stallings foldings and subgroups of free groups we re cast in a more combinatorial and computational form the topological approach of j stallings to the study of subgroups of free groups

a homogeneous domination approach to state feedback of stochastic high order feedforward nonlinear systems this paper investigates stochastic high order feedforward nonlinear systems for the first time by introducing the homogeneous domination approach and solving several troublesome obstacles in the design and analysis procedure a state feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

global finite time stabilisation for a class of stochastic high order time varying nonlinear systems abstractin this paper the problem of global finite time stabilisation by state feedback is investigated for a class of stochastic high order nonlinear systems with time varying nonlinearities based on the generalised stochastic lyapunov theorem on finite time stability and by skillfully using the method of adding a power integrator a continuous state feedback controller is successfully constructed to guarantee that the closed loop system is globally finite time stable in probability finally several simulation examples are provided to illustrate the effectiveness of the proposed method

separable subsets of gferf negatively curved groups a word hyperbolic group g is called gferf if every quasiconvex subgroup coincides with the intersection of finite index subgroups containing it we show that in any such group the product of finitely many quasiconvex subgroups is closed in the profinite topology on g

brief paper sliding mode control for ito stochastic systems with markovian switching this paper deals with the problem of sliding mode control smc for a class of nonlinear uncertain stochastic systems with markovian switching by introducing some specified matrices the connections among the designed sliding surfaces corresponding to every mode are established furthermore the present sliding mode controller including the transition rates of modes can cope with the effect of markovian switching by means of linear matrix inequalities lmis with equality constraint sufficient conditions are derived such that the sliding motions on the specified sliding surfaces are stochastically stable with c disturbance attenuation level finally a numerical example is given to illustrate the applicability of the present method

adaptive fuzzy tracking control for stochastic nonlinear systems with unknown time varying delays an adaptive fuzzy controller is presented for a class of stochastic nonlinear systems an quadratic function is constructed to give the condition of the stability of systems the scheme guarantees the stability of closed loop system in the mean square sense the drawback of the quartic moment approach is overcome and the method is simplified this paper addresses the problem of adaptive tracking control for a class of stochastic strict feedback nonlinear time varying delays systems using fuzzy logic systems fls in this paper quadratic functions are used as lyapunov functions to analyze the stability of systems other than the fourth moment approach proposed by h deng and m krstic and the hyperbolic tangent functions are introduced to deal with the hessian terms this approach overcomes the drawback of the traditional quadratic moment approach and reduce the complexity of design procedure and controller based on the backstepping technique the appropriate lyapunov krasovskii functionals and the fls the adaptive fuzzy controller is well designed the proposed adaptive fuzzy controller guarantees that all the signals in the closed loop system are bounded in probability and the tracking error can converge to a small residual set around the origin in the mean square sense

adaptive controller design for tracking and disturbance attenuation in parametric strict feedback nonlinear systems the authors develop a systematic procedure for obtaining robust adaptive controllers that achieve asymptotic tracking and disturbance attenuation for a class of nonlinear systems which are described in the parametric strict feedback form and are subject to additional exogenous disturbance inputs their approach to adaptive control is performance based where the objective for the controller design is not only to find an adaptive controller but also to construct an appropriate cost functional compatible with desired asymptotic tracking and disturbance attenuation specifications with respect to which the adaptive controller is worst case optimal three main issues of the paper are the backstepping methodology worst case identification schemes and singular perturbations analysis closed form expressions have been obtained for an adaptive controller and the corresponding value function a numerical example involving a third order system is given

the equivalence between infinite horizon optimal control of stochastic systems with exponential of integral performance index and stochastic differential games a new method based on the theory of large deviations from the invariant measure is introduced for the analysis of stochastic systems with an infinite horizon exponential of integral performance index it is shown that the infinite horizon optimal exponential of integral stochastic control problem is equivalent to a stationary stochastic differential game for an auxiliary system as an application of the developed technique the infinite horizon risk sensitive lqg problem is analyzed for both the completely observed and partially observed case

