gain constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays this paper is concerned with the gain constrained recursive filtering problem for a class of time varying nonlinear stochastic systems with probabilistic sensor delays and correlated noises the stochastic nonlinearities are described by statistical means that cover the multiplicative stochastic disturbances as a special case the phenomenon of probabilistic sensor delays is modeled by introducing a diagonal matrix composed of bernoulli distributed random variables taking values of 1 or 0 which means that the sensors may experience randomly occurring delays with individual delay characteristics the process noise is finite step autocorrelated the purpose of the addressed gain constrained filtering problem is to design a filter such that for all probabilistic sensor delays stochastic nonlinearities gain constraint as well as correlated noises the cost function concerning the filtering error is minimized at each sampling instant where the filter gain satisfies a certain equality constraint a new recursive filtering algorithm is developed that ensures both the local optimality and the unbiasedness of the designed filter at each sampling instant which achieving the pre specified filter gain constraint a simulation example is provided to illustrate the effectiveness of the proposed filter design approach

technical communique sliding mode control of singular stochastic hybrid systems this paper is concerned with the sliding mode control smc of nonlinear singular stochastic systems with markovian switching an integral sliding surface function is designed and the resulting sliding mode dynamics is a full order markovian jump singular stochastic system by introducing some specified matrices a new sufficient condition is proposed in terms of strict linear matrix inequality lmi which guarantees the stochastic stability of the sliding mode dynamics then a smc law is synthesized for reaching motion moreover when there exists an external disturbance the 2 disturbance attenuation performance is analyzed for the sliding mode dynamics some related sufficient conditions are also established

the freiheitssatz for poisson algebras abstract we prove the freiheitssatz for poisson algebras in characteristic zero we also give a new proof of the tameness of automorphisms for two generated free poisson algebras and show that an analogue of the commutator test theorem is equivalent to the two dimensional classical jacobian conjecture

recursive estimators of signals from measurements with stochastic delays using covariance information least squares linear one stage prediction filtering and fixed point smoothing algorithms for signal estimation using measurements with stochastic delays contaminated by additive white noise are derived the delay is considered to be random and modelled by a binary white noise with values zero or one these values indicate that the measurements arrive in time or they are delayed by one sampling time recursive estimation algorithms are obtained without requiring the state space model generating the signal but just using covariance information about the signal and the additive noise in the observations as well as the delay probabilities

linear and nonlinear inverse scattering in this paper we discuss one dimensional scattering and inverse scattering for the helmholtz equation on the half line from the point of view of the layer stripping by full or nonlinear scattering we mean the transformation between the index of refraction actually half of its logarithmic derivative and the reflection coefficient we refer to this mapping as nonlinear scattering because the mapping itself is nonlinear another appropriate name is multiple scattering as this model includes the effects of multiple reflections by linear scattering we mean the born or single scattering approximation this is the frechet derivative of the full scattering transform at the constant index of refraction which can be calculated to be exactly the fourier transform in j sylvester d p winebrenner and f gylys colwell siam j appl math 56 1996 pp 736 754 we introduced a variant of layer stripping based on causality and the riesz transform rather than on trace formulas see a brickstein and

layer stripping for the helmholtz equation we develop a new layer stripping technique for the inverse scattering problem for the one dimensional helmholtz equation on the half line the technique eliminates the use of trace formulas relying instead on a nonlinear plancherel equality that provides a simple and precise characterization of the reflection data we prove both convergence of the algorithm and wellposedness of the forward and inverse scattering problems

enveloping algebras satisfying a polynomial identity in this paper we study ordinary and restricted enveloping algebras satisfying a polynomial identity we first show how the methods of j bergen and d s passman j algebra in press can be used to handle u l in all characteristics and u l if the latter ring is prime in particular we offer a simpler proof of the result of yu a bachturin j austral math soc 18 1974 10 21 on ordinary enveloping algebras in characteristic p 0 our main theorem asserts that in general u l is p i if and only if l has a restricted subalgebra of finite codimension which is essentially commutative these results are clearly the lie algebra analogs of the p i group ring theorems of m k smith j algebra 18 1971 477 499 and d s passman pacific j math 36 1971 467 483

fault detection filter design for markovian jump singular systems with intermittent measurements this paper addresses the problem of fault detection filter design for discrete time markovian jump singular systems with intermittent measurements the measurement transmission from the plant to the fault detection filter is assumed to be imperfect and a stochastic variable is utilized to model the phenomenon of data missing our attention is focused on the design of a fault detection filter such that the residual system is stochastically markovian jump admissible and satisfies some expected performances a new necessary and sufficient condition for a class of discrete time markovian jump singular systems to be stochastically markovian jump admissible is proposed in the form of strict linear matrix inequalities sufficient conditions are established for the existence of the fault detection filter finally a numerical example is provided to demonstrate the usefulness and applicability of the developed theoretical results

