nonlinear complementary filters on the special orthogonal group this paper considers the problem of obtaining good attitude estimates from measurements obtained from typical low cost inertial measurement units the outputs of such systems are characterized by high noise levels and time varying additive biases we formulate the filtering problem as deterministic observer kinematics posed directly on the special orthogonal group so 3 driven by reconstructed attitude and angular velocity measurements lyapunov analysis results for the proposed observers are derived that ensure almost global stability of the observer error the approach taken leads to an observer that we term the direct complementary filter by exploiting the geometry of the special orthogonal group a related observer termed the passive complementary filter is derived that decouples the gyro measurements from the reconstructed attitude in the observer inputs both the direct and passive filters can be extended to estimate gyro bias online the passive filter is further developed to provide a formulation in terms of the measurement error that avoids any algebraic reconstruction of the attitude this leads to an observer on so 3 termed the explicit complementary filter that requires only accelerometer and gyro outputs is suitable for implementation on embedded hardware and provides good attitude estimates as well as estimating the gyro biases online the performance of the observers are demonstrated with a set of experiments performed on a robotic test bed and a radio controlled unmanned aerial vehicle

on global diffeomorphisms of euclidian space as is well known the first attempt at characterizing global diffeomorphisms of ir goes back to the 1906 work of hadamard l since that time progress in the global diffeomorphism problem has been rather slow notable contributions are those of levy 2 who generalized hadamard s theorem to banach spaces and of banach and mazur 3 and caccioppoli 4 who proved the so called properness criterion saying that a proper local homeomorphism of a banach space is a global homeomorphism the standard proofs of the theorems of hadamard and levy and of banach mazur and caccioppoli rely upon ideas of what is now called covering space theory via the important homotopy lifting property of coverings see e g 5 this approach makes it clear that it is only lack of compactness of ir that allows for the existence of noninjective local homeomorphisms when n l 2 the complex exponential when n 2 being the most famous example the theorems mentioned above were found again by various authors sometimes in special cases and sometimes in a different framework but always through some variant of the same argument a synthesis was made by rheinboldt 6 in 1969 part of his results were rediscovered five years later by plastock 7 and given a somewhat simpler exposition for the special case of banach spaces other contributions were made by meisters and olech 8 global homeomorphisms of bounded domains in i meyer 9 complementing the work of levy and radulescu and radulescu lo expanding upon plastock s results many other articles have been devoted to special cases where extra hypotheses are introduced consistently with the problem at hand for instance polynomial mappings only are relevant to the jacobian conjecture of algebraic geometry and hypotheses about the spectrum of the derivative at each point come up in a natural way in global stability questions for differential equations the new results presented in this paper have been obtained through arguments from critical point theory and differential topology here the central notion is that of admissible flow given a mapping f ii ir the main property of what we call an f admissible flow q ir x ii f o i f o is that for every x e ir f o the function t jf q t x l where 1 1 is the euclidean norm is strictly increasing and tends to 0 resp 00 as t tends to co resp 00 the basic feature we prove is that a local diffeomorphism f is a global one if and only if f o zi and there is an f admissible flow this statement makes it clear that 0 plays a special role regarding f admissibility and the condition f o 0 cannot be eliminated as examples will show the introduction of f admissibility followed the author s remark that in hilbert space hadamard s theorem could be derived from the mountain pass theorem of ambrosetti and

two direct methods in linear programming abstract in this paper we introduce two direct methods for solving some classes of linear programming problems the first method produces the extreme vertex or a neighboring vertex with respect to the extreme point the second method is based on the game theory both these methods can be used in the preparation of the starting point for the simplex method the efficiency of the improved simplex method whose starting point is constructed by these introduced methods is compared with the original simplex method and the interior point methods and illustrated by examples also we investigate the elimination of excessive constraints

incompatibility of diophantine equations arising from the strong factorial conjecture abstract in the present article we establish new evidence in support of the strong factorial conjecture of edo and van den essen 2 by proving it in several special cases for example we show that the conjecture holds for powers of linear forms and sums of prime powers of the variables finally we show one way of constructing new examples of polynomials satisfying the conjecture using known examples

