a note on lie centrally metabelian group algebras abstract letkbe a field of characteristic 3 and letgbe a non abelian group it is shown that the group algebrakgis lie centrally metabelian if and only if the commutator subgroupg is cyclic of order 3 in view of the results of 2 this settles completely the characterization of lie centrally metabelian group algebras in characteristic not equal to 2

lie properties of crossed products abstract let f g be a crossed product of a group g and the field f we study the lie properties of f g in order to obtain a characterization of those crossed products which are upper lower lie nilpotent and lie n m engel

hierarchical gradient parameter estimation algorithm for hammerstein nonlinear systems using the key term separation principle in this paper we use the hierarchical identification principle to decompose a hammerstein controlled autoregressive system into three subsystems apply the key term separation principle to express the system output as a linear combination of the system parameters and then derive a hierarchical gradient parameter estimation algorithm for identifying all subsystems finally a multi innovation stochastic gradient algorithm is presented to improve the estimation accuracy by making full of the identification innovation the simulation results show that the proposed algorithm is effective

partially mode dependent l2 l filtering for discrete time nonhomogeneous markov jump systems with repeated scalar nonlinearities abstract this paper is concerned with the problem of partially mode dependent l 2 l filtering for discrete time nonhomogeneous markov jump systems mjss with repeated scalar nonlinearities our main purpose is to design a partially mode dependent l 2 l filter such that the filtering error system is stochastically stable with l 2 l performance the time varying transition probabilities tps are depicted as a polytope by adopting the diagonally dominant lyapunov functional and based on linear matrix inequalities lmis sufficient conditions are presented for the existence of the filter three examples are given to validate the effectiveness of our results

lie centre by metabelian group algebras over commutative rings abstract lie centre by metabelian group algebras over fields have been classified by various authors this classification is extended to group algebras over commutative rings

on clusterings good bad and spectral we motivate and develop a natural bicriteria measure for assessing the quality of a clustering that avoids the drawbacks of existing measures a simple recursive heuristic is shown to have poly logarithmic worst case guarantees under the new measure the main result of the article is the analysis of a popular spectral algorithm one variant of spectral clustering turns out to have effective worst case guarantees another finds a good clustering if one exists

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

higher order moment stability region for markov jump systems based on cumulant generating function this paper is concerned with the solution of higher order moment stability region for markov jump systems with respect to cases of both known and unknown transition probabilities by exploring the cumulant generating function the original stochastic system with markov jumping modes is transformed to a deterministic system then based on the estimation of matrix eigenvalues the explicit solution for higher order moment stability region is expressed in terms of transition probabilities operation modes state transition matrix and its dimension and the moment order several examples are presented to illustrate the effectiveness of the proposed method and its associated algorithm

a 5 engel associative algebra whose group of units is not 5 engel abstract let r be an associative ring with unity and let r and u r denote the associated lie ring with a b a b b a and the group of units of r respectively in 1983 gupta and levin proved that if r is a nilpotent lie ring of class c then u r is a nilpotent group of class at most c the aim of the present note is to show that in general a similar statement does not hold if r is n engel we construct an algebra r over a field of characteristic 2 3 such that the lie algebra r is 5 engel but the group u r is not

necessary and sufficient conditions for analysis and synthesis of markov jump linear systems with incomplete transition descriptions this technical note is concerned with exploring a new approach for the analysis and synthesis for markov jump linear systems with incomplete transition descriptions in the study not all the elements of the transition rate matrices trms in continuous time domain or transition probability matrices tpms in discrete time domain are assumed to be known by fully considering the properties of the trms and tpms and the convexity of the uncertain domains necessary and sufficient criteria of stability and stabilization are obtained in both continuous and discrete time numerical examples are used to illustrate the results

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

fixed order robust h sub spl infin filter design for markovian jump systems with uncertain switching probabilities this paper discusses the fixed order robust h sub spl infin filtering problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertainties under consideration are assumed to be norm bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix respectively first a criterion based on linear matrix inequalities is provided for testing the h sub spl infin filtering level of a filter over all the admissible uncertainties then a sufficient condition for the existence of the fixed order robust h sub spl infin filters is established in terms of the solvability of a set of linear matrix inequalities with equality constraints to determine the filter a globally convergent algorithm involving convex optimization is suggested finally a numerical example is used to illustrate that the developed theory is more effective than the existing results

brief on robust stabilization of markovian jump systems with uncertain switching probabilities this brief paper is concerned with the robust stabilization problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertain markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix first a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities then a sufficient condition is proposed for the design of robust state feedback controllers a globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively finally a numerical simulation is used to illustrate the developed theory