asymptotic governing equation for wave propagation along weakly non uniform euler bernoulli beams abstract non uniformity in beams arises either from manufacturing imperfections or by design and can have a singular impact on the qualitative properties of the vibratory response of the beam to describe the mechanism causing such large changes on the dynamics of the beam we derived asymptotically a simpler equation in the form ss q s s 0 the coefficient function q s is given by equation 52 herein in terms of the beam flexural rigidity the mass per unit length and the tensile force applied to the beam the equation is asymptotic to the non uniformity of the beam but under certain restrictions namely of having constant tension and a constant product of the beam mass per unit length and flexural rigidity it is an exact governing equation for wave propagation along bernoulli euler beams and it has a helmholtz like form the behavior of the equation is systematically explored and illustrated through numerical results

brief paper robust filtering with stochastic nonlinearities and multiple missing measurements this paper is concerned with the filtering problem for a class of discrete time uncertain stochastic nonlinear time delay systems with both the probabilistic missing measurements and external stochastic disturbances the measurement missing phenomenon is assumed to occur in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over the interval 01 such a probabilistic distribution could be any commonly used discrete distribution over the interval 01 the multiplicative stochastic disturbances are in the form of a scalar gaussian white noise with unit variance the purpose of the addressed filtering problem is to design a filter such that for the admissible random measurement missing stochastic disturbances norm bounded uncertainties as well as stochastic nonlinearities the error dynamics of the filtering process is exponentially mean square stable by using the linear matrix inequality lmi method sufficient conditions are established that ensure the exponential mean square stability of the filtering error and then the filter parameters are characterized by the solution to a set of lmis illustrative examples are exploited to show the effectiveness of the proposed design procedures

discriminants and automorphism groups of veronese subrings of skew polynomial rings we study important invariants and properties of the veronese subalgebras of q skew polynomial rings including their discriminant center and automorphism group as well as cancellation property and the tits alternative

frequency coalescence and mode localization phenomena a geometric theory physical systems the natural frequencies of which depend parametrically on certain quantities may exhibit the phenomenon of frequency coalescence when two or more natural frequencies become equal or the phenomenon of avoided crossings when two or more frequencies approach rapidly and then avoid crossing each other in the process the natural modes undergo significant variations it is shown that both phenomena can be described in a unified manner from the singularities of the mapping from the complex parameter plane into the complex frequency plane in particular the formation of a saddle point in the frequency plane and a branch point in the parameter space is the basis for explaining the properties associated with these phenomena the question of sensitivity of the system response near such singularities is subsequently examined it is shown that the development of a branch point singularity in the complex parameter plane can cause large or even infinite sensitivity of the system about this point depending on the distance of the branch point from the real axis in the parameter space it is further shown that mode localization is also associated with the appearance of a branch point near the real axis of the complex parameter plane which causes the large sensitivity that characterizes the phenomenon the theory is applied to examples of conservative and dissipative systems undergoing free vibrations

the vibration of a non prismatic beam on an inertial elastic half plane abstract the problem of vibration of a non prismatic beam resting on an inertial elastic half plane described by classical elastokinetics equations is solved using chebyshev series approximation as a result closed analytical formulae for the sought solution s coefficients the passive foundation pressure function and the system displacement function were obtained the method was applied to solve the problem of harmonically excited vibration

reflection of flexural waves in geometrically periodic beams abstract the paper focuses on the reflection characteristics of elastic beams having a periodically varying cross sectional area assuming a weak sinusoidal variation of the beam cross sectional area assuming a weak sinusoidal variation of the beam cross section along its axis perturbation methods are employed to determine flexural resonance conditions and analyze the resonant destructive interaction of flexural waves with the periodic beam this interaction is represented in the form of coupled wave equations which are solved analytically together with relevant boundary conditions at the ends of the periodic section of the beam the reflection coefficient is then calculated for beams having different types of periodicity this study is intended to provide guidelines to control passively the flexural vibration in beams

on lie solvable restricted enveloping algebras abstract in this note we study the lie derived lengths of a restricted enveloping algebra u l for a non abelian restricted lie algebra l over a field of positive characteristic p for p 2 we show that if the lie derived length of u l is minimal then u l is lie nilpotent moreover we investigate the case when the strong lie derived length of u l is minimal for odd p we establish a classification of lie centrally metabelian restricted enveloping algebras

vibration of non uniform rods and beams we show that for some non uniform rods and beams the equation of motion can be transformed into the equation of motion for a uniform rod or beam then when the ends are completely fixed the eigenvalues of the non uniform continuum are the same as those of uniform rods or beams for other end support conditions exact solutions are obtained an efficient procedure is used to analyze the free vibration of non uniform beams with general shape and arbitrary boundary conditions simple formulas are presented for predicting the fundamental natural frequency of non uniform beams with various end support conditions

