linear systems with signed solutions linear systems ax b for which the sign patterns a and b completely determine the set of sign patterns of vectors in the solution set are studied these systems generalize the existing notion of sign solvable linear systems linear systems with signed solutions are characterized in terms of two classes of matrices the first class l matrices plays a central role in the study of sign solvable linear systems the second class is new and generalizes the class of s matrices that arise in sign solvable linear systems several constructions for the new class of matrices are given

demonstration de l integrabilite des equations differentielles ordinaires soit donne le systeme d equations differentielles ramene a la forme normale begin array 20 c frac d x 1 dt varphi 1 t x 1 x n quad quad quad quad quad quad frac d x n dt varphi n t x 1 x n end array 0444 ou les n sont des fonctions continues aux environs de t b x1 a1 x n a n dans cette note on prouve que l on peut determiner un intervalle b b et dans cet intervalle n fonctions x1 x n de t qui satisfont aux equations donnees et qui pour t b prennent les valeurs a1 a n

on the digraphs of sign solvable linear systems abstract a linear system of equations ax b is sign solvable if it is solvable and both its solvability and the sign pattern of its solution vector x are uniquely determined by the sign patterns of a and b it was proved in l bassett j maybee j quirk economitrica 36 1968 544 563 r a bruali b l shader matrices of sign solvable linear systems cambridge university press cambridge 1995 that the sign solvability of a linear system ax b in standard form and with a square coefficient matrix a can be described in terms of the signed digraph s a of the matrix a with a specified vertex subset depending on the sign pattern of the vector b in this paper we define the notion of w sign solvable signed digraphs which represent precisely the sign solvable linear systems in standard form we give necessary and sufficient conditions for the underlying unsigned digraphs of w sign solvable signed digraphs in terms of forbidden subdigraphs we also give several necessary and sufficient conditions for strongly connected w sign solvable signed digraphs

approximate controllability of partial neutral functional differential systems of fractional order with state dependent delay we prove the approximate controllability of control systems governed by a class of partial neutral functional differential systems of fractional order with state dependent delay in an abstract space sufficient conditions for approximate controllability of the control systems are established provided the approximate controllability of the corresponding linear control systems the results are obtained by using the krasnoselskii schaefer type fixed point theorem with the fractional power of operators an example is provided to illustrate the main results

predecessor property full combinatorial column rank and the height characteristics of an m matrix abstract for a loopless acyclic transitive directed graph we give a new result about the relation between the t predecessor property of subsets of its levels and the property of having full combinatorial column rank for certain blocks in its adjacency matrix as a corollary we give new lower bounds for the i th height characteristic number of a singular m matrix an open question about determining the height characteristics of singular m matrices with a prescribed singular graph is also posed

semi discretization method for delayed systems summary the paper presents an ecient numerical method for the stability analysis of linear delayed systems the method is based on a special kind of discretization technique with respect to the past eect only the resulting approximate system is delayed and also time periodic but still it can be transformed analytically into a high dimensional linear discrete system the method is applied to determine the stability charts of the mathieu equation with continuous time delay copyright 2002 john wiley sons ltd

vertex algebras and the class algebras of wreath products the jucys murphy elements for wreath products gamma n gamma wr s n associated to any finite group gamma are introduced and they play an important role in our study of the connections between class algebras of gamma n for all n and vertex algebras we construct an action of a variant of the mathcal w 1 infty algebra acting irreducibly on the direct sum mathcal r gamma of the class algebras of gamma n for all n in a group theoretic manner we establish various relations between convolution operators using jm elements and heisenberg algebra operators acting on mathcal r gamma as applications we obtain two distinct sets of algebra generators for the class algebra of gamma n and establish various stability results concerning products of normalized conjugacy classes of gamma n and the power sums of jucys murphy elements etc we introduce a stable algebra which encodes the class algebra structures of gamma n for all n whose structure constants are shown to be non negative integers in the symmetric group case that is when gamma is trivial we recover and strengthen in a uniform approach various results of lascoux and thibon kerov and olshanski and farahat and higman etc

