae are proved for the autocorrelation and crosscorrelation merit factors of sequence pairs formed using linear combinations of multiplicative characters data is presented that shows that the asymptotic behavior is closely approximated by sequences of modest length

efficient computation of root numbers and class numbers of parametrized families of real abelian number fields let k m be a parametrized family of simplest real cyclic cubic quartic quintic or sextic number fields of known regulators e g the so called simplest cubic and quartic fields associated with the polynomials p m x x3 mx2 m 3 x 1 and p m x x 4 mx 3 6x 2 mx 1 we give explicit formulas for powers of the gaussian sums attached to the characters associated with these simplest number fields we deduce a method for computing the exact values of these gaussian sums these values are then used to efficiently compute class numbers of simplest fields finally such class number computations yield many examples of real cyclotomic fields q p of prime conductors p 3 and class numbers h p greater than or equal to p however in accordance with vandiver s conjecture we found no example of p for which p divides h p

a polynomial approach to eigenstructure assignment using projection with eigenvalue trade off a novel eigenstructure assignment method is presented which trades exact closed loop eigenvalue location against an improvement in the associated closed loop eigenvector match against membership of a desired set via either constrained or unconstrained optimizations the polynomial approach removes the dependence of the cost functions on the closed loop eigenvector by describing the allowable desired eigenvector subspace as a function of the eigenvalue location a fixed wing aircraft example is used to demonstrates the benefit of eigenvalue trade off over basic projection

on eigenstructure assignment in linear multivariable systems the eigenvalue assignment approach of brogan 1 2 is generalized and extended to the assignment of the entire closed loop eigenstructure of linear multivariable systems the set of assignable eigenvectors and generalized eigenvectors emerges naturally in the solution and is given moreover in an explicit parametric form two numerical examples are worked out to demonstrate the application of the procedure

parameterization of the class of deadbeat controllers this technical note deals with the problem of parameterizing the class of deadbeat controllers for a given system through the minimum of parameters it is shown that if n and m are dimensions of the state vector and control vector respectively and the i s are the controllability indexes then almost the whole class of deadbeat controllers is explicitly parameterizable through mn mu 1 3 mu 2 2m 1 mu m parameters

the stability of feedback control with nonlinear saturating actuator time domain approach sufficient conditions for stability of closed loop systems with a saturating actuator are derived from the viewpoint of time domain the bellman gronwall inequality is used to investigate the stability of these systems three kinds of controllers are considered to treat this constrained control problem finally an example is given to illustrate the results

an angular momentum approach to quadratic fourier transform hadamard matrices gauss sums mutually unbiased bases the unitary group and the pauli group the construction of unitary operator bases in a finite dimensional hilbert space is reviewed through a nonstandard approach combining angular momentum theory and representation theory of su 2 a single formula for the bases is obtained from a polar decomposition of su 2 and is analyzed in terms of cyclic groups quadratic fourier transforms hadamard matrices and generalized gauss sums weyl pairs generalized pauli operators and their application to the unitary group and the pauli group naturally arise in this approach

parameterization of reduced order compensator in the frequency domain after a brief survey of the relations between time and frequency domain representations of the observer based linear state feedback loop the parameterization of the compensator is discussed it is shown that the free parameters specified by the state feedback matrix k and the output error feedback matrix l in the time domain appear as coefficients in the polynomial matrices dtilde s and s characterizing the closed loop dynamics in the frequency domain these polynomial matrices can either be chosen arbitrarily pole placement problem or they may be derived as solutions from the corresponding optimal control or the optimal estimation problems respectively starting from the polynomial matrices dtilde s and s the doubly coprime fractional representations of the system and of the compensator transfer matrices can be computed directly without recurrence to the time domain results from these representations the right and left coprime compensator matrix fraction descriptions can easily be evalu

parametric output feedback control with response insensitivity a recent parameterization of the class of linear output feedback controllers that assign a set of desired self conjugate eigenvalues to the closed loop system is used to formulate and solve a fundamental response insensitivity problem it is established to what extent output feedback control can be used to render the closed loop system response insensitive to possibly many not necessarily small parameter variations in the open loop state space model a non conservative sequential design procedure is developed for making as many of the closed loop system eigenmodes as possible totally insensitive while retaining arbitrary assignment of the maximum number of closed loop eigenvalues the main result is a class of desensitizing fixed gain output feedback controllers explicitly specified by a set of free parameters which may be chosen to satisfy additional design requirements conditions are given for total modal decoupling insensitivity to possibly many not necessarily small parameter variations in the open l