a hypersurace which has the abhyankar moh property let x be an algebraic subset of cn we say that x has the abhyankarmoh property a m p if for any polynomial embedding f x cn there exists a polynomial automorphism f of cn such that f is a restriction of this automorphism to the set x in 6 10 11 20 it was shown that if dim x is sufficiently small relatively to n and if x has nice singularities then x has the a m p and the problem of extending the polynomial embedding of x into cn has in general many solutions unfortunately if dim x is big enough in comparison with n the situation is more difficult in particular if x is a generic hypersurface of degree n in cn n 2 then the problem of extending the polynomial embedding of x into cn has no more than one solution see 8 abhyankar and moh proved see 1 2 that a line in c2 has the a m p it can be easily inferred from this that the cross k2 x c2 x1 x2 0 has the a m p the analogous questions for a hyperplane and the n cross kn x cn x1 xn 0 in the n space n 2 has been open cf 1 and conjecture 12 in 12 the question for a hyperplane is still open moreover in the case n 2 no example of a hypersurface which had the a m p has been known

characterizing injectivity of classes of maps via classes of matrices abstract we present a framework for characterizing injectivity of classes of maps on cosets of a linear subspace by injectivity of classes of matrices using our formalism we characterize injectivity of several classes of maps including generalized monomial and monotonic not necessarily continuous maps in fact monotonic maps are special cases of component wise affine maps further we study compositions of maps with a matrix and other composed maps in particular rational functions our framework covers classical injectivity criteria based on mean value theorems for vector valued maps and recent results obtained in the study of chemical reaction networks

an exponential formula for polynomial vector fields ii lie series exponential substituition and rooted trees abstract grobner s lie series and the exponential formula provide different explicit formulas for the flow generated by a finite dimensional polynomial vector field the present paper gives 1 a generalization of the lie series in case of non commuting variables called exponential substituition 2 a structural understanding of the three formulas and their mutual relationships in terms of rooted trees and 3 as a byproduct new results on the enumeration coding and statistics of different kinds of rooted trees

optimal estimation theory for dynamic systems with set membership uncertainty an overview in many problems such as linear and nonlinear regressions parameter and state estimation of dynamic systems state space and time series prediction interpolation smoothing and functions approximation one has to evaluate some unknown variable using available data the data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables typically the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory an interesting alternative approach referred to as set membership or unknown but bounded ubb error description has been investigated since the late 1960s in this approach uncertainty is described by an additive noise which is known only to have given integral typically l2 of l1 or componentwise l bounds in this paper we review the main results of this theory with special attention to the most recent advances obtained in the case of componentwise bounds

d log and formal flow for analytic isomorphisms of n space given a formal map f f1 fn of the form z higher order terms we give tree expansion formulas and as sociated algorithms for the d log of f and the formal flow ft the coefficients which appear in these formulas can be viewed as certain generalizations of the bernoulli numbers and the bernoulli polynomials moreover the coefficient polynomials in the formal flow formula coincide with the strict order polynomials in combina torics for the partially ordered sets induced by trees applications of these formulas to the jacobian conjecture are discussed

the jacobian conjecture linear triangularization for homogeneous polynomial maps in dimension three let k be a field of characteristic zero and f k3 k3 a polynomial map of the form f x h where h is homogeneous of degree d 2 we show that the jacobian conjecture is true for such mappings more precisely we show that if jh is nilpotent there exists an invertible linear map t such that t 1ht 0 h2 x1 h3 x1 x2 where the hi are homogeneous of degree d as a consequence of this result we show that all generalized druzkowski mappings f x h x1 l1d xn lnd where li are linear forms for all i and d 2 are linearly triangularizable if jh is nilpotent and rkjh 3

on the existence of global analytic conjugations for polynomial mappings of yagzhev type abstract consider a mappingf c n c nof the form identity plus a term with polynomial components that are homogeneous of the third degree and suppose that the jacobian determinant of this mapping is constant throughout c n polynomial mapping of yagzhev type as a stronger version of the classical jacobian conjecture the question has been posed whether for some values of c 0 there exists a global change of variables conjugation on c nthrough which the mapping fbecomes its linear part at the origin van den essen has recently produced a simple yagzhev mapping for which no suchpolynomialconjugation exists we show here that van den essen s example still admitsglobal analyticconjugations the question on the existence of global conjugations for general yagzhev maps is then still open