solvable symmetric poisson algebras and their derived lengths abstract let l be a lie algebra over a field of positive characteristic and let s l and s l denote respectively the symmetric poisson algebra and the truncated symmetric poisson algebra of l as a natural continuation of the work by monteiro alves and petrogradsky in 9 we investigate the structure of l when s l or s l is solvable we first disprove a conjecture stated in 9 about solvability of s l and s l in characteristic 2 next the derived lengths of s l are studied in particular we provide bounds for the derived lengths of s l establish when s l is metabelian and characterize truncated symmetric poisson algebras of minimal derived length

phononic band gaps and vibrations in one and two dimensional mass spring structures the vibrational response of finite periodic lattice structures subjected to periodic loading is investigated special attention is devoted to the response in frequency ranges with gaps in the band structure for the corresponding infinite periodic lattice the effects of boundaries viscous damping and imperfections are studied by analyzing two examples a 1 d filter and a 2 d wave guide in 1 d the structural response in the band gap is shown to be insensitive to damping and small imperfections in 2 d the similar effect of damping is noted for one type of periodic structure whereas for another type the band gap effect is nearly eliminated by damping in both 1 d and 2 d it is demonstrated how the free structural boundaries affect the response in the band gap due to local resonances finally 2 d wave guides are considered by replacing the periodic structure with a homogeneous structure in a straight and a 90 bent path and it is shown how the vibrational response is confined to the paths in the band gap frequency ranges

recursive estimation of discrete time signals from nonlinear randomly delayed observations in this paper one stage prediction filtering and fixed point smoothing problems are addressed for nonlinear discrete time stochastic systems with randomly delayed measurements perturbed by additive white noise the observation delay is modelled by a sequence of independent bernoulli random variables whose values zero or one indicate that the real observation arrives on time or it is delayed one sampling time and hence the available measurement to estimate the signal is not updated assuming that the state space model generating the signal to be estimated is unknown and only the covariance functions of the processes involved in the observation equation are available recursive estimation algorithms based on linear approximations of the real observations are proposed

optimal linear estimators for systems with random sensor delays multiple packet dropouts and uncertain observations this paper is concerned with the optimal linear estimation problem for linear discrete time stochastic systems with random sensor delays packet dropouts and uncertain observations we develop a unified model to describe the mixed uncertainties of random delays packet dropouts and uncertain observations by three bernoulli distributed random variables with known distributions based on the proposed model the optimal linear estimators that only depend on probabilities are developed via an innovation analysis approach their solutions are given in terms of a riccati equation and a lyapunov equation they can deal with the optimal linear filtering prediction and smoothing for systems with random sensor delays packet dropouts and uncertain observations in a unified framework simulation results show the effectiveness of the proposed optimal linear estimators

wave propagation in continuous periodic structures research contributions from southampton 1964 1995 abstract after brief reference to some early studies by other investigators this paper focuses mainly on methods developed at the university of southampton since 1964 to analyze and predict the free and forced wave motion in continuous periodic engineering structures beginning with receptance methods which have been applied to periodic beams and rib skin structures it continues with a method of direct solution of the wave equation this uses floquet s principle and has been applied to beams and quasi one dimensional periodic plates and cylindrical shells sample curves of the propagation and attenuation constants pertaining to these structures are presented a limited discussion of the transfer matrix then follows after which the method of space harmonics is introduced as the method best suited to the prediction of sound radiated from a vibrating periodic structure reviewed next are some theorems and variational principles relating to periodic structures which have been developed at southampton and which form a basis for finding natural frequencies of finite structures or for computing free and forced wave notion by energy methods this has led to the finite element method in its standard and hierarchical forms being used to study wave motion in genuine two dimensional and three dimensional structures examples of this work are shown the method of phased array receptance functions is then introduced as possibly the easiest way of setting up exact equations for the propagation constants of uniform quasi one dimensional periodic structures a summary is finally presented of the limited and early work performed at southampton on simple disordered periodic structures

wave propagation in two dimensional periodic lattices plane wave propagation in infinite two dimensional periodic lattices is investigated using floquet bloch principles frequency bandgaps and spatial filtering phenomena are examined in four representative planar lattice topologies hexagonal honeycomb kagome lattice triangular honeycomb and the square honeycomb these topologies exhibit dramatic differences in their long wavelength deformation properties long wavelength asymptotes to the dispersion curves based on homogenization theory are in good agreement with the numerical results for each of the four lattices the slenderness ratio of the constituent beams of the lattice or relative density has a significant influence on the band structure the techniques developed in this work can be used to design lattices with a desired band structure the observed spatial filtering effects due to anisotropy at high frequencies short wavelengths of wave propagation are consistent with the lattice symmetries

kirwan surjectivity for quiver varieties for algebraic varieties defined by hyperkahler or more generally algebraic symplectic reduction it is a long standing question whether the hyperkahler kirwan map on cohomology is surjective we resolve this question in the affirmative for nakajima quiver varieties we also establish similar results for other cohomology theories and for the derived category our proofs use only classical topological and geometric arguments