approximate controllability of fractional nonlocal delay semilinear systems in hilbert spaces we study the existence and approximate controllability of a class of fractional nonlocal delay semilinear differential systems in a hilbert space the results are obtained by using semigroup theory fractional calculus and schauder s fixed point theorem multi delay controls and a fractional nonlocal condition are introduced furthermore we present an appropriate set of sufficient conditions for the considered fractional nonlocal multi delay control system to be approximately controllable an example to illustrate the abstract results is given

identifying digital and fractional transfer functions from a frequency response in this article an existing exact algorithm for identifying a continuous transfer function from frequency data giving major importance to phase data is further developed the new version allows identifying a digital transfer function or a continuous fractional order transfer function with a fixed order of commensurability i e a ratio of two polynomials in s this is straightforward if the desired transfer function is to have only zeros or only poles if a transfer function with both zeros and poles is sought however a numerical method must be resorted to

zero forcing for sign patterns we introduce a new variant of zero forcing signed zero forcing the classical zero forcing number provides an upper bound on the maximum nullity of a matrix with a given graph i e zero nonzero pattern our new variant provides an analogous bound for the maximum nullity of a matrix with a given sign pattern this allows us to compute for instance the maximum nullity of a z matrix whose graph is l kn the line graph of a clique

on digraphs and forbidden configurations of strong sign nonsingular matrices a square real matrix a called a strong sign nonsingular matrix or s2ns matrix if all matrices with the same sign pattern as a nonsingular and the inverses of these matrices all have the same sign pattern a digraph which is the underlying digraph of the signed digraph of an s2ns matrix with a negative main diagonal is called an s2ns digraph in 9 thomassen gave a characterization of strongly connected s2ns digraphs in terms of the forbidden subdigraphs in 2 brualdi and shader constructed minimal forbidden configurations for s2ns digraphs for the general cases where the digraphs considered are not necessarily strongly connected they also proposed the problem about the existence of new minimal forbidden configurations other than those found in 2 9 in this paper we construct infinitely many new basic minimal forbidden configurations and thus obtain the answer this problem we also obtain several necessary conditions for minimal forbidden configurations and give a generalization of thomassen s theorem

symmetric groups and the cup product on the cohomology of hilbert schemes let c sn be the z module of integer valued class functions on the symmetric group sn we introduce a graded version of the con volution product on c sn and show that there is a degree preserving ring isomorphism c sn h hilb n a 2 z to the cohomology of the hilbert scheme of points in the complex affine plane

heisenberg algebra and hilbert schemes of points on projective surfaces the purpose of this paper is to throw a bridge between two seemingly unrelated subjects one is the hilbert scheme of points on projective surfaces which has been intensively studied by various people see e g i br es g61 g62 the other is the infinite dimensional heisenberg algebra which is closely related to affine lie algebras see e g k we shall construct a representation of the heisenberg algebra on the homology group of the hilbert scheme in other words the homology group will become a fock space the basic idea is to introduce certain correspondences in the product of the hilbert scheme then they define operators on the homology group by a well known procedure they give generators of the heisenberg algebra and the only thing we must check is that they satisfy the defining relation here we remark that the components of the hilbert scheme are parameterized by numbers of points and our representation will be constructed on the direct sum of homology groups of all components our correspondences live in the product of the different components thus it is quite essential to study all components together our construction has the same spirit as the author s construction nal na4 of representations of affine lie algebras on homology groups of moduli spaces of instantons 1 on ale spaces which are minimal resolutions of simple singularities certain correspondences called hecke correspondences were used to define operators these twist instantons along curves irreducible components of the exceptional set while ours twist ideals around points in fact the hilbert scheme of points can be considered as the moduli space of rank 1 vector bundles or more precisely torsion free sheaves our construction should be considered as a first step to extend nal na4 to general 4 manifolds the same program was also proposed by ginzburg kapranov and vasserot gkv

the farahat higman ring of wreath products and hilbert schemes we study the structure constants of the class algebra rz n of the wreath products n associated to an arbitrary finite group with respect to the basis of conjugacy classes we show that a suitable filtration on rz n gives rise to the graded ring g n with non negative integer structure constants independent of n some of which are computed which are then encoded in a farahat higman ring g the real conjugacy classes of come to play a distinguished role and are treated in detail in the case when is a subgroup of sl2 c the above results provide new insight to the cohomology rings of hilbert schemes of points on a quasi projective surface x