monte carlo em for missing covariates in parametric regression models we propose a method for estimating parameters for general parametric regression models with an arbitrary number of missing covariates we allow any pattern of missing data and assume that the missing data mechanism is ignorable throughout when the missing covariates are categorical a useful technique for obtaining parameter estimates is the em algorithm by the method of weights proposed in ibrahim 1990 journal of the american statistical association85 765 769 we extend this method t o continuous or mixed categorical and continuous covariates and for arbitrary parametric regression models by adapting a monte carlo version of the em algorithm as discussed by wei and tanner 1990 journal of the american statistical association85 699 704 in addition we discuss the gibbs sampler for sampling from the conditional distribution of the missing covariates given the observed data and show that the appropriate complete conditionals are log concave the log concavity property of the conditional distributions will facilitate a straightforward implementation of the gibbs sampler via the adaptive rejection algorithm of gilks and wild 1992 applied statistics41 337 348 we assume the model for the response given the covariates is an arbitrary parametric regression model such as a generalized linear model a parametric survival model or a nonlinear model we model the marginal distribution of the covariates as a product of one dimensional conditional distributions this allows us a great deal of flexibility in modeling the distribution of the covariates and reduces the number of nuisance parameters that are introduced in the e step we present examples involving both simulated and real data

global optimal attitude estimation using uncertainty ellipsoids a deterministic attitude estimation problem for a rigid body in a potential field with bounded attitude and angular velocity measurement errors is considered an attitude estimation algorithm that globally minimizes the attitude estimation error is obtained assuming that the initial attitude the initial angular velocity and measurement noise lie within given ellipsoidal bounds an uncertainty ellipsoid that bounds the attitude and the angular velocity of the rigid body is obtained the center of the uncertainty ellipsoid provides point estimates and the size of the uncertainty ellipsoid measures the accuracy of the estimates the point estimates and the uncertainty ellipsoids are propagated using a lie group variational integrator and its linearization respectively the attitude and angular velocity estimates are optimal in the sense that the sizes of the uncertainty ellipsoids are minimized

two applications of analytic functors we apply the theory of analytic functors to two topics related to theoretical computer science one is a mathematical foundation of certain syntactic well quasi orders and well orders appearing in graph theory the theory of term rewriting systems and proof theory the other is a new verification of the lagrange good inversion formula using several ideas appearing in semantics of lambda calculi especially the relation between categorical traces and fixpoint operators copyright 2002 elsevier science b v

the jacobian conjecture reduction of degree and formal expansion of the inverse introduction i the jacobian conjecture 1 statement of the jacobian problem first observations 2 some history of the jacobian conjecture 3 faulty proofs 4 the use of stabilization and of formal methods ii the reduction theorem 1 notation 2 statement of the reduction theorem 3 reduction to degree 3 4 proof of the reduction theorem 5 r linearization and unipotent reduction 6 nilpotent rank 1 jacobians iii the formal inverse 1 notation 2 abhyankar s inversion formula 3 the terms gj 4 the tree expansion g lt a t lfptf 5 calculations references

a topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon we show that a continuous dynamical system on a state space that has the structure of a vector bundle on a compact manifold possesses no globally asymptotically stable equilibrium this result is directly applicable to mechanical systems having rotational degrees of freedom in particular the result applies to the attitude motion of a rigid body in light of this result we explain how attitude stabilizing controllers obtained using local coordinates lead to unwinding instead of global asymptotic stability

estimating migration rates using tag recovery data tag recovery data are used to estimate migration rates among a set of strata the model formulation is a simple matrix extension of the formulation of a tag recovery experiment discussed by brownie et al 1985 statistical inference from band recovery data a handbook 2nd edition washington d c u s department of the interior estimation is more difficult because of the convolution of parameters between release and recovery and this convolution may cause estimates of the survival migration parameters to have low precision derived parameters of emigration immigration harvest derivation and overall net survival are also estimated the models are applied to estimate the migration of pacific herring among spawning grounds off the west coast of canada if animals can be re released after being recaptured the model corresponds in its migration survival components to that of arnason 1972 researches in popiulation ecology 13 97 113 this correspondence is developed leading to more efficient estimators of these parameters

computation of minimum time feedback control laws for discrete time systems with state control constraints the problem of finding a feedback law that drives the state of a linear discrete time system to the origin in minimum time subject to state control constraints is considered algorithms are given to obtain facial descriptions of the m step admissible sets these descriptions are then used to characterize the complete class of minimum time feedback laws moreover the characterization leads to a conceptually simple on line implementation the main ideas are illustrated with two simple examples