probability guaranteed h finite horizon filtering for a class of nonlinear time varying systems with sensor saturations in this paper the probability guaranteed h finite horizon filtering problem is investigated for a class of nonlinear time varying systems with uncertain parameters and sensor saturations the system matrices are functions of mutually independent stochastic variables that obey uniform distributions over known finite ranges attention is focused on the construction of a time varying filter such that the prescribed h performance requirement can be guaranteed with probability constraint by using the difference linear matrix inequalities dlmis approach sufficient conditions are established to guarantee the desired performance of the designed finite horizon filter the time varying filter gains can be obtained in terms of the feasible solutions of a set of dlmis that can be recursively solved by using the semi definite programming method a computational algorithm is specifically developed for the addressed probability guaranteed h finite horizon filtering problem finally a simulation example is given to illustrate the effectiveness of the proposed filtering scheme 2012 elsevier b v all rights reserved

filtering and fault detection for nonlinear systems with polynomial approximation this paper is concerned with polynomial filtering and fault detection problems for a class of nonlinear systems subject to additive noises and faults the nonlinear functions are approximated with polynomials of a chosen degree different from the traditional methods the approximation errors are not discarded but formulated as low order polynomial terms with norm bounded coefficients the aim of the filtering problem is to design a least squares filter for the formulated nonlinear system with uncertain polynomials and an upper bound of the filtering error covariance is found and subsequently minimized at each time step the desired filter gain is obtained by recursively solving a set of riccati like matrix equations and the filter design algorithm is therefore applicable for online computation based on the established filter design scheme the fault detection problem is further investigated where the main focus is on the determination of the threshold on the residual due to the nonlinear and time varying nature of the system under consideration a novel threshold is determined that accounts for the noise intensity and the approximation errors and sufficient conditions are established to guarantee the fault detectability for the proposed fault detection scheme comparative simulations are exploited to illustrate that the proposed filtering strategy achieves better estimation accuracy than the conventional polynomial extended kalman filtering approach the effectiveness of the associated fault detection scheme is also demonstrated

recursive filtering for discrete time linear systems with fading measurement and time correlated channel noise this paper is concerned with the recursive filtering problem for discrete time linear systems with fading measurement and time correlated channel noise the phenomenon of measurement fading appears in a random way and the fading phenomenon for each sensor is described by an individual random variable taking a value in a given interval the time correlated channel noise is depicted as a linear system model with white noise using the measurement differencing method and some results obtained in this paper a recursive filtering algorithm for the system under consideration is proposed the proposed algorithm is optimal in the sense of linear minimum mean square error and does not increase computation and storage load with time computer simulations are carried out to evaluate the performance of the proposed algorithm

distributed filtering for a class of time varying systems over sensor networks with quantization errors and successive packet dropouts this paper is concerned with the distributed finite horizon filtering problem for a class of time varying systems over lossy sensor networks the time varying system target plant is subject to randomly varying nonlinearities rvns caused by environmental circumstances the lossy sensor network suffers from quantization errors and successive packet dropouts that are described in a unified framework two mutually independent sets of bernoulli distributed white sequences are introduced to govern the random occurrences of the rvns and successive packet dropouts through available output measurements from not only the individual sensor but also its neighboring sensors according to the given topology a sufficient condition is established for the desired distributed finite horizon filter to ensure that the prescribed average filtering performance constraint is satisfied the solution of the distributed filter gains is characterized by solving a set of recursive linear matrix inequalities a simulation example is provided to show the effectiveness of the proposed filtering scheme

on universal lie nilpotent associative algebras abstract we study the quotient q i a of a free algebra a by the ideal m i a generated by the ith commutator of any elements in particular we completely describe such quotient for i 4 for i 3 this was done previously by feigin and shoikhet we also study properties of the ideals m i a e g when m i a m j a is contained in m i j 1 a by a result of gupta and levin it is always contained in m i j 2 a

event based h_ infty filter design for a class of nonlinear time varying systems with fading channels and multiplicative noises in this paper a general event triggered framework is developed to deal with the finite horizon h infty filtering problem for discrete time varying systems with fading channels randomly occurring nonlinearities and multiplicative noises an event indicator variable is constructed and the corresponding event triggered scheme is proposed such a scheme is based on the relative error with respect to the measurement signal in order to determine whether the measurement output should be transmitted to the filter or not the fading channels are described by modified stochastic rice fading models some uncorrelated random variables are introduced respectively to govern the phenomena of state multiplicative noises randomly occurring nonlinearities as well as fading measurements the purpose of the addressed problem is to design a set of time varying filter such that the influence from the exogenous disturbances onto the filtering errors is attenuated at the given level quantified by a h infty norm in the mean square sense by utilizing stochastic analysis techniques sufficient conditions are established to ensure that the dynamic system under consideration satisfies the h infty filtering performance constraint and then a recursive linear matrix inequality rlmi approach is employed to design the desired filter gains simulation results demonstrate the effectiveness of the developed filter design scheme