on the asymptotic connection between two exponential sums the relation between the exponential sums sn x p n 0n 1exp ixnp and t0 t0 x n p n 1 e n nexp ixnpe pn n where x 0 and p 0 is investigated it is demonstrated that there is an asymptotic connection as n which is found numerically to be valid provided the variable x satisfies the restriction xnp o n when p 1 the sum t0 is shown to be associated with a zeta function defined by z s n 1 exp i e an n s for real and a 0

modal synthesis of multivariable systems with observers of specified order abstract the problem of pole assignment in multivariable linear systems with observers of a given order v is considered by way of a simple proof a very general result is established which constitutes an extension of all theorems known in the literature on pole assignment via observers on its basis an efficient design algorithm is worked out

feynman s path integral and mutually unbiased bases our previous work on quantum mechanics in hilbert spaces of finite dimension n is applied to elucidate the deep meaning of feynman s path integral pointed out by g svetlichny he speculated that the secret of the feynman path integral may lie in the property of mutual unbiasedness of temporally proximal bases we confirm the corresponding property of the short time propagator by using a specially devised n n approximation of quantum mechanics in applied to our finite dimensional analogue of a free quantum particle

averages over hyperplanes sum product theory in vector spaces over finite fields and the erdos falconer distance conjecture we prove a pointwise and average bound for the number of incidences between points and hyperplanes in vector spaces over finite fields while our estimates are in general sharp we observe an improvement for product sets and sets contained in a sphere we use these incidence bounds to obtain significant improvements on the arithmetic problem of covering f q the finite field with q elements by a a a a where a is a subset f q of sufficiently large size we also use the incidence machinery and develop arithmetic constructions to study the erdos falconer distance conjecture in vector spaces over finite fields we prove that the natural analog of the euclidean erdos falconer distance conjecture does not hold in this setting on the positive side we obtain good exponents for the erdos falconer distance problem for subsets of the unit sphere in f d q and discuss their sharpness this results in a reasonably complete description of the erdos falconer distance problem in higher dimensional vector spaces over general finite fields

eigenstructure assignment in linear multivariable systems a parametric solution this paper generalizes a recently reported method 1 of closed loop eigenstructure assignment via state feedback in a linear multivariable system with n states and r control inputs by introducing a lemma on the differentiation of determinants the class of assignable eigenvectors and generalized eigenvectors associated with the assigned eigenvalues is explicitly described by a complete set of n r dimensional free parameter vectors this parametric characterization conveniently organizes the nonuniqueness of the solution of the eigenvalue assignment problem and thereby provides an efficient means of further modifying the system dynamic response a numerical example is worked out to demonstrate the feasibility of the method

strictly proper projective controllers for disturbance attenuation a design methodology is presented which applies projective controls to the disturbance attenuation problem for large flexible structures through this method low order strictly proper controllers are designed which improve the disturbance attenuation properties of the system a new parameterization of the closed loop system in terms of free parameters in the projective controller leads to an auxiliary minimization problem which determines the parameters of the controller a flexible structure example demonstrates the use of this methodology

parameterizations of the state feedback controllers for linear multivariable systems abstract a general framework is constructed upon which an explicit parametric formula can be derived for state feedback controllers containing all the possible combination of parameters the relation between the parameters is nonlinear in general and therefore many different constraint may be imposed by the designer to obtain desired performance criteria a couple of illustrative examples are presented

brief paper dynamic controllers in linear multivariable systems the theory of pole assignment in multivariable stationary linear systems using a controller of given order is reassessed novel proofs both simpler and more general than hitherto are given enabling efficient design algorithms to be formulated examples of such algorithms are worked out