linearized polynomial maps over finite fields abstract we consider polynomial maps described by so called multivariate linearized polynomials these polynomials are defined using a fixed prime power say q linearized polynomials have no mixed terms considering invertible polynomial maps without mixed terms over a characteristic zero field we will only obtain up to a linear transformation of the variables triangular maps which are the most basic examples of polynomial automorphisms however over the finite field f q automorphisms defined by linearized polynomials have in general an entirely different structure namely we will show that the linearized polynomial maps over f q are in one to one correspondence with matrices having coefficients in a univariate polynomial ring over f q furthermore composition of polynomial maps translates to matrix multiplication implying that invertible linearized polynomial maps correspond to invertible matrices this alternate description of the linearized polynomial automorphism subgroup leads to the solution of many famous conjectures most notably the jacobian conjecture for this kind of polynomials and polynomial maps

continuous covariates in mark recapture recovery analysis a comparison of methods time varying individual covariates are problematic in experiments with marked animals because the covariate can typically only be observed when each animal is captured we examine three methods to incorporate time varying individual covariates of the survival probabilities into the analysis of data from mark recapture recovery experiments deterministic imputation a bayesian imputation approach based on modeling the joint distribution of the covariate and the capture history and a conditional approach considering only the events for which the associated covariate data are completely observed the trinomial model after describing the three methods we compare results from their application to the analysis of the effect of body mass on the survival of soay sheep ovis aries on the isle of hirta scotland simulations based on these results are then used to make further comparisons we conclude that both the trinomial model and bayesian imputation method perform best in different situations if the capture and recovery probabilities are all high then the trinomial model produces precise unbiased estimators that do not depend on any assumptions regarding the distribution of the covariate in contrast the bayesian imputation method performs substantially better when capture and recovery probabilities are low provided that the specified model of the covariate is a good approximation to the true data generating mechanism

foliations and polynomial diffeomorphisms of mathbb r 3 let y f g h mathbb r 3 to mathbb r 3 be a c 2 map and let spec y denote the set of eigenvalues of the derivative dy p when p varies in mathbb r 3 we begin proving that if for some 0 spec y cap epsilon epsilon emptyset then the foliation mathcal f k with k in f g h made up by the level surfaces k constant consists just of planes as a consequence we prove a bijectivity result related to the three dimensional case of jelonek s jacobian conjecture for polynomial maps of mathbb r n

a question of rentschler and the dixmier problem the following theorem is the main result of the paper theorem let r and t be somewhat commutative algebras with the same holonomic number and let r t be an algebra homomorphism then every holonomic t module m is via a holonomic r module and has finite length as an r module when applied to the weyl algebra this result gives a positive answer to a question of rentschler in the important case where r d x and t d y are rings of differential operators on smooth irreducible algebraic affine varieties x and y of the same dimension the result means that holonomicity is preserved by twisting by an arbitrary algebra homomorphism a short proof is given of the well known fact that an affirmative solution to the dixmier problem whether every algebra endomorphism of the weyl algebra an is an automorphism implies the jacobian conjecture the dixmier problem has a positive answer if and only if the twisted from both sides a n bimodule an is simple for each to begin with it is not even clear whether it is finitely generated the theorem implies that it has finite length moreover the bimodule is holonomic thus simple subfactors of it have the least possible gelfand kirillov dimension