linear operators which preserve sign nonsingular matrices abstract we characterize the linear operators that preserve the set of sign nonsingular matrices we show that if a linear operator t preserves the set of sign nonsingular matrices then t preserves the set of matrices of term rank 1 then by a result of beasley and pullman on preservers of matrices of term rank 1 we can obtain the structure of t

linear operators preserving l matrices abstract we investigate the linear operators that preserve the set of l matrices we show that a linear operator t preserves the set of l matrices and t is also one to one on the set of cells if and only if t strongly preserves the set of l matrices in each case t preserves the set of matrices of term rank 1 then by a result of beasley and pullman on preservers of matrices of term rank 1 we can obtain the structure of t

nearly l matrices and generalized row sign balanced matrices abstract a real matrix a is called an l matrix if every matrix with the same sign pattern as a has linearly independent columns a nearly l matrix is a matrix which is not an l matrix but each matrix obtained by deleting one of its columns is an l matrix a generalized row sign balanced grsb matrix is a matrix which can be transformed to a matrix having both positive and negative entries in each row by multiplying some of its columns by 1 in this paper we study the relations between l matrices nearly l matrices and grsb matrices we obtain a complete characterization of nearly l matrices in terms of grsb matrices by comparing this result with a well known theorem about l indecomposable barely l matrices we find an interesting duality relation between l matrices and grsb matrices we also use grsb matrices to characterize the conditional s matrices which are closely related to nearly l matrices and the conditionally sign solvable linear systems finally we propose some unsolved problems for further research

stabilisability analysis of high order unstable processes by fractional order controllers in this article the sufficient stabilisability criteria for unstable time delay processes by fractional order controllers are investigated the process is a high order system with a single unstable pole which also has a stable zero the adopted approach to derive the sufficient conditions for stability is based on the well known nyquist stability criterion stabilisability is studied by applying fractional order proportional integral and proportional derivative controllers and the results are given in terms of the maximum allowable value of time delay additionally limitations on the parameters of the controllers which must be taken into account in the controller design are proposed

transition curves for the quasi periodic mathieu equation in this work we investigate an extension of mathieu s equation the quasi periodic qp mathieu equation given by ddot psi delta eps cos t cos omega t psi 0 for small eps and irrational omega of interest is the generation of stability diagrams that identify the points or regions in the delta omega parameter plane for fixed eps for which all solutions of the qp mathieu equation are bounded numerical integration is employed to produce approximations to the true stability diagrams both directly and through contour plots oflyapunov exponents in addition we derive approximate analytic expressions for transition curves using two distinct techniques 1 a regular perturbation method under which transition curves delta delta omega eps are each expanded in powers of eps and 2 the method of harmonic balance utilizing hill s determinants both analytic methods deliver results in good agreement with those generated numerically in the sense that pre

a necessary condition of viability for fractional differential equations with initialization in this paper viability results for nonlinear fractional differential equations with the riemann liouville derivative are proved we give a necessary condition for fractional viability of a locally closed set with respect to a nonlinear function

generators of the hecke algebra of s2n bn abstract in analogy with the set of jucys murphy elements a set of ring generators for the hecke algebra of the gel fand pair s 2 n b n where b n is the hyperoctahedral subgroup of the symmetric group s 2 n is constructed various consequences are presented a conjecture of s matsumoto is proven

weight bases of gelfand tsetlin type for representations of classical lie algebras this paper completes a series devoted to explicit constructions of finite dimensional irreducible representations of the classical lie algebras here the case of odd orthogonal lie algebras of type b is considered two previous papers dealt with c and d types a weight basis for each representation of the lie algebra 2n 1 is constructed the basis vectors are parametrized by gelfand tsetlin type patterns explicit formulae for the matrix elements of generators of 2n 1 in this basis are given the construction is based on the representation theory of the yangians