poisson brackets and two generated subalgebras of rings of polynomials let a f x1 x2 xn be a ring of polynomials over a field f on the variables x1 x2 xn it is well known see for example 11 that the study of automorphisms of the algebra a is closely related with the description of its subalgebras by the theorem of p m cohn 4 a subalgebra of the algebra f x is free if and only if it is integrally closed the theorem of a zaks 13 says that the dedekind subalgebras of the algebra a are rings of polynomials in a single variable a nowicki and m nagata 8 proved that the kernel of any nontrivial derivation of the algebra f x y char f 0 is also a ring of polynomials in a single generator an original solution of the occurrence problem for the algebra a using the groebner basis was given by d shannon and m sweedler 9 however the method of the groebner basis does not give any information about the structure of concrete subalgebras recall that the solubility of the occurrence problem for rings of polynomials over fields of characteristic 0 was proved earlier by g noskov 7 the present paper is devoted to the investigation of the structure of twogenerated subalgebras of a in the sequel we always assume that f is an arbitrary field of characteristic 0 let us denote by f the highest homogeneous part of an element f a and by f1 f2 fk the subalgebra of a generated by the elements f1 f2 fk a definition 1 a pair of polynomials f1 f2 a is called reduced if they satisfy the following conditions 1 f1 f2 are algebraically dependent 2 f1 f2 are algebraically independent 3 f1 f2 f2 f1 recall that a pair f1 f2 with condition 3 is usually called reduced condition 1 means that we exclude the trivial case when f1 f2 are algebraically independent we do not consider the case when f1 f2 are algebraically dependent concerning this case recall the well known theorem of s s abhyankar and t t moh 1 which says that if f g f x and f g f x then f or f

poisson pi algebras we study poisson algebras satisfying polynomial identities in particular such algebras satisfy customary identities farkas 1998 1999 our main result is that the growth of the corresponding codimensions of a poisson algebra with a nontrivial identity is exponential with an integer exponent we apply this result to prove that the tensor product of poisson pi algebras is a pi algebra we also determine the growth of the poisson grassmann algebra and of the hamiltonian algebras

polynomial and poisson dependence in free poisson algebras and free poisson fields abstract we prove that any two poisson dependent elements in a free poisson algebra and a free poisson field of characteristic zero are algebraically dependent thus answering positively a question from makar limanov and umirbaev 2007 8 we apply this result to give a new proof of the tameness of automorphisms for free poisson algebras of rank two see makar limanov and umirbaev 2011 9 makar limanov et al 2009 10

optimal estimation for discrete time linear systems in the presence of multiplicative and time correlated additive measurement noises in this paper the state estimation problem for discrete time linear systems influenced by multiplicative and time correlated additive measurement noises is considered where the multiplicative noises are zero mean white noise sequences and the time correlated additive noise is described by a linear system model with white noise an optimal linear estimator for the system under consideration is proposed which does not require computing the inverse of state transition matrix the proposed estimator has a recursive structure and has time independent computation and storage load computer simulations are carried out to demonstrate the performance of the proposed estimator the simulation results show the superiority of the proposed estimator

optimal full order and reduced order estimators for discrete time systems with multiple packet dropouts this paper is concerned with the estimation problem for discrete time stochastic linear systems with multiple packet dropouts based on a recently developed model for multiple packet dropouts the original system is transferred to a stochastic parameter system by augmentation of the state and measurement the optimal full order linear filter of the form of employing the received outputs at the current and last time instants is investigated the solution to the optimal linear filter is given in terms of a riccati difference equation governed by packet arrival rate the optimal filter is reduced to the standard kalman filter when there are no packet dropouts the steady state filter is also studied a sufficient condition for the existence of the steady state filter is given and the asymptotic stability of the optimal filter is analyzed at last a reduced order filter is investigated

gain constrained kalman filtering for linear and nonlinear systems this paper considers the state estimation problem with a constraint on the data injection gain special cases of this problem include the enforcing of a linear equality constraint in the state vector the enforcing of unbiased estimation for systems with unknown inputs and simplification of the estimator structure for large scale systems both the one step gain constrained kalman predictor and the two step gain constrained kalman filter are presented the latter is extended to the nonlinear case yielding the gain constrained unscented kalman filter two illustrative examples are presented

extended kalman filtering with stochastic nonlinearities and multiple missing measurements in this paper the extended kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon both deterministic and stochastic nonlinearities are included in the system model where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances the phenomenon of measurement missing occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval 0 1 such a probability distribution is allowed to be any commonly used distribution over the interval 0 1 with known conditional probability the aim of the addressed filtering problem is to design a filter such that in the presence of both the stochastic nonlinearities and multiple missing measurements there exists an upper bound for the filtering error covariance subsequently such an upper bound is minimized by properly designing the filter gain at each sampling instant it is shown that the desired filter can be obtained in terms of the solutions to two riccati like difference equations that are of a form suitable for recursive computation in online applications an illustrative example is given to demonstrate the effectiveness of the proposed filter design scheme