reversion of power series and the extended raney coefficients in direct as well as diagonal reversion of a system of power series the reversion coefficients may be expressed as polynomials in the coefficients of the original power series these polynomials have coefficients which are natural numbers raney coefficients we provide a combinatorial interpretation for raney coefficients specifically each such coefficient counts a certain collection of ordered colored trees we also provide a simple determinantal formula for raney coefficients which involves multinomial coefficients let f1 fn be polynomials in variables x1 xn with complex coefficients where n 2 suppose for each i fi xi higher degree terms and the jacobian determinant of f1 fn is equal to 1 then the jacobian conjecture 1 9 asserts in this case that x1 xn are also polynomials in f1 fn with complex coefficients this long standing conjecture has not been solved even for n 2 since it can be proved that x1 xn are formal power series in f1 fn with complex coefficients the jacobian conjecture asserts that these power series are really polynomials this provides the motivation for this paper let f1 fn be power series in variables x1 xn of the form fi xi higher degree terms with indeterminate coefficients for each i it is known e g 2 chapter iii section 4 4 proposition 5 p 219 that f f1 fn has a unique compositional inverse i e there exists g g1 gn where each gi is a power series in variables x1 xn such that f g 1 and g f 1 or equivalently fi g1 gn xi and gi f1 fn xi for all i there are various methods in the literature to find the coefficients of gi in this paper we shall present two new ones since each coefficient of gi is a polynomial in the indeterminate coefficients of f1 fn it is enough to find the coefficients of these polynomials we will refer to these coefficients as the extended raney coefficients in the first method generating functions in infinitely many variables are used to show that each raney coefficient has a combinatorial interpretation as the number of colored trees in a certain collection theorems 2 4 and 2 5 in received by the editors april 4 1994 1991 mathematics subject classification primary 13f25 05a15 05c05 13p99 secondary 32a05

laplace s method on a computer algebra system with an application to the real valued modified bessel functions we examine a maple implementation of two distinct approaches to laplace s method used to obtain asymptotic expansions of laplace type integrals one algorithm uses power series reversion whereas the other expands all quantities in taylor or puiseux series these algorithms are used to derive asymptotic expansions for the real valued modified bessel functions of pure imaginary order and real argument that mimic the well known corresponding expansions for the unmodified bessel functions

bayesian estimation of movement and survival probabilities from capture recapture data summary the arnason schwarz model is usually used for estimating survival and movement probabilities of animal populations from capture recapture data the missing data structure of this capture recapture model is exhibited and summarised via a directed graph representation taking advantage of this structure we implement a gibbs sampling algorithm from which bayesian estimates and credible intervals for survival and movement probabilities are derived convergence of the algorithm is proved using a duality principle we illustrate our approach through a real example

the inverse function theorem and the jacobian conjecture for free analysis we establish an invertibility criterion for free polynomials and free functions evaluated on some tuples of matrices we show that if the derivative is nonsingular on some domain closed with respect to direct sums and similarity the function must be invertible thus as a corollary we establish the jacobian conjecture in this context furthermore our result holds for commutative polynomials evaluated on tuples of commuting matrices

global attitude and gyro bias estimation based on set valued observers a b s t r a c t the problem of attitude and rate gyro bias estimation is addressed by resorting to measurements acquired from rate gyros and vector observations a set valued observer svo is proposed that has no singulari ties and that for any initial conditions provides a bounding set with guarantees of containing the actual unknown rotation matrix the sensor readings are assumed to be corrupted by bounded measurement noise and constant gyro bias conditions for the boundedness of the estimated sets are established and implementation details are discussed the feasibility of the technique is demonstrated in simulation

note on the markus yamabe conjecture for gradient dynamical systems abstract let v r n r n be a c 1 vector field which has a singular point o and its linearization is asymptotically stable at every point of r n we say that the vector field v satisfies the markus yamabe conjecture if the critical point o is a global attractor of the dynamical system x v x in this note we prove that if v is a gradient vector field i e v f f c 2 then the basin of attraction of the critical point o is the whole r n thus implying the markus yamabe conjecture for this class of vector fields an analogous result for discrete dynamical systems of the form x m 1 f x m is proved

a sufficient condition in order that the real jacobian conjecture in r 2 holds let f f g r2 r2 be a polynomial map such that det df x y is different from zero for all x y r2 and f 0 0 0 0 we prove that for the injectivity of f it is sufficient to assume that the higher homogeneous terms of the polynomials ffx ggx and ffy ggy do not have real linear factors in common the proofs are based on qualitative theory of dynamical systems