measurable viability theorems and the hamilton jacobi bellman equation abstract we prove viability and invariance theorems for systems with dynamics depending on time in a measurable way and having time dependent state constraints x t f t x t x t p t in the above t p t is an absolutely continuous set valued map and t x f t x is a set valued map which is measurable with respect to t and upper semicontinuous or continuous or locally lipschitz with respect to x for this aim we investigate infinitesimal generators of reachable maps and the lebesgue points of set valued maps the results are applied to define and to study lower semicontinuous solutions of the hamilton jacobi bellman equation u t h t x u x 0 with the hamiltonian h measurable with respect to time locally lipschitz with respect to x and convex in the last variable

stability of linear time invariant fractional delay systems of retarded type in the space of delay parameters this paper presents a new method for assessing the bounded input bounded output stability of a class of fractional delay systems with commensurate orders and multiple commensurate delays of retarded type in the proposed method first by mapping the principal sheet of the riemann surface and a pseudo delay transformation an auxiliary polynomial is generated then this auxiliary polynomial is employed to find roots of the characteristic equation on the imaginary axis the properties of the root path close to these roots are used to identify intervals of delay values in which the system is stable the obtained results are illustrated via some numerical examples

hierarchical least squares identification methods for multivariable systems for multivariable discrete time systems described by transfer matrices we develop a hierarchical least squares iterative hlsi algorithm and a hierarchical least squares hls algorithm based on a hierarchical identification principle we show that the parameter estimation error given by the hlsi algorithm converges to zero for the deterministic cases and that the parameter estimates by the hls algorithm consistently converge to the true parameters for the stochastic cases the algorithms proposed have significant computational advantage over existing identification algorithms finally we test the proposed algorithms on an example and show their effectiveness

simultaneous state estimation and parameter identification in linear fractional order systems using coloured measurement noise abstractin the present paper the identification and estimation problem of a single input single output siso fractional order state space system will be addressed a siso state space model is considered in which parameters and also state variables should be estimated the canonical fractional order state space system will be transformed into a regression equation by using a linear transformation and a shift operator that are appropriate for identification the identification method provided in this paper is based on a recursive identification algorithm that has the capability of identifying the parameters of fractional order state space system recursively another subject that will be addressed in this paper is a novel fractional order kalman filter suitable for the systems with coloured measurement noise the promising performance of the proposed methods is verified using two stable fractional order systems

vertex algebras and the cohomology ring structure of hilbert schemes of points on surfaces using vertex algebra techniques we determine a set of generators for the cohomology ring of the hilbert schemes of points on an arbitrary smooth projective surface over the field of complex numbers

conversion of descriptor representations to state space form an extension of the shuffle algorithm abstractthis paper proposes a systematic procedure for the determination of state space models from an available descriptor representation of a linear dynamic system the goal is to determine a state equation a set of algebraic equations and an output equation in terms of the state and input variables it is shown that standard methods may fail to convert the descriptor representation to state space form even for simple electrical circuit models obtained from kirchoff s laws and constitutive element equations a novel procedure to address this problem is then proposed as an extension of the classic shuffle algorithm combined with a singular value decomposition approach in addition to an illustrative example involving a simple electrical circuit the proposed method is employed in a case study involving the modelling of three dimensional rlc networks with a large number of components

rectangular l matrices abstract an l matrix is an m by n 0 1 1 matrix a such that every m by n real matrix with the same sign pattern as a has linearly independent rows the most widely studied l matrices are the square l matrices also called sign nonsingular matrices in this paper we investigate rectangular l matrices we obtain and study a decomposition theorem for l matrices we introduce two new classes of l matrices which for square matrices reduce to sign nonsingular matrices the maximum number of columns for matrices in each of these classes is obtained and those matrices attaining the maximum are characterized

fractional delayed damped mathieu equation this paper investigates the dynamical behaviour of the fractional delayed damped mathieu equation this system includes three different phenomena fractional order time delay parametric resonance the method of harmonic balance is employed to achieve approximate expressions for the transition curves in the parameter plane the n 0 and n 1 transition curves both lower and higher order approximations are obtained the dependencies of these curves on the system parameters and fractional orders are determined previous results for the transition curves reported for the damped mathieu equation delayed second order oscillator and fractional mathieu equation are confirmed as special cases of the results for the current system