restriction and kakeya phenomena for finite fields the restriction and kakeya problems in euclidean space have received much attention in the last few decades and they are related to many problems in harmonic analysis partial differential equations pdes and number theory in this paper we initiate the study of these problems on finite fields in many cases the euclidean arguments carry over easily to the finite setting and are in fact somewhat cleaner but there are some new phenomena in the finite case which deserve closer study

multistage parametric eigenstructure assignment by output feedback control this paper develops an efficient multistage parametric approach for eigenstructure assignment in linear multivariable systems by output feedback control the sets of closed loop eigenvalues and associated eigenvectors are suitably divided into subsets and the entire eigenstructure is constructed by parts in two or more consecutive stages this allows the subsets of right and left eigenvectors to be assigned in separate stages and thus the computational algorithm is relaxed from the orthogonality conditions the number of effective free parameters beyond eigenvalue assignment is determined and the notion of redistributing these parameters among the assignable right and left eigenvectors is introduced numerical examples are included to demonstrate the design procedure

spectral analysis of the affine graph over the finite ring abstract we apply two methods to the block diagonalization of the adjacency matrix of the cayley graph defined on the affine group the affine group will be defined over the finite ring z p n z the method of irreducible representations will allow us to find nontrivial eigenvalue bounds for two different graphs one of these bounds will result in a family of ramanujan graphs the method of covering graphs will be used to block diagonalize the affine graphs using a galois group of graph automorphisms in addition we will demonstrate the method of covering graphs on a generalized version of the graphs of lubotzky et al a lubotzky r phillips p sarnak ramanujan graphs combinatorica 8 1988 261 277

feedback gain optimization in decentralized eigenvalue assignment abstract this paper develops a new design procedure for minimizing the norm of a decentralized output feedback matrix which assigns a user specified set of eigenvalues two distinct approaches which can be meshed together as a unified design tool are derived assuming one has computed a decentralized feedback matrix which assigns a desired spectrum the first approach describes an iterative algorithm which reduces an algebraic cost function e g the frobenius norm of the feedback gains while maintaining the desired spectrum this algorithm allows for small movements in the eigenvalues the iteration step is based on the first order variational behaviour of the eigenvalue eigenvector equations the second algorithm modifies a continuation method for decentralized eigenvalue assignment to include an optimizing factor numerical considerations for the design procedures are discussed an example showing the improvement possible by the application of the procedure is also given

linking forms reciprocity for gauss sums and invariants of 3 manifolds we study invariants of 3 manifolds derived from finite abelian groups equipped with quadratic forms these invariants arise in turaev s theory of modular categories and generalize those of h murakami t ohltsuki and m okada the crucial algebraic tool is a new reciprocity formula for gauss sums generalizing classical formulas of cauchy kronecker krazer and siegel we use this reciprocity formula to give an explicit formula for the invariants and to generalize them to higher dimnensions

eigenstructure assignment via linear state feedback control in fahmy and o reilly 1982 a b a parametric solution for the linear state feedback eigenstructure assignment problem is developed this approach is here modified in such a way as to accommodate the case where the set of closed loop eigenvalues and the set of open loop eigenvalues have elements in common it is particularly shown that each common eigenvalue introduces a number of partially free design parameter vectors in addition to the original free ones the paper concludes with illustrative numerical examples

eigenstructure assignment in multivariable linear systems abstract a new design method of regulators using state feedback is developed this method not only assigns eigenvalues to the closed loop system but also assigns parts of the closed loop eigenvector structure illustration of the method in the case of a two link manipulator is included a new robustness measure is introduced

eigenvalue clustering in subregions of the complex plane eigenvalue clustering in subregions of the complex plane is investigated for multivariable linear feedback systems critical constraints of all the eigenvalues of a perturbed system causing it to stay within a specified region of the nominal system arc discussed a design procedure is developed for the selection of a parametrized class of state feedback gains for eigenvalue clustering an illustration of the method for the case of a bounded frequency region is included

equidistribution of gauss sums and kloosterman sums let m be a positive integer fix a nontrivial additive character for each finite field f q to state the first result of this paper we also fix r distinct multiplicative characters 1 r for each finite field f q with more than r elements we shall prove that when varies over multiplicative characters of f q other than the m th roots of open image in new window the r tuples open image in new window of angles of gauss sums are asymptotically equidistributed on the r dimensional torus s1 r as q goes to infinity