the jacobian conjecture and the extensions of polynomial embeddings let x be an algebraic subset of c we say that x has the abhyanka r moh property amp if for any polynomial embedding 4 x of there exists a polynomial au tomorphism b of c such that b is a restriction of this au tomorphism to the set x in 3 9 it was shown that if dim x is sufficiently small relatively to n and if x has nice singularities then x has the am p and the problem of extending the polynomial embedding of x into c has in general many solutions unfortunately if dim x is big enough in compar ison with n the situation is more difficult in particular if x is a generic hypersurface of degree n in n 2 then the problem of extending the polynomial embedding of x into c has no more than one solution see 5 abhyankar and mob proved see 1 that a line in c 2 has the amp it can be easily inferred from this that the c r o s s k 2 x g 2 xl x2 0 has the amp the analogous questions for a hyperplane and the n cross k x c x l x 0 in the n space n 3 are open cf 1 and conjecture 12 in 6 moreover in the case n 3 no example of a hypersurface which has the a m p is known on the other hand in 4 we showed that for every n 2 the smooth hypersurface x x c xl x 2 2 is any non zero complex constant does not have the amp we recall an important conjecture connected with this subject

set valued observers and optimal disturbance rejection a set valued observer also called guaranteed state estimator produces a set of possible states based on output measurements and models of exogenous signals we consider the guaranteed state estimation problem for linear time varying systems with a priori magnitude bounds on exogenous signals we provide an algorithm to propagate the set of possible states based on output measurements and show that the centers of these sets provide optimal estimates in an l sup spl infin induced norm sense we then consider the utility of set valued observers for disturbance rejection with output feedback and derive the following general separation structure an optimal controller can consist of a set valued observer followed by a static nonlinear function on the observed set of possible states a general construction of this function is provided in the scalar control case furthermore in the special case of full control i e the number of control inputs equals the number of states optimal output feedback controllers can take the form of an optimal estimate of the full state feedback controller

intrinsic filtering on lie groups with applications to attitude estimation this paper proposes a probabilistic approach to the problem of intrinsic filtering of a system on a matrix lie group with invariance properties the problem of an invariant continuous time model with discrete time measurements is cast into a rigorous stochastic and geometric framework building upon the theory of continuous time invariant observers we introduce a class of simple filters and study their properties without addressing the optimal filtering problem we show that akin to the kalman filter for linear systems the error equation is a markov chain that does not depend on the state estimate thus when the filter s gains are held fixed the noisy error s distribution is proved to converge to a stationary distribution under some convergence properties of the filter with noise turned off we also introduce two novel tools of engineering interest the discrete time invariant extended kalman filter for which the trusted covariance matrix is shown to converge and the invariant ensemble kalman filter the methods are applied to attitude estimation allowing to derive novel theoretical results in this field and illustrated through simulations on synthetic data

the linear dependence problem for power linear maps abstract let bl l 1 k be m nl complex matrices and let x l c n l l 1 k be complex vector variables we show that the components of the map h b 1 x 1 d 1 b k x k d k are linearly dependent over c if and only if det b 1 b 1 d 1 b k b k d k 0 where means the hadamard product x and x d denote the conjugate transpose and the dth hadamard power of a matrix x respectively connections are established between the homogenous dependence problem hdp n d which arises in the study of the jacobian conjecture and the dependence problem for power linear maps pldp n d an algorithm is given to compute counterexamples to pldp n d from those to hdp n d and counterexamples to pldp n 3 are obtained for all n 67

the nagata automorphism is wild it is proved that the well known nagata automorphism of the polynomial ring in three variables over a field of characteristic zero is wild that is it can not be decomposed into a product of elementary automorphisms

an extension of the cormack jolly seber model for continuous covariates with application to microtus pennsylvanicus recent developments in the cormack jolly seber cjs model for analyzing capture recapture data have focused on allowing the capture and survival rates to vary between individuals several methods have been developed in which capture and survival are functions of auxiliary variables that may be discrete constant over time or apply to the population as a whole but the problem has not been solved for continuous covariates that vary with both time and individual this article proposes a new method to handle such covariates by modeling changes over time via a diffusion process and using logistic functions to link the variable to the cjs capture and survival rates bayesian methods are used to estimate the model parameters the method is applied to study the effect of body mass on the survival of the north american meadow vole microtus pennsylvanicus

a nonlinear position and attitude observer on se 3 using landmark measurements this paper addresses the problem of position and attitude estimation based on landmark readings and velocity measurements a derivation of a nonlinear observer on se 3 is presented using a lyapunov function conveniently expressed as a function of the difference between the estimated and the measured landmark coordinates the resulting feedback laws are explicit functions of the landmark measurements and velocity readings exploiting the sensor information directly in the observer the proposed observer yields almost global asymptotic stabilization of the position and attitude errors and exponential convergence in any closed ball inside the region of attraction also it is shown that the asymptotic convergence of the estimation error trajectories is shaped by the landmark geometry and observer design parameters the problem of non ideal velocity readings is also considered and the observer is augmented to compensate for bias in the angular and linear velocity measurements the resulting position attitude and bias estimation errors are shown to converge exponentially fast to the desired equilibrium points for bounded initial estimation errors simulation results are presented to illustrate the stability and convergence properties of the observer