model simplification and optimal control of stochastic singularly perturbed systems under exponentiated quadratic cost we study the optimal control of a general class of stochastic singularly perturbed linear systems with perfect and noisy state measurements under positively and negatively exponentiated quadratic cost the expected cost function to be minimized is actually taken as the long term time average of the logarithm of the expected value of an exponentiated quadratic loss we identify appropriate slow and fast subproblems obtain their optimum solutions compatible with the corresponding measurement structure and subsequently study the performances they achieve on the full order system as the singular perturbation parameter epsilon becomes sufficiently small with the expressions given in all cases being exact to within o sqrt epsilon it is shown that the composite controller obtained by appropriately combining the optimum slow and fast controllers achieves a performance level close to the optimal one whenever the full order problem has a solution the slow controller on the other hand achieves asymptotically as epsilon to 0 only a finite performance level but not necessarily optimal provided that the fast subsystem is open loop stable if the intensity of the noise in the system dynamics decreases to zero however the slow controller also achieves a performance level close to the optimal one the paper also presents a more direct derivation than heretofore available of the solution to the linear exponential quadratic gaussian leqg problem under noisy state measurements which allows for a general quadratic cost with cross terms in the exponent and correlation between system and measurement noises and obtains both necessary and sufficient conditions for existence of an optimal solution such a general leqg problem is encountered in the slow fast decomposition of the full order problem even if the original problem does not feature correlated noises in this general context the paper also establishes a complete equivalence between the leqg problem and the hi optimal control problem with measurement feedback though this equivalence does not extend to the slow and fast subproblems arrived at after time scale separation

brief paper inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable after considering the stabilization of a class of high order stochastic nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input in this brief paper we further address the problem of state feedback inverse optimal stabilization in probability i e our redesigned stabilizing backstepping controller is also optimal with respect to meaningful cost functionals

further results on global adaptive stabilisation for a class of uncertain stochastic nonlinear systems this paper considers the global adaptive stabilisation for a class of uncertain stochastic nonlinear systems comparing with the existing relevant literature the systems under investigation allow more serious unknowns uncertainties more importantly by remarkably reducing the dimension of dynamic compensator for system unknowns from n to 2 and considerably diminishing the overparametrisation in the existing literature this paper proposes an improved design scheme for adaptive state feedback controllers it is turned out that with the designed controller in loop all the closed loop system states are globally bounded and the original system states converge to the origin both in the sense of probability one a simulation example is also given to demonstrate the effectiveness of the theoretical results

on the profinite topology on negatively curved groups abstract let h and k be quasiconvex subgroups of a negatively curved locally extended residually finite lerf group g it is shown that if h is malnormal in g then the double coset kh is closed in the profinite topology of g in particular this is true if g is the fundamental group of an atoroidal lerf hyperbolic 3 manifold and h is the fundamental group of a totally geodesic boundary component of such manifold

robust h control for a class of nonlinear discrete time delay stochastic systems with missing measurements this paper is concerned with the problem of robust h output feedback control for a class of uncertain discrete time delayed nonlinear stochastic systems with missing measurements the parameter uncertainties enter into all the system matrices the time varying delay is unknown with given low and upper bounds the nonlinearities satisfy the sector conditions and the missing measurements are described by a binary switching sequence that obeys a conditional probability distribution the problem addressed is the design of an output feedback controller such that for all admissible uncertainties the resulting closed loop system is exponentially stable in the mean square for the zero disturbance input and also achieves a prescribed h performance level by using the lyapunov method and stochastic analysis techniques sufficient conditions are first derived to guarantee the existence of the desired controllers and then the controller parameters are characterized in terms of linear matrix inequalities lmis a numerical example is exploited to show the usefulness of the results obtained

global output feedback stabilization for a class of uncertain time varying nonlinear systems abstract this paper investigates the global output feedback stabilization for a class of uncertain time varying nonlinear systems the remarkable structure of the systems is the presence of uncertain control coefficients and unmeasured states dependent growth whose rate is inherently time varying and of unknown polynomial of output and consequently the systems have heavy nonlinearities serious uncertainties unknowns and serious time variations this forces us to explore a time varying plus adaptive methodology to realize the task of output feedback stabilization rather than a purely adaptive one detailedly based on a time varying observer and transformation an output feedback controller is designed by skillfully combining adaptive technique time varying technique and well known backstepping method it is shown that with the appropriate choice of the design parameters functions all the signals of the closed loop system are bounded and furthermore the original system states globally converge to zero it is worth mentioning that the heavy nonlinearities are compensated by an updating law while the serious unknowns and time variations are compensated by a time varying function the designed controller is still valid when the system has an additive input disturbance which essentially different from those studied previously may not be periodic or bounded by any known constant