mathcal h_ infty control for 2 d markov jump systems in roesser model this paper considers the problem of asynchronous mathcal h infty control for two dimensional 2 d markov jump systems the underlying system is described based upon the roesser model especially the hidden markov model is employed when dealing with the asynchronization between a controlled system and a controller and the relation between them is constructed through a conditional probability matrix based on the lyapunov function technique the asymptotic mean square stability and mathcal h infty noise attenuation performance are investigated for the closed loop 2 d system moreover the controller gain can be obtained by solving a convex optimization problem an example is presented to show the effectiveness and potential of the proposed new design technique

nonmatrix varieties and nil generated algebras whose units satisfy a group identity abstract letr denote the group of units of an associative algebrarover an infinite fieldf we prove that ifris unitarily generated by its nilpotent elements thenr satisfies a group identity precisely whenrsatisfies a nonmatrix polynomial identity as an application we examine the group algebrafgof a torsion groupgand the restricted enveloping algebrau l of ap nil restricted lie algebral giambruno sehgal and valenti recently proved that if the group of units fg satisfies a group identity thenfgsatisfies a polynomial identity thus confirming a conjecture of brian hartley we show that in fact fg satisfies a group identity if and only iffgsatisfies a nonmatrix polynomial identity in the case of restricted enveloping algebras we prove thatu l satisfies a group identity if and only ifu l satisfies the engel condition

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

state estimation and sliding mode control of markovian jump singular systems this paper is concerned with the state estimation and sliding mode control problems for continuous time markovian jump singular systems with unmeasured states firstly a new necessary and sufficient condition is proposed in terms of strict linear matrix inequality lmi which guarantees the stochastic admissibility of the unforced markovian jump singular system then the sliding mode control problem is considered by designing an integral sliding surface function an observer is designed to estimate the system states and a sliding mode control scheme is synthesized for the reaching motion based on the state estimates it is shown that the sliding mode in the estimation space can be attained in a finite time some conditions for the stochastic admissibility of the overall closed loop system are derived finally a numerical example is provided to illustrate the effectiveness of the proposed theory

network properties revealed through matrix functions the emerging field of network science deals with the tasks of modeling comparing and summarizing large data sets that describe complex interactions because pairwise affinity data can be stored in a two dimensional array graph theory and applied linear algebra provide extremely useful tools here we focus on the general concepts of centrality communicability and betweenness each of which quantifies important features in a network some recent work in the mathematical physics literature has shown that the exponential of a network s adjacency matrix can be used as the basis for defining and computing specific versions of these measures we introduce here a general class of measures based on matrix functions and show that a particular case involving a matrix resolvent arises naturally from graph theoretic arguments we also point out connections between these measures and the quantities typically computed when spectral methods are used for data mining tasks such as clustering and ordering we finish with computational examples showing the new matrix resolvent version applied to real networks

stabilization for markovian jump nonlinear systems with partly unknown transition probabilities via fuzzy control abstract this paper is concerned with the stability and stabilization problems for a class of nonlinear systems with markovian jump parameters the takagi sugeno t s fuzzy model is employed to represent the markovian jump nonlinear systems with partly unknown transition probabilities in contrast with the certain or uncertain transition probabilities investigated recently the concept of partly unknown transition probabilities does not need any knowledge of the unknown elements some sufficient conditions for stochastic stability and stabilization conditions with a mode dependent fuzzy controller are derived for the markovian jump fuzzy systems in terms of linear matrix inequalities lmis a numerical example is provided to illustrate the design developed in this paper

brief paper stability and stabilization of markovian jump linear systems with partly unknown transition probabilities in this paper the stability and stabilization problems of a class of continuous time and discrete time markovian jump linear system mjls with partly unknown transition probabilities are investigated the system under consideration is more general which covers the systems with completely known and completely unknown transition probabilities as two special cases the latter is hereby the switched linear systems under arbitrary switching moreover in contrast with the uncertain transition probabilities studied recently the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements the sufficient conditions for stochastic stability and stabilization of the underlying systems are derived via lmis formulation and the relation between the stability criteria currently obtained for the usual mjls and switched linear systems under arbitrary switching are exposed by the proposed class of hybrid systems two numerical examples are given to show the validity and potential of the developed results