preclusion of switch behavior in networks with mass action kinetics we study networks taken with mass action kinetics and provide a jacobian criterion that applies to an arbitrary network to preclude the existence of multiple positive steady states within any stoichiometric class for any choice of rate constants we are concerned with the characterization of injective networks that is networks for which the species formation rate function is injective in the interior of the positive orthant within each stoichiometric class we show that a network is injective if and only if the determinant of the jacobian of a certain function does not vanish the function consists of components of the species formation rate function and a maximal set of independent conservation laws the determinant of the function is a polynomial in the species concentrations and the rate constants linear in the latter and its coefficients are fully determined the criterion also precludes the existence of degenerate steady states further we relate injectivity of a network to that of the network obtained by adding outflow or degradation reactions for all species

on the length of polynomial automorphisms of the affine plane the automorphism group of the affine plane is a mysterious and challenging object although we know that it is an amalgamated product of two well known subgroups many questions are still unsolved moreover the group has the structure of an infinite dimensional algebraic group but the interactions between these two structures are not yet clear in this paper we study the length of an element defined using the amalgamated structure with respect to the algebraic structure if the ground field is of characteristic zero we prove that the length is a lower semicontinuous function on the group

injectivity and almost global asymptotic stability of hurwitz vector fields abstract we present in dimension n 3 a survey of examples to the jacobian conjecture the weak markus yamabe conjecture furthermore we show and construct new examples of vector fields where the origin is almost globally asymptotic stable by using the novel concept of density functions introduced by rantzer

polynomial maps with nilpotent jacobians in dimension three abstract in this paper we first classify all polynomial maps of the form h u x y v x y z h x y v x y z in certain conditions then we classify some polynomial maps of the form h u x y v x y z h x y z

on the algebraic identifiability of finite impulse response channels driven by linearly precoded signals it is common in wireless communications to perform some form of linear precodingoperation on the source signal prior to transmission over a channel although the traditional reason for precoding is to improve the performance of the communication system this paper draws attention to the fact that the receiver can identify the impulse response of the channel without any prior knowledge of the transmitted signal simply by solving a system of polynomial equations since different precoders lead to different systems of equations this paper addresses the fundamental issue of determiningwhich classes of linear precoders lead to a system of equations havinga unique solution in doingso basic properties of polynomial equations which are useful for studyingother identifiability issues commonly encountered in eng ineeringand the applied sciences are presented 2004 elsevier b v all rights reserved

topologies and structures of the cremona groups we study the algebraic structure of the n dimensional cremona group and show that it is not an algebraic group of innite dimension ind group if n 2 we describe the obstruction to this which is of a topological nature by contrast we show the existence of a euclidean topology on the cremona group which extends that of its classical subgroups and makes it a topological group

approximate set valued observers for nonlinear systems a set valued observer svo produces a set of possible states based on output measurements and a priori models of exogenous disturbances and noises previous work considered linear time varying systems and unknown but bounded exogenous signals in this case the sets of possible state vectors take the form of polytopes whose centers are optimal state estimates these polytopic sets can be computed by solving several small linear programs an svo can be constructed conceptually for nonlinear systems however the set of possible state vectors no longer takes the form of polytopes which in turn inhibits their explicit computation this paper considers an extended svo as in the extended kalman filter the state equations are linearized about the state estimate and a linear svo is designed along the linearization trajectory under appropriate observability assumptions it is shown that the extended svo provides an exponentially convergent state estimate in the case of sufficiently small initial condition uncertainty and provides a nondivergent state estimate in the case of sufficiently small exogenous signals

a new class of invertible polynomial maps abstract in this paper we present a new large class of polynomial maps f x h a n a n definition 1 1 on every commutative ring a for which the jacobian conjecture is true in particular h does not need to be homogeneous we also show that for all h in this class satisfying h 0 0 the n th iterate h h 0