finite time stabilization of stochastic high order nonlinear systems with ft siss inverse dynamics this paper aims to solve the finite time stabilization problem for stochastic high order nonlinear systems with stochastic inverse dynamics by characterizing unmeasured stochastic inverse dynamics with finite time stochastic input to state stability ft siss borrowing from some ideas of the lyapunov function sign function backstepping and ft siss methods and using stochastic finite time stability theory a new design and analysis method is given to guarantee global finite time stability in probability of the closed loop stochastic systems

on the structure of two generated hyperbolic groups we show that every two generated torsion free one ended word hyperbolic group has virtually cyclic outer automorphism group this is done by computing the jsj decomposition for two generator hyperbolic groups we further prove that two generated torsion free word hyperbolic groups are strongly accessible this means that they can be constructed from groups with no nontrivial cyclic splittings by applying finitely many free products with amalgamation and hnn extensions over cyclic subgroups

shrinkwrapping and the taming of hyperbolic 3 manifolds we introduce a new technique for finding cat 1 surfaces in hyperbolic 3 manifolds we use this to show that a complete hyperbolic 3 manifold with finitely generated fundamental group is geometrically and topologically tame

the equivalence of some residual properties of word hyperbolic groups abstract we show that every word hyperbolic group is residually finite if and only if every word hyperbolic group has a finite quotient

risk sensitive control and dynamic games for partially observed discrete time nonlinear systems solves a finite horizon partially observed risk sensitive stochastic optimal control problem for discrete time nonlinear systems and obtains small noise and small risk limits the small noise limit is interpreted as a deterministic partially observed dynamic game and new insights into the optimal solution of such game problems are obtained both the risk sensitive stochastic control problem and the deterministic dynamic game problem are solved using information states dynamic programming and associated separated policies a certainty equivalence principle is also discussed the authors results have implications for the nonlinear robust stabilization problem the small risk limit is a standard partially observed risk neutral stochastic optimal control problem

lyapunov like techniques for stochastic stability the purpose of this paper is to study the stabilizability problem for control stochastic nonlinear systems driven by a wiener process sufficient conditions for the existence of stabilizing feedback laws that are smooth except possibly at the equilibrium point of the system are provided by means of stochastic lyapunov like techniques the notion of dynamic asymptotic stability in probability of control stochastic differential systems is introduced and the stabilization by means of dynamic controllers is studied

stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function a more general class of stochastic non linear systems with unmodelled dynamics and uncertain non linear functions are considered in this paper with the concept of isps being extended to stochastic case by combining changing supply function technique with backstepping design technique an adaptive output feedback controller is proposed it is shown that all the solutions of the closed loop system are uniformly bounded in probability and the output can be regulated to an arbitrarily small neighbourhood of the origin in probability a simulation example demonstrates the control scheme

adaptive backstepping controller design using stochastic small gain theorem a more general class of stochastic nonlinear systems with unmodeled dynamics and uncertain nonlinear functions are considered in this paper with the concept of input to state practical stability isps and nonlinear small gain theorem being extended to stochastic case by combining stochastic small gain theorem with backstepping design technique an adaptive output feedback controller is proposed it is shown that the closed loop system is practically stable in probability a simulation example demonstrates the control scheme

robust h_ infty control for nonlinear stochastic systems a sliding mode approach this paper considers the sliding mode control for nonlinear stochastic systems modeled by ito stochastic differential equations it is noted that there exist state and exogenous disturbance dependent noise in the controlled systems by utilizing h infin disturbance attenuation technique a novel sliding mode control method is proposed such that the resultant system is asymptotically stable in probability with a prescribed h infin performance sufficient conditions for the solvability of these problems are derived via nonlinear hamilton jacobi hj type inequalities moreover it is shown that for a class of special nonlinear stochastic systems the h infin sliding mode control design can be obtained by solving linear matrix inequalities lmis finally a numerical simulation example is given

irreducible affine varieties over a free group i irreducibility of quadratic equations and nullstellensatz the object of this paper which consists of two parts is to describe irreducible varieties over free groups and to characterize finitely generated fully residually free groups we prove that any variety over a free group f can be defined by a finite number of systems of equations s 1 in triangular form where quadratic words play the role of leading terms algebraically irreducible varieties are exactly the varieties whose coordinate groups are fully residually f the crucial point of the classification of fully residually free groups is to prove that the coordinate groups of irreducible varieties are embeddable into lyndon s free z x group f since every finitely generated fully residually free group is a free factor of the coordinate group of an irreducible variety and the group f is fully residually f we obtain a characterization of finitely generated fully residually free groups as subgroups of f the group f and its subgroups have been studied extensively during the last several years in particular every finitely generated subgroup of f hence every finitely generated fully residually free group can be obtained from free abelian groups of finite rank by finitely many free products with amalgamation and hnn extensions of the type where amalgamated and associated subgroups are free abelian of finite rank in particular this implies that every finitely generated fully residually free group is finitely presented there are three parts to this paper algebraic geometry over free groups the theory of free exponential groups and makanin razborov s machinery to deal with equations over free groups 11 14 13 the algebraic geometry approach has been shown to be very usefull in dealing with equations over groups it provides necessary topological means and a method to transcribe geometric notions into pure group theoretic language following baumslag myasnikov remeslennikov 1 we use the standard algebraic geometry notions such as variety zariski topology irreducibility of varieties radicals and coordinate groups some of the ideas of the algebraic geometry approach go back to r lyndon 9 e rips j stallings 16