on parametric state feedback design an explicit parametric expression for the controller gain matrix in linear state variable feedback is derived it involves both the case where the set of closed loop eigenvalues does not include any open loop eigenvalue and the case where the two eigenvalue sets have elements in common some advantages of this new explicit parameterization of the controller gain matrix are illustrated by two numerical examples

eigenvalue assignment robustness the analysis for autonomous system matrices abstract new techniques are presented for the analysis of eigenvalue assignment robustness the basic idea is to use a root locus approach to ensure that the eigenvalues of a dynamic system under parameter perturbations are restricted in the distinct desired regions no restriction is imposed on the shapes of the specified regions both the norm bound and the element bound for the allowable perturbations are obtained scaling techniques are proposed to increase the allowable element bound the proposed methods are applicable to the continuous time case as well as to the discrete time case when the eigenvalues are just required to locate in the stable region the proposed criteria will become the stability robustness criteria

littlewood polynomials with small l4 norm abstract littlewood asked how small the ratio f 4 f 2 where denotes the l norm on the unit circle can be for polynomials f having all coefficients in 1 1 as the degree tends to infinity since 1988 the least known asymptotic value of this ratio has been 7 6 4 which was conjectured to be minimum we disprove this conjecture by showing that there is a sequence of such polynomials derived from the fekete polynomials for which the limit of this ratio is less than 22 19 4

sets with integral distances in finite fields given a positive integer n a finite field f q of q elements q odd and a non degenerate quadratic form q on f n q in this paper we study the largest possible cardinality of subsets f n q with pairwise integral q distances that is for any two vectors x x 1 x n y y 1 y n e one has q x y u 2 for some u f q

robust eigenstructure assignment for multi input systems abstract a new eigenstructure assignment scheme for multi input systems is proposed it is well known that for multi input systems the feedback gain is not unique and so cannot be used to obtain a desired set of closed poles in this paper the set of all such gains is parametrized by a matrix partition scheme it is shown that this non uniqueness of the feedback gains can be used to improve the robustness and noise rejection properties of the closed system when it is subject to possible uncertainties an illustrative example is included

the discrete linear time invariant time optimal control problem an overview a review of two decades of investigation into one of the fundamental problems of control theory the discrete linear time invariant time optimal control problem is presented two classes of multi input time optimal controller one based on system controllability and the other on eigenvalue assignment are considered in some detail also discussed are the dual state reconstruction problem the deadbeat control of linear systems with inaccessible state and other extensions the exposition is a unifying one and involves only that matrix algebra commonly encountered in control theory

state decomposition for singular perturbation order reduction a modal approach singular perturbation techniques for order reduction are based on decomposing the high order system into two parts approximation of the high order system dynamics by the low order model is mainly dependent on this partition this paper introduces a measure for the degree of dependence of the state variables on the high order dominant eigenvalues by means of this measure it is not only possible to find an appropriate decomposition yielding a good low order model but also to get an indication of the order of the reduced model two illustrative examples demonstrate the main results

dixon selberg summation over local number fields the character summation formula analogous to dixon s theorem for the hypergeometric function 3f2 is derived for r and qp

symmetrization of the hurwitz zeta function and dirichlet l functions we consider the hurwitz zeta function z s a and form two parts zc and zk by symmetric and antisymmetric combinations of z s a a ndz s 1ka we consider the properties of zc and zk and then show that each may be decomposed into parts denoted by p and n each of which obeys a functional equation of the dirichlet l type with a multiplicative factor of k1 for the functions n we show the results of this procedure for rational az p q with qz1 2 3 4 5 6 7 8 10 and demonstrate that the functions p and n have some of the key properties of dirichlet l functions

computational methods for parametric lq problems a survey iterative methods for finding the optimal constant feedback gains for parametric lq problems notably for optimal constant output feedback problems are surveyed the connections of several methods to loss function expansions are discussed with important implications to the understanding of their convergence properties especially the descent anderson moore method levine athans like methods and the newton method are considered convergence results are also included the initialization problem and the output feedback stabilization problem are also discussed furthermore it is shown that the concepts and methods surveyed in this paper are useful in solving many realistic generalized parametric lq problems as well notably so called robust parametric lq problems