complete abelian integrals for polynomials whose generic fiber is biholomorphic to c abstract let h be a polynomial of degree m 1 on c 2 such that its generic fiber is biholomorphic to c and let be an arbitrary polynomial 1 form of degree n on c 2 we give an upper bound depending only on m and n for the number of isolated zeros of the complete abelian integral defined by h and

the lned and lfed conjectures for algebraic algebras abstract let k be a field of characteristic zero and a a k algebra such that all the k subalgebras generated by finitely many elements of a are finite dimensional over k a k e derivation of a is a k linear map of the form i for some k algebra endomorphism of a where i denotes the identity map of a in this paper we first show that for all locally finite k derivations d and locally finite k algebra automorphisms of a the images of d and i do not contain any nonzero idempotent of a we then use this result to show some cases of the lfed and lned conjectures proposed in 21 more precisely we show the lned conjecture for a and the lfed conjecture for all locally finite k derivations of a and all locally finite k e derivations of the form i with being surjective in particular both conjectures are proved for all finite dimensional k algebras furthermore some finite extensions of derivations and automorphism to inner derivations and inner automorphisms respectively have also been established this result is not only crucial in the proofs of the results above but also interesting on its own right

a new method for analysing discrete life history data with missing covariate values summary regular censusing of wild animal populations produces data for estimating their annual survival however there can be missing covariate data for instance time varying covariates that are measured on individual animals often contain missing values by considering the transitions that occur from each occasion to the next we derive a novel expression for the likelihood for mark recapture recovery data which is equivalent to the traditional likelihood in the case where no covariate data are missing and which provides a natural way of dealing with covariate data that are missing for whatever reason unlike complete case analysis this approach does not exclude incompletely observed life histories uses all available data and produces consistent estimators in a simulation study it performs better overall than alternative methods when there are missing covariate data

a coupled nonlinear spacecraft attitude controller and observer with an unknown constant gyro bias and gyro noise we propose a new algorithm for estimating constant biases in gyro measurements of angular velocity and demonstrate that the resulting estimates converge to the true bias values exponentially fast the new observer is then combined with a nonlinear attitude tracking control strategy in a certainty equivalence fashion and the combination shown via lyapunov analysis to produce globally stable closed loop dynamics with asymptotically perfect tracking of any commanded attitude sequence the analysis is then extended to consider the effects of stochastic measurement noise in the gyro in addition to the bias a simulation is given for a rigid spacecraft tracking a specified time varying attitude sequence to illustrate the theoretical claims

dual operators and lagrange inversion in several variables the original lagrange inversion formula which gives explicitly the inverse under composition of a formal series was obtained by lagrange in 1770 through formal computations involving logarithms of inlmite products see lagrange 121 there exists an extensive literature on various versions of the inversion formula obtained by algebraic analytic and combinatorial methods comtet 3 gives a survey and an ample bibliography during the last ten years there have appeared several papers on generalizations and new proofs of the inversion formula in 1974 abhyankar obtained an inversion formula using algebraic methods see bass connell and wright 11 several authors have related lagrange inversion with rota s finite operator calculus 151 for example joni 8 garsia and joni 4 hofhauer 7 and roman and rota 14 joyal and labelle used a combinatorial theory of formal series to obtain inversion formulas see 9 l i and viskov 161 used ideas from lie algebra theory to prove formulas similar to abhyankar s in the present paper we use operator methods to obtain inversion formulas in several variables that generalize the formulas of abhyankar joni and viskov we get our results studying an algebra with involution of linear operators on the algebra of formal laurent series in several indeterminates we also show that by means of an anti isomorphism of operator algebras which we call the operator bore1 transform the study of finite operator calculus can be reduced to the study of certain groups of operators on the algebra of formal laurent series our approach may be considered as an algebraic analogue of the complex variable methods used by good 5 to obtain the lagrange inversion formula as a consequence of the change of variables theorem for the

on additive nilpotency of jacobian matrices of polynomial maps abstract let h c n c n be a polynomial map jh the jacobian matrix of h and v h the linear subspace of m n c spanned by j h c n the set of evaluated jacobian matrices of h we describe the dimension of v h through a power linear gorni zampieri mate of h and give a numerical algorithm for computing this dimension and determining whether jh is additive nilpotent i e whether v h is a nilpotent subspace