hilbert space compression for free products and hnn extensions abstract we investigate the behavior of equivariant and non equivariant hilbert space compression under group constructions given the equivariant or non equivariant hilbert space compression of two groups we find bounds on the compression of their free product we also investigate the case of hnn extensions of a group relative to a subgroup which is finite or of finite index

the residual finiteness of negatively curved polygons of finite groups a subgroup m g is almost malnormal provided that for each g g m the intersection m g m is finite it is proven that the free product of two virtually free groups amalgamating a finitely generated almost malnormal subgroup is residually finite a consequence of a generalization of this result is that an acute angled n gon of finite groups is residually finite if n 4 another consequence is that if g acts properly discontinuously and cocompactly on a 2 dimensional hyperbolic building whose chambers have acute angles and at least 4 sides then g is residually finite

robust fuzzy design for nonlinear uncertain stochastic systems via sliding mode control this paper deals with the sliding mode control smc problem for nonlinear stochastic time delay systems by means of fuzzy approach the takagi sugeno t s fuzzy stochastic time delay model with parametric uncertainties and unknown nonlinearities is presented a sufficient condition for the exponential stability in mean square of the sliding motion is also derived moreover it is shown that when the linear matrix inequalities lmis with equality constraint are feasible the designs of both sliding surface and sliding mode controller can be easily obtained via convex optimization a simulation example illustrating the proposed method is given

square nearly nonpositive sign pattern matrices abstract a sign pattern matrix a is called square nearly nonpositive if all entries but one of a 2 are nonpositive we characterize the irreducible sign pattern matrices that are square nearly nonpositive further we determine the maximum resp minimum number of negative entries that can occur in a 2 when a is irreducible square nearly nonpositive snnp and then we characterize the sign patterns that achieve this maximum resp minimum number finally we discuss some spectral properties of the sign patterns which are square nonpositive or square nearly nonpositive

bellman equations of risk sensitive control risk sensitive control problems are considered existence of a nonnegative solution to the bellman equation of risk sensitive control is shown the result is applied to prove that no breaking down occurs asymptotic behaviour of the nonnegative solution is studied in relation to ergodic control problems and the relationship between the asymptotics and the large deviation principle is noted

risk sensitive control on an infinite time horizon stochastic control problems on an infinite time horizon with exponential cost criteria are considered the donsker varadhan large deviation rate is used as a criterion to be optimized the optimum rate is characterized as the value of an associated stochastic differential game with an ergodic expected average cost per unit time cost criterion if we take a small noise limit a deterministic differential game with average cost per unit time cost criterion is obtained this differential game is related to robust control of nonlinear systems

rational subgroups of biautomatic groups centralizers of finite subsets in biautomatic groups are them selves biautomatic every polycyclic subgroup of a biautomatic group is abelian by finite

output feedback control of a class of high order stochastic nonlinear systems this article investigates the problem of output feedback stabilisation for a class of high order stochastic non linear systems in which the diffusion terms depend on unmeasurable states besides the output by introducing a new rescaling transformation adopting an effective observer and choosing the appropriate lyapunov function an output feedback controller is constructed to ensure that the equilibrium at the origin of the closed loop system is globally asymptotically stable in probability the output can be regulated to the origin almost surely and the problem of inverse optimal stabilisation in probability is solved the efficiency of the output feedback controller is demonstrated by several simulation examples