q extension of mehta s eigenvectors of the finite fourier transform for q a root of unity it is shown that the continuous q hermite polynomials for q a root of unity have simple transformation properties with respect to the classical fourier transform this result is then used to construct q extended eigenvectors of the finite fourier transform in terms of these polynomials

dynamical order assignment for linear descriptor systems this paper considers the problem of dynamical order assignment for linear descriptor systems by derivative feedback control the approach is based on an ability to adjust the number of infinite non dynamical modes of the system within a permissible range increasing the dynamical order enables the designer to implement specific otherwise unrealizable control strategies on the other hand dynamical order reduction simplifies the design procedures for a large scale system the solution is obtained by imbedding the descriptor space problem in an equivalent state space problem where a zero value eigenvalue with a prescribed geometric multiplicity is assigned to a linear state system by proportional feedback control

phase operators temporally stable phase states mutually unbiased bases and exactly solvable quantum systems we introduce a one parameter generalized oscillator algebra that covers the case of the harmonic oscillator algebra and discuss its finite and infinite dimensional representations according to the sign of the parameter we define an hamiltonian operator associated with and examine the degeneracies of its spectrum for the finite when 0 and the infinite when 0 representations of we construct the associated phase operators and build temporally stable phase states as eigenstates of the phase operators to overcome the difficulties related to the phase operator in the infinite dimensional case and to avoid the degeneracy problem for the finite dimensional case we introduce a truncation procedure which generalizes the one used by pegg and barnett for the harmonic oscillator this yields a truncated generalized oscillator algebra where s denotes the truncation order we construct two types of temporally stable states for as eigenstates of a phase operator and as eigenstates of a polynomial in the generators of two applications are considered in this paper the first concerns physical realizations of and in the context of one dimensional quantum systems with finite morse system or infinite poschl teller system discrete spectra the second deals with mutually unbiased bases used in quantum information

analysis of quantum walks with time varying coin on d dimensional lattices in this paper we present a study of discrete time quantum walks whose underlying graph is a d dimensional lattice the dynamical behavior of these systems is of current interest because of their applications in quantum information theory as tools to design quantum algorithms we assume that at each step of the walk evolution the coin transformation is allowed to change so that we can use it as a control variable to drive the evolution in a desired manner we give an exact description of the possible evolutions and of the set of possible states that can be achieved with such a system in particular we show that it is possible to go from a state where there is probability 1 for the walker to be found in a vertex to a state where all the vertices have equal probability we also prove a number of properties of the set of admissible states in terms of the number of steps needed to obtain them we provide explicit algorithms for state transfer in low dimensional cases as well as results that allow to reduce algorithms on two dimensional lattices to algorithms on the one dimensional lattice the cycle

robust eigenstructure assignment via dynamical compensators abstract based on a proposed complete parametric approach for eigenstructure assignment in multivariable linear systems via dynamical compensators insightful parametrizations of the closed loop eigenvalues sensitivities to the perturbed elements in the open loop system matrices are obtained and an effective algorithm for eigenvalue assignment with minimum sensitivity in multivariable linear systems via dynamical compensators is then proposed the algorithm does not contain going back procedures and allows the closed loop eigenvalues to be conveniently optimized within desired regions a numerical example demonstrates its effect simplicity and numerical property

a generalization of the strassen converse this note is devoted to a generalization of the strassen converse let gn r 0 n 1 be a sequence of measurable functions such that for every n 1 gn x y2 c gn x gn y and gn x y2 c gn x gn y for all x y r where 0 c is a constant which is independent of n let x xn n 1 be a sequence of i i d random variables assume that there exist r 1 and a function 0 0 with limt t depending only on the sequence gn n 1 such that lim supn gn x1 x2 e x r a s whenever e x r and ex 0 we prove the converse result namely that lim supn gn x1 x2 a s implies e x r and ex 0 if in addition lim supn gn c c for all c 0 some applications are provided to illustrate this result

about two trigonometric matrices abstract let r s be coprime integers s 1 and odd the characteristic polynomials of the matrices sin rmn s 0 and sin rmn s 0 mn s 1 are determined