associative rings with metabelian adjoint group abstract the set of all elements of an associative ring r not necessarily with a unit element forms a monoid under the circle operation r s r s rs on r whose group of all invertible elements is called the adjoint group of r and denoted by r the ring r is radical if r r it is proved that a radical ring r is lie metabelian if and only if its adjoint group r is metabelian this yields a positive answer to a question raised by s jennings and repeated later by a krasil nikov furthermore for a ring r with unity whose multiplicative group r is metabelian it is shown that r is lie metabelian provided that r is generated by r and r modulo its jacobson radical is commutative and artinian this implies that a local ring is lie metabelian if and only if its multiplicative group is metabelian

a multi innovation generalized extended stochastic gradient algorithm for output nonlinear autoregressive moving average systems this paper proposes a generalized extended stochastic gradient gesg algorithm for estimating the parameters of a class of wiener nonlinear autoregressive moving average systems using the gradient search in order to improve the convergence rates of the gesg algorithm a multi innovation gesg algorithm is derived the simulation results indicate that the proposed algorithms can effectively estimate the parameters of a class of output nonlinear systems

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

kalman filtering for continuous time uncertain systems with markovian jumping parameters studies the problem of kalman filtering for a class of uncertain linear continuous time systems with markovian jumping parameters the system under consideration is subjected to time varying norm bounded parameter uncertainties in the state and measurement equations stochastic quadratic stability of the above system is analyzed a state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties which is in terms of solutions of two sets of coupled algebraic riccati equations

the fiedler vector of a laplacian tensor for hypergraph partitioning based on recent advances in spectral hypergraph theory l qi and z luo tensor anaysis spectral theory and special tensors siam philadelphia 2017 we explore the fiedler vector of an even uniform hypergraph which is the z eigenvector associated with the second smallest z eigenvalue of a normalized laplacian tensor arising from the hypergraph then we develop a novel tensor based spectral method for partitioning vertices of the hypergraph for this purpose we extend the normalized laplacian matrix of a simple graph to the normalized laplacian tensor of an even uniform hypergraph the corresponding fiedler vector is related to the cheeger constant of the hypergraph then we establish a feasible optimization algorithm to compute the fiedler vector according to the normalized laplacian tensor the convergence of the proposed algorithm and the probability of obtaining the fiedler vector of the hypergraph are analyzed theoretically finally preliminary numerical experiments illustrate that the new a

radical rings with soluble adjoint groups abstract an associative ring r not necessarily with an identity is called radical if it coincides with its jacobson radical which means that the set of all elements of r forms a group denoted by r under the circle operation r s r s rs on r it is proved that every radical ring r whose adjoint group r is soluble must be lie soluble moreover if the commutator factor group of r has finite torsion free rank then r is locally nilpotent

the torsion subgroup of the additive group of a lie nilpotent associative ring of class 3 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 a 1 a 2 a n inductively by a b a b b a a 1 a 2 a n a 1 a n 1 a n n 3 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 let t 3 2 be the two sided ideal of the ring z x generated by all elements a 1 a 2 a 3 a 4 and a 1 a 2 a 3 a 4 a 5 a i z x it has been recently proved in 22 that the additive group of z x t 4 is a direct sum a b where a is a free abelian group isomorphic to the additive group of z x t 3 2 and b t 3 2 t 4 is an elementary abelian 3 group a basis of the free abelian summand a was described explicitly in 22 the aim of the present article is to find a basis of the elementary abelian 3 group b

analysis and synthesis of markov jump linear systems with time varying delays and partially known transition probabilities in this note the stability analysis and stabilization problems for a class of discrete time markov jump linear systems with partially known transition probabilities and time varying delays are investigated the time delay is considered to be time varying and has a lower and upper bounds the transition probabilities of the mode jumps are considered to be partially known which relax the traditional assumption in markov jump systems that all of them must be completely known a priori following the recent study on the class of systems a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality lmi formulation and the design of the stabilizing controller is further given a numerical example is used to illustrate the developed theory

brief paper mode dependent h filtering for discrete time markovian jump linear systems with partly unknown transition probabilities in this paper the problem of h filtering for a class of discrete time markovian jump linear systems mjls with partly unknown transition probabilities is investigated the considered systems are more general which cover the mjls with completely known and completely unknown transition probabilities as two special cases a mode dependent full order filter is constructed and the bounded real lemma brl for the resulting filtering error system is derived via lmi formulation then an improved version of the brl is further given by introducing additional slack matrix variables to eliminate the cross coupling between system matrices and lyapunov matrices among different operation modes finally the existence criterion of the desired filter is obtained such that the corresponding filtering error system is stochastically stable with a guaranteed h performance index a numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results