irreducible affine varieties over a free group ii systems in triangular quasi quadratic form and description of residually free groups abstract we shall prove the conjecture of myasnikov and remeslennikov 4 which states that a finitely generated group is fully residually free every finite set of nontrivial elements has nontrivial images under some homomorphism into a free group if and only if it is embeddable in the lyndon s exponential groupfz x which is thez x completion of the free group herez x is the ring of polynomials of one variable with integer coefficients historically lyndon s attempts to solve tarski s famous problem concerning the elementary equivalence of free groups of different ranks led him to introducefz x an free group is a groupgsuch that the class of formulas true ing is the same as the class of formulas true in a nonabelian free group a finitely generated group is free if and only if it is fully residually free 22 our result gives an algebraic description of free groups we shall give an algorithm to represent a solution set of an arbitrary system of equations overfas a union of finite number of irreducible components in the zariski topology onfn the solution set for every system is contained in the solution set of a finite number of systems in triangular form with quadratic words as leading terms the possibility of such a decomposition for a solution set was conjectured by razborov in 20 and also by rips we shall give a description of systems of equations determining irreducible components using methods developed in 13 19 it is possible to find some of these methods in 18 we are thankful to e rips for attracting our attention to these techniques

separating quasiconvex subgroups of right angled artin groups a graph group or right angled artin group is a group given by a presentation where the only relators are commutators of the generators a graph group presentation corresponds in a natural way to a simplicial graph with each generator corresponding to a vertex and each commutator relator corresponding to an edge suppose that g is a graph group whose corresponding graph is a tree and h is a subgroup of g we show that if h is quasiconvex with respect to either the word metric on g or the cat 0 metric on the universal cover of the standard complex for g then h is separable that is h is the intersection of finite index subgroups of g we also discuss some consequences relating to certain 3 manifold groups

kernel risk sensitive loss definition properties and application to robust adaptive filtering nonlinear similarity measures defined in kernel space such as correntropy can extract higher order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non gaussian signal processing and machine learning in this paper we propose a new similarity measure in kernel space called the kernel risk sensitive loss krsl and provide some important properties we apply the krsl to adaptive filtering and investigate the robustness and then develop the mkrsl algorithm and analyze the mean square convergence performance compared with correntropy the krsl can offer a more efficient performance surface thereby enabling a gradient based method to achieve faster convergence speed and higher accuracy while still maintaining the robustness to outliers theoretical analysis results and superior performance of the new algorithm are confirmed by simulation

some sign patterns that allow a real inverse pair b and b 1 abstract a sign pattern matrix is a matrix whose entries are from the set 0 for a real matrix b by sgn b we mean the sign pattern matrix in which each positive negative zero entry is replaced by 0 if a is an n by n sign pattern matrix then the sign pattern class of a is defined by q a b m n r sgn b a our purpose here is to investigate patterns that allow some b and b 1 to be in q a to this end we establish global necessary conditions we obtain necessary and sufficient conditions for certain classes of patterns and we provide several construction algorithms to obtain classes of patterns that have the inverse pair property

solvable groups with polynomial dehn functions given a finitely presented group h finitely generated subgroup b of h and a monomorphism b h we obtain an upper bound of the dehn function of the corresponding hnn extension g hh t j t i1 bt b i in terms of the dehn function of h and the distortion of b in g using such a bound we construct first examples of non polycyclic solvable groups with polynomial dehn functions the constructed groups are metabelian and contain the solvable baumslag solitar groups in particular this answers a question posed by birget ol shanskii rips and sapir

elementary theory of free non abelian groups we prove that any two non abelian free groups have the same elementary theory and that this theory is decidable these results solve two questions that were raised by tarski in 1945

practical output feedback risk sensitive control for stochastic nonlinear systems with stable zero dynamics this paper addresses the design problem of practical or satisfaction output feedback controls for stochastic strict feedback nonlinear systems in observer canonical form with stable zero dynamics under long term average tracking risk sensitive cost criteria the cost function adopted here is of the quadratic integral type usually encountered in practice rather than the quartic integral one used to avoid difficulty in control design and performance analysis of the closed loop system a sequence of coordinate diffeomorphisms is introduced to separate the zero dynamics from the entire system so that the transformed system has an appropriate form suitable for integrator backstepping design for any given risk sensitivity parameter and desired cost value by using the integrator backstepping methodology an output feedback control is constructively designed such that a the closed loop system is bounded in probability and b the long term average risk sensitive cost is upper bounded by the desired value in addition this paper does not require the uniform boundedness of the gain functions of the system noise furthermore an example is given to show the effectiveness of the theory

sign patterns of matrices and their inverses abstract we study the sign pattern relationship between a matrix and its inverse to do so we examine the graph whose vertices are the sign pattern matrices and whose edges connect those which are possible sign patterns of a matrix and its inverse we have bounds for the degree connectivity radius and diameter of this graph in addition we have the complete description for the 3 3 case