on kalman filtering with nonlinear equality constraints the state space description of some physical systems possess nonlinear equality constraints between some state variables in this paper we consider the problem of applying a kalman filter type estimator in the presence of such constraints we categorize previous approaches into pseudo observation and projection methods and identify two types of constraints those that act on the entire distribution and those that act on the mean of the distribution we argue that the pseudo observation approach enforces neither type of constraint and that the projection method enforces the first type of constraint only we propose a new method that utilizes the projection method twice once to constrain the entire distribution and once to constrain the statistics of the distribution we illustrate these algorithms in a tracking system that uses unit quaternions to encode orientation

h filtering with randomly occurring sensor saturations and missing measurements in chap 5 the h filtering problem is studied for a class of nonlinear systems with randomly occurring incomplete information where the considered incomplete information includes both the sensor saturations and the missing measurements a new phenomenon of sensor saturation namely randomly occurring sensor saturation ross is first put forward in order to better reflect the reality in a networked environment then a novel sensor model is established to account for both the ross and missing measurement in a unified representation based on this sensor model a regional h filter with a certain ellipsoid constraint is designed such that the filtering error dynamics is locally mean square asymptotically stable and the h norm requirement is satisfied

the vibration of a complete euler bernoulli beam of constant depth and breadth proportional to axial co ordinate raised to a positive exponents the complete euler bernoulli beam considered in this paper is sharp ended of constant depth and of breadth proportional to xs where x is the axial co ordinate measured from the sharp end the theory of vibration of uniform beams s 0 is documented in text books forsgreater than 0 the mode shape differential equation is linear fourth order with variable coefficients for non integer values ofs the four solution functions are converging power series for integer values ofs except whensis an integer multiple of 4 one or possibly two of the solution functions contain logarithmic terms the sharp end of a complete beam must be free because it cannot sustain a bending moment of shearing force and as a result the space function will consist of two power series for alls in the present paper ideal clamped pinned sliding and free boundary conditions are considered at the big end the frequency equation is a 2 x 2 determinant equated to zero the first four non zero dimensionless natural frequencies are tabulated for fr cl fr pn fr sl and fr fr beams for values of the breadth exponentsvarying from 0 to 5 for various values ofsgraphs of the distortion of the mode shapes from the corresponding mode shape of uniform beams are presented the position of nodes zero slope anti nodes zero bending moment inflexion and zero shearing force are tabulated for various vales ofs to illustrate the drift from the corresponding position s of a uniform beam

a lie algebra generalization of the amitsur levitski theorem 0 1 if r is any algebra over a field f and xi e r i l k let iix 1 y 1 e r denote the alternating sum of products z sg 0 x x over all permutations 0 of l k one says that r satisfies the k fold standard identity if ix xk 0 for any choice xi e r of course if pc r is any subspace of r one can restrict one s attention to p and say that p satisfies the k fold standard identity if 1 x1 x 0 for any choice xi f p now the amitsur levitski theorem asserts that the n x n matrix algebra m n f satisfies the 2n fold standard identity for a survey and history of this theorem see 9 1 see also 17 i it is of course enough to consider the case where f c some time ago see 3 we came upon a proof of the amitsur levitski theorem from the point of lie algebra cohomology the cohomology of m n c as a lie algebra is an exterior algebra with primitive generators having degrees 1 2 2n 1 the failure of m n cc to have a primitive class in degree 2n 1 leads to the trace relation tr x x 0 for any xi e m n c for i i 2n 1 but this quickly implies the amitsur levitski theorem in fact the argument can be pushed further if d g m n cc denotes the lie algebra of all n x n skew symmetric matrices one knows that d has no primitive class in degree 2n 1 in case n is even this led to a new identity in 3 1 for iz even

recursive filtering with random parameter matrices multiple fading measurements and correlated noises this paper is concerned with the recursive filtering problem for a class of discrete time nonlinear stochastic systems with random parameter matrices multiple fading measurements and correlated noises the phenomenon of measurement fading occurs in a random way and the fading probability for each sensor is governed by an individual random variable obeying a certain probability distribution over the known interval b k c k such a probability distribution could be any commonly used discrete distribution over the interval b k c k that covers the bernoulli distribution as a special case the process noise and the measurement noise are one step autocorrelated respectively the process noise and the measurement noise are two step cross correlated the purpose of the addressed filtering problem is to design an unbiased and recursive filter for the random parameter matrices stochastic nonlinearity and multiple fading measurements as well as correlated noises intensive stochastic analysis is carried out to obtain the filter gain characterized by the solution to a recursive matrix equation the proposed scheme is of a form suitable for recursive computation in online applications a simulation example is given to illustrate the effectiveness of the proposed filter design scheme

the poisson center and polynomial maximal poisson commutative subalgebras especially for nilpotent lie algebras of dimension at most seven abstract let g be a finite dimensional lie algebra over an algebraically closed field k of characteristic zero we collect some general results on the poisson center of s g including some simple criteria regarding its polynomiality and also on certain poisson commutative subalgebras of s g these facts are then used to complete our previous work on the subject ooms 2009 o5 5 i e to give an explicit description for the poisson center of all indecomposable nilpotent lie algebras of dimension at most seven among other things we also provide a polynomial maximal poisson commutative subalgebra of s g enjoying additional properties as a by product we show that a conjecture by milovanov is valid in this situation these results easily carry over to the enveloping algebra u g