classes of sign nonsingular matrices with a specified number of zero entries abstract an n by n matrix bn is sign nonsingular sns if every matrix with the same sign pattern as bn is nonsingular a given sns matrix determines an equivalence class with respect to transposition and multiplication by permutation and signature matrices of sns matrices all of which have the same number of zero entries such a matrix is maximal if no zero entry can be set nonzero so that the resulting matrix is sns and is fully indecomposable if it does not have an n k by k zero submatrix for some k where 1 k n 1 for fixed n the hessenberg matrix is known to represent the unique equivalence class with the minimum number of zero entries namely n 1 2 we prove that for n 5 there is exactly one equivalence class of fully indecomposable maximal sns matrices with n 1 2 1 zero entries similarly for n 5 we prove that there are exactly two such equivalence classes having n 1 2 2 zero entries for these proofs we identify two new infinite classes of fully indecomposable maximal sns matrices which can be obtained by stretching known sns matrices

reduced order kalman filter for a continuous time fractional order system using fractional order average derivative abstract this paper investigates two kinds of reduced order kalman filters for a continuous time fractional order system with uncorrelated and correlated process and measurement noises the fractional order average derivative is adopted to enhance the discretization accuracy for the investigated continuous time fractional order system the uncorrelated and correlated cases for the process and measurement noises are treated by the reduced order kalman filters to achieve the robust estimation for a part of states of a fractional order system the truncation issue is considered to implement the practical application of the proposed state estimation algorithm finally two examples for uncorrelated and correlated noises are offered to verify the effectiveness of the proposed reduced order kalman filters

wreath hecke algebras and centralizer construction for wreath products abstract generalizing the centralizer construction of molev and olshanski on symmetric groups we study the structures of the centralizer z m n of the wreath product g n m in the group algebra of g n for any n m we establish the connection between z m n and a generalization of degenerate affine hecke algebras introduced in our earlier work

ideals of the cohomology rings of hilbert schemes and their applications we study the ideals of the rational cohomology ring of the hilbert scheme x n of n points on a smooth projective surface x as an application for a large class of smooth quasi projective surfaces x we show that every cup product structure constant of h x n is independent of n moreover we obtain two sets of ring generators for the cohomology ring h x n similar results are established for the chen ruan orbifold cohomology ring of the symmetric product in particular we prove a ring isomorphism between h x n c and h orb x n sn c for a large class of smooth quasi projective surfaces with numerically trivial canonical class

degenerate affine hecke algebras and centralizer construction for the symmetric groups in our recent papers the centralizer construction was applied to the series of classical lie algebras to produce the quantum algebras called twisted yangians here we extend this construction to the series of the symmetric groups s n we study the stable properties of the centralizers of s n m in the group algebra c s n as n with m fixed we construct a limit centralizer algebra a and describe its algebraic structure the algebra a turns out to be closely related with the degenerate affine hecke algebras we also show that the so called tame representations of s yield a class of natural a modules

fractional discrete time linear control systems with initialisation linear control systems with fractional differences and finite memory are considered the evaluation of trajectories of such systems is studied the extension of the classical notion of observability and controllability is given and developed the necessary and sufficient conditions for observability and controllability are proved

a numerical method for stability windows and unstable root locus calculation for linear fractional time delay systems this paper aims to provide a numerical algorithm able to locate all unstable poles and therefore the characterization of the stability as a function of the delay for a class of linear fractional order neutral systems with multiple commensurate delays we start by giving the asymptotic position of the chains of poles and the conditions for their stability for a small delay when these conditions are met the root continuity argument and some simple substitutions allow us to determine the locations where some roots cross the imaginary axis providing therefore the complete characterization of the stability windows the same method can be extended to provide the position of all unstable poles as a function of the delay

stability of linear time periodic delay differential equations via chebyshev polynomials this paper presents a new technique for studying the stability properties of dynamic systems modeled by delay differential equations ddes with time periodic parameters by employing a shifted chebyshev polynomial approximation in each time interval with length equal to the delay and parametric excitation period the dynamic system can be reduced to a set of linear difference equations for the chebyshev expansion coefficients of the state vector in the previous and current intervals this defines a linear map which is the infinite dimensional floquet transition matrix u two different formulas for the computation of the approximate u whose size is determined by the number of polynomials employed are given the first one uses the direct integral form of the original system in state space form while the second uses a convolution integral variation of parameters formulation additionally a variation on the former method for direct application to second order systems is also shown an error analysis is presented which allows the number of polynomials employed in the approximation to be selected in advance for a desired tolerance an extension of the method to the case where the delay and parametric periods are commensurate is also shown stability charts are produced for several examples of time periodic ddes including the delayed mathieu equation and a model for regenerative chatter in impedance modulated turning the results indicate that this method is an effective way to study the stability of time periodic ddes