the word problem in the baumslag group with a non elementary dehn function is polynomial time decidable abstract we prove that the word problem in the baumslag group g 1 2 a b a a b a 2 which has a non elementary dehn function is decidable in polynomial time

on the bass lubotzky question about quotients of hyperbolic groups abstract we prove at theorem 1 that any non elementary hyperbolic group g possesses a non trivial finitely presented quotient q having no non trivial subgroups of finite indices the theorem was commissioned in august 1997 by h bass and a lubotzky because the statement was required to constructing of their counter examples to platonov s conjecture on the representation rigid linear groups bl theorem 2 gives three equivalent reformulations of the known problem on existence of non residually finite hyperbolic groups

mixed 3 manifolds are virtually special letm be a compact oriented irreducible 3 manifold which is neither a graph manifold nor a hyperbolic manifold we prove that 1m is virtually special

a novel alleviating fuzzy control algorithm for a class of nonlinear stochastic systems in pure feedback form abstract in this paper a novel alleviating computation adaptive fuzzy control scheme is presented for a class of uncertain stochastic nonlinear pure feedback systems different from the existing results that are based on traditional back stepping schemes as well as approximation technique of fuzzy logic systems flss for stochastic nonlinear systems this new approach assumes that the norm of optimal approximation parameter vector of flss is bounded by unknown parameter at each design step of this new approach fewer bounded adaptive parameters need to be adjusted thus this new approach can alleviate the online computation burden and improve the robust control performance meanwhile combining lyapunov theorem analysis it is proven that all the signals in the closed loop system are uniformly ultimately bounded uub and the tracking error can converge to a small neighborhood of zero the good performance of this approach is well demonstrated in a simulation example

the bianchi groups are separable on geometrically finite subgroups let d be a square free positive integer and od the ring of integers in q p id the main result of this paper is that the groups psl 2 od are

on the hyperbolicity of small cancellation groups and one relator groups in the article a result relating to maps finite planar connected and simply connected 2 complexes that satisfy a c p t it is shown that a finitely generated onerelator group g whose reduced relator r is of the form r at0at1 atn 1 where the words ti are distinct and have no occurrences of the letter a 1 is not hyperbolic if and only if one has in the free group that 1 n 2 and t0t 1 1 is a proper power 2 n 3 and for some i it is true with subscripts mod 3 that tit 1 i 1tit 1 i 2 1 3 n 4 and for some i it is true with subscripts mod 4 that tit 1 i 1ti 2t 1 i 3 1

output feedback control design for strict feedback stochastic nonlinear systems under a risk sensitive cost in this note we study the problem of output feedback control design for a class of strict feedback stochastic nonlinear systems under an infinite horizon risk sensitive cost criterion the controller designed can guarantee an arbitrary small long term average cost for arbitrary risk sensitivity parameter and achieve boundedness in probability for the closed loop system using the integrator backstepping methodology furthermore the controller preserves the equilibrium at the origin of the nonlinear system

how many negative entries can a2 have abstract a matrix whose entries are and 0 is called a sign pattern matrix we first characterize sign patterns a such that a 2 0 further we determine the maximum number of negative entries that can occur in a 2 whenever a 2 0 and then we characterize the sign patterns that achieve this maximum number next we find the maximum number of negative entries that can occur in the square of any sign pattern matrix and provide a class of sign patterns that achieve this maximum we also determine the maximum number of negative entries in the square of any real matrix finally we discuss the spectral properties of the sign patterns whose squares contain the maximum number of negative entries in the special case when a 2 0 and in the general case that includes any sign pattern

a combination theorem for special cube complexes we prove that certain compact cube complexes have special nite covers this means they have nite covers whose fundamental groups are quasiconvex subgroups of right angled artin groups as a result we obtain linearity and the separability of quasiconvex subgroups for the groups we consider our result applies in particular to a compact negatively curved cube complex whose hyperplanes do not self intersect for a cube complex with word hyperbolic fundamental group we show that it is virtually special if and only if its hyperplane stabilizers are separable in a nal application we show that the fundamental groups of every simple type uniform arithmetic hyperbolic manifolds are cubical and virtually special

backstepping controller design for nonlinear stochastic systems under a risk sensitive cost criterion this paper develops a methodology for recursive construction of optimal and near optimal controllers for strict feedback stochastic nonlinear systems under a risk sensitive cost function criterion the design procedure follows the integrator backstepping methodology