on nonlinear h_ infty filtering for discrete time stochastic systems with missing measurements in this paper the h infin filtering problem is investigated for a general class of nonlinear discrete time stochastic systems with missing measurements the system under study is not only corrupted by state dependent white noises but also disturbed by exogenous inputs the measurement output contains randomly missing data that is modeled by a bernoulli distributed white sequence with a known conditional probability a filter of very general form is first designed such that the filtering process is stochastically stable and the filtering error satisfies h infin performance constraint for all admissible missing observations and nonzero exogenous disturbances under the zero initial condition the existence conditions of the desired filter are described in terms of a second order nonlinear inequality such an inequality can be decoupled into some auxiliary ones that can be solved independently by taking special form of the lyapunov functionals as a consequence a linear time invariant filter design problem is discussed for the benefit of practical applications and some simplified conditions are obtained finally two numerical simulation examples are given to illustrate the main results of this paper

the lie structure of enveloping algebras abstract this paper examines the lie structure of restricted universal enveloping algebras u l over fields of characteristic p 0 it is determined precisely when u l considered as a lie algebra is soluble for p 2 nilpotent or satisfies the engel condition

on commuting polynomial automorphisms of mathbb c k k 3 we characterize the polynomial automorphisms of mathbb c 3 which commute with a regular automorphism we use their meromorphic extension to mathbb p 3 and consider their dynamics on the hyperplane at infinity we conjecture the additional hypothesis under which the same characterization is true in all dimensions we give a partial answer to a question of s smale that in our context can be formulated as follows can any polynomial automorphism of mathbb c k be the uniform limit on compact sets of polynomial automorphisms with trivial centralizer i e c f simeq mathbb z

mode localization and eigenvalue loci veering phenomena in disordered structures an investigation of the effects of disorder on the modes of vibration of nearly periodic structures is presented it is shown that in structures with close eigenvalues small structural irregularities result in both strong localization of the mode shapes and abrupt veering away or mutual repulsion of the loci of the eigenvalues when these are plotted against a parameter representing the disorder in the system perturbation methods for the eigenvalue problem are applied to predict the occurrence of strong localization and eigenvalue loci veering which are shown to be two manifestations of the same phenomenon also perturbation methods that handle the dramatic effects of small disorder are developed to analyze eigenvalue loci veering and strong localization two representative disordered nearly periodic structures are studied a mistuned assembly of coupled oscillators and a multi span beam with irregular spacing of the supports

frequency analysis of a heterogeneous perforated panel using a super element formulation abstract heterogeneous perforated panels represent a wide class of structural elements with holes where perforations and matrix are of dissimilar materials e g metallic member of a perforated hybrid joint with resin fillings there is a variety of objectives for introducing holes e g weight saving or mechanical interlock where there is a regular pattern to the arrangement of holes the perforated element can be assimilated to a lattice in the present study numerical analysis has been conducted on investigating the shock frequency filtering phenomenon encountered in two dimensional 2d lattice structures a super element of the primitive cell unit cell of the lattice has been formulated and applied in conjunction with the floquet bloch s principle to study the shock response characteristics plane wave propagation is investigated by constructing the first brillouin zone of the primitive cell in associated fourier space k space the frequency characteristics are presented in the band structure diagram the study emphasizes the existence of frequency pass and stop bands and the extent of this phenomenon the frequency filtering effects of the heterogeneous perforated 2d lattice has shown its potential value to improve the structural performance of perforated hybrid joints subjected to dynamic loads

lie structure of truncated symmetric poisson algebras abstract the paper naturally continues series of works on identical relations of group rings enveloping algebras and other related algebraic structures let l be a lie algebra over a field of characteristic p 0 consider its symmetric algebra s l n 0 u n u n 1 which is isomorphic to a polynomial ring it also has a structure of a poisson algebra where the lie product is traditionally denoted by this bracket naturally induces the structure of a poisson algebra on the ring s l s l x p x l which we call a truncated symmetric poisson algebra we study lie identical relations of s l namely we determine necessary and sufficient conditions for l under which s l is lie nilpotent strongly lie nilpotent solvable and strongly solvable where we assume that p 2 to specify the solvability we compute the strong lie nilpotency class of s l also we prove that the lie nilpotency class coincides with the strong lie nilpotency class in case p 3 shestakov proved that the symmetric algebra s l of an arbitrary lie algebra l satisfies the identity x y z 0 if and only if l is abelian we extend this result for the strong lie nilpotency and the strong solvability of s l we show that the solvability of s l and s l in case char k 2 is different from other characteristics namely we construct examples of such algebras which are solvable but not strongly solvable we use delta sets for lie algebras and the theory of identical relations of poisson algebras also we study filtrations in poisson algebras and prove results on products of terms of the lower central series for poisson algebras