the cup product of hilbert schemes for k3 surfaces to any graded frobenius algebra a we associate a sequence of graded frobenius algebras a n so that there is canonical isomorphism of rings h x 2 n h x n 2n for the hilbert scheme x n of generalised n tuples of any smooth projective surface x with numerically trivial canonical bundle

symmetrical functions and macdonald s result for top connexion coefficients in the symmetrical group abstract in unpublished work macdonald gave an indirect proof that the connexion coefficients for certain symmetric functions coincide with the connexion coefficients of the class algebra of the symmetric group we give a direct proof of this result and demonstrate the use of these functions in a number of combinatorial questions associated with ordered factorisations of permutations into factors of specified cycle type including factorisations considered up to commutation in the symmetric group several related properties of the symmetric functions are given

mixed dominating matrices abstract we characterize the class of matrices for which the set of supports of nonnegative vectors in the null space can be determined by the signs of the entries of the matrix this characterization is in terms of mixed dominating matrices which are defined by the nonexistence of square submatrices that have nonzeros of opposite sign in each row the class of mixed dominating matrices is contained in the class of l matrices from the theory of sign solvability and generalizes the class of s matrices we give a polynomial time algorithm to decide if a matrix is mixed dominating we derive combinatorial conditions on the face lattice of a gale transform of a matrix in this class

sign nonsingular matrices and even cycles in directed graphs a sign nonsingular matrix or l mahix a is a real m x n matrix such that the columns of any real m x n matrix with the same sign pattern as a are linearly independent the problem of recognizing square l matrices is equivalent to that of finding an even cycle in a directed graph in this paper we use graph theoretic methods to investigate l matrices in particular we determine the maximum number of nonzero elements in square l matrices and we characterize completely the semicomplete l matrices i e the square l matrices a j such that at least one of a and ajl is nonzero for any i j and those square l matrices which are combinatorially symmetric i e the main diagonal has only nonzero entries and a j 0 iff a jr 0 we also show that for any n x n l matrix there is an i such that the total number of nonzero entries in the i th row and i th column is less than n unless the matrix has a completely specified structure finally we discuss the algorithmic aspects

transition curves in a parametrically excited pendulum with a force of elliptic type this article investigates the equilibria and stability of a pendulum when the support has a prescribed motion defined by an elliptic function stability charts are generated in the parameter plane for different values of the elliptic function modulus numerical integration and floquet theory are used to generate stability charts that are later obtained through harmonic balance analysis it is shown that the size and location of the instability tongues is directly linked to the elliptic function modulus comparisons are also made between the stability charts of mathieu s equation and those of the pendulum when the prescribed motion is defined by an elliptic function

recursive structure of s matrices and an o m2 algorithm for recognizing strong sign solvability abstract an s matrix is an m m 1 real matrix a such that for each matrix a of the same sign pattern as a a s columns are the vertices of an m simplex in r m that has the origin in its interior an s matrix is one that can be made into an s matrix by replacing some columns with their negatives such matrices are of interest because of their fundamental role in the study of sign solvability new results on the recursive structure of these classes of matrices are presented here and are used as the basis of algorithms of time complexity o m 2 for recognizing members of the classes and for testing the strong sign solvability of linear systems

topological orbifold models and quantum cohomology rings we discuss the topological sigma model on an orbifold target space we describe the moduli space of classical minima for computing correlation functions involving twisted operators and show through a detailed computation of an orbifold ofcp1 by the dihedral groupd4 how to compute the complete ring of observables through this procedure we compute all the rings of dihedralcp1 orbifolds we then considercp2 d4 and show how the techniques of topologicalanti topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds

stability chart for the delayed mathieu equation in the space of system parameters the closedform stability chart is determined for the delayed mathieu equation defined as t cost x t bx t2 this stability chart makes the connection between t