h control for discrete time markov jump systems with uncertain transition probabilities in this technical note the h control problem for a class of discrete time markov jump systems mjss with uncertain transition probabilities tps is investigated the uncertain information of transition probabilities is quantized by gaussian transition probability density function pdf in light of the proposed descriptions the mjss with gaussian pdf of tps cover the systems with precisely known and partially known tps as two special cases sufficient conditions for the existence of h controller of the underlying systems are derived in term of linear matrix inequalities a numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results

lie centrally metabelian group rings let l r denote the associated lie ring of an associative ring r under the lie multiplication x y xy yx x y r then r is said to be lie centrally metabelian if the lie ring l r is centrally metabelian that is x1 x2 x3 x4 x5 0 for all x1 x2 x3 x4 x5 r let g be a group and k be a field such that the group ring kg is lie centrally metabelian if char k 0 then it is known that g is abelian in this paper we have obtained two results on lie centrally metabelian group rings when char k p 3 the first states that if char k p 3 then kg is lie centrally metabelian if and only if g is abelian the second result proves that if char k 3 and kg is lie centrally metabelian then the commutator subgroup g is a finite 3 engel 3 group of exponent at most 9 and consequently nilpotent of class at most 4 further it has been shown that if kg is lie solvable and char k p is sufficiently large then g is abelian at the end we obtain an interesting result which shows that 2 u r 1 2 l r r for any ring r where 2 u r and 2 l r denote the second derived term of the unit group u r and the associated lie ring l r of r respectively as a consequence the unit group u r is metabelian if the lie ring l r is metabelian

transition probability bounds for the stochastic stability robustness of continuous and discrete time markovian jump linear systems this paper considers the robustness of stochastic stability of markovian jump linear systems in continuous and discrete time with respect to their transition rates and probabilities respectively the continuous time discrete time system is described via a continuous valued state vector and a discrete valued mode which varies according to a markov process chain by using stochastic lyapunov function approach and kronecker product transformation techniques sufficient conditions are obtained for the robust stochastic stability of the underlying systems which are in terms of upper bounds on the perturbed transition rates and probabilities analytical expressions are derived for scalar systems which are straightforward to use numerical examples are presented to show the potential of the proposed techniques

fault detection for discrete time markov jump linear systems with partially known transition probabilities in this article the fault detection fd problem for a class of discrete time markov jump linear system mjls with partially known transition probabilities is investigated the proposed systems are more general which relax the traditional assumption in markov jump systems that all the transition probabilities must be completely known a residual generator is constructed and the corresponding fd is formulated as an h filtering problem by which the error between residual and fault are minimised in the h sense the linear matrix inequality based sufficient conditions for the existence of fd filter are derived a numerical example on a multiplier accelerator model economic system is given to illustrate the potential of the developed theoretical results

an efficient and accurate method to compute the fiedler vector based on householder deflation and inverse power iteration the fiedler vector of a graph plays a vital role in many applications but it is usually very expensive in that it involves the solution of an eigenvalue problem in this paper we introduce the inverse power method incorporated with the householder deflation to compute the fiedler vector in the inverse power iterations the coefficient matrix is formed implicitly to take advantage of the sparsity the linear systems encountered at each iteration must be symmetric positive definite thus the conjugate gradient method is used in addition preconditioning techniques are introduced to reduce the computation cost any kind of preconditioning techniques with dropping can be used for the graphs related to some of the sparse matrices downloaded from the uf sparse matrix collection the experiments are compared to the known novel schemes the results show that the provided method is more accurate while it is slower than mc73 sequentially it has good parallel efficiency compared with tracemin in addition it is insensitive to the selection of parameters which is superior to the other two methods

spectral clustering and its use in bioinformatics we formulate a discrete optimization problem that leads to a simple and informative derivation of a widely used class of spectral clustering algorithms regarding the algorithms as attempting to bi partition a weighted graph with n vertices our derivation indicates that they are inherently tuned to tolerate all partitions into two non empty sets independently of the cardinality of the two sets this approach also helps to explain the difference in behaviour observed between methods based on the unnormalized and normalized graph laplacian we also give a direct explanation of why laplacian eigenvectors beyond the fiedler vector may contain fine detail information of relevance to clustering we show numerical results on synthetic data to support the analysis further we provide examples where normalized and unnormalized spectral clustering is applied to microarray data here the graph summarizes similarity of gene activity across different tissue samples and accurate clustering of samples is a key task in bioinformatics