brief paper optimal linear estimation for systems with multiple packet dropouts this paper is concerned with the optimal linear estimation problem for linear discrete time stochastic systems with multiple packet dropouts based on a packet dropout model the optimal linear estimators including filter predictor and smoother are developed via an innovation analysis approach the estimators are computed recursively in terms of the solution of a riccati difference equation of dimension equal to the order of the system state plus that of the measurement output the steady state estimators are also investigated a sufficient condition for the convergence of the optimal linear estimators is given simulation results show the effectiveness of the proposed optimal linear estimators

h sub spl infin filtering for multiple time delay measurements the aim of this paper is to study the h sub spl infin filtering problem for linear continuous time systems with both current and multiple time delay measurements the key technique applied for deriving the filter is the reorganized innovation analysis approach in krein space a necessary and sufficient condition for the existence of an h sub spl infin filter is derived and the solution to the h sub spl infin filter is given in terms of solutions of riccati and matrix differential equations an example is finally presented to show the effectiveness of the proposed approach

the tame and the wild automorphisms of polynomial rings in three variables let c f x1 x2 xn be the polynomial ring in the variables x1 x2 xn over a field f and let autc be the group of automorphisms of c as an algebra over f an automorphism autc is called elementary if it has a form x1 xi 1 xi xi 1 xn 7 x1 xi 1 xi f xi 1 xn where 0 6 f f f x1 xi 1 xi 1 xn the subgroup of autc generated by all the elementary automorphisms is called the tame subgroup and the elements from this subgroup are called tame automorphisms of c non tame automorphisms of the algebra c are called wild it is well known 6 9 10 11 that the automorphisms of polynomial rings and free associative algebras in two variables are tame at present a few new proofs of these results have been found see 5 8 however in the case of three or more variables the similar question was open and known as the generation gap problem 2 3 or tame generators problem 8 the general belief was that the answer is negative and there were several candidate counterexamples see 5 8 12 7 19 the best known of them is the following automorphism aut f x y z constructed by nagata in 1972 see 12 x x x yz z y y 2 x yz x x yz z z z

lie solvable enveloping algebras of characteristic two abstract lie solvable restricted enveloping algebras were characterized by riley and shalev except when the ground field is of characteristic 2 we resolve the characteristic 2 case here which completes the classification as an application of our result we obtain a characterization of ordinary lie algebras over any field whose enveloping algebra is lie solvable

lie identities on enveloping algebras of restricted lie superalgebras abstract let l be a restricted lie superalgebra with its restricted enveloping algebra u l over a field f of characteristic p 2 then u l can be viewed both as a lie algebra and a lie superalgebra we characterize l when u l is lie solvable lie nilpotent or lie super nilpotent

tame and wild coordinates of z x y abstract algorithms to decide whether a polynomial is a coordinates tame coordinate respectively of z x y are given moreover if a polynomial p z x y is a coordinate tame coordinate respectively the algorithms effectively construct a concrete automorphism of z x y that sends x to p the algorithm to determine tame coordinate is applicable to r x y where r is an euclidean domain while the algorithm to determine coordinate is applicable to d x y where d is a unique factorization domain

the additive group of a lie nilpotent associative ring abstract let z x be the free unital associative ring freely generated by an infinite countable set x x 1 x 2 define a left normed commutator x 1 x 2 x n by a b a b b a a b c a b c for n 2 let t n be the two sided ideal in z x generated by all commutators a 1 a 2 a n a i z x it can be easily seen that the additive group of the quotient ring z x t 2 is a free abelian group recently bhupatiraju etingof jordan kuszmaul and li have noted that the additive group of z x t 3 is also free abelian in the present note we show that this is not the case for z x t 4 more precisely let t 3 2 be the ideal in z x generated by t 4 together with all elements a 1 a 2 a 3 a 4 a 5 a i z x we prove that t 3 2 t 4 is a non trivial elementary abelian 3 group and the additive group of z x t 3 2 is free abelian

three power series techniques the techniques and concepts we present are flags of regular schemes and their persistence under blow up the gauss bruhat decomposition of the group of formal automorphisms of affine space and coordinate free initial ideals all three are used to construct and study invariants for resolution of singularities

lower central series of free algebras in symmetric tensor categories abstract we continue the study of the lower central series of a free associative algebra initiated by feigin and shoikhet 2007 fs we generalize via schur functors the constructions of the lower central series to any symmetric tensor category specifically we compute the modified first quotient b 1 and second and third quotients b 2 and b 3 of the series for a free algebra t v in any symmetric tensor category generalizing the main results of feigin and shoikhet 2007 fs and arbesfeld and jordan 2010 aj in the case a m n t c m n we use these results to compute the explicit hilbert series finally we prove a result relating the lower central series to the corresponding filtration by two sided associative ideals confirming a conjecture from etingof et al 2009 ekm and another one from arbesfeld and jordan 2010 aj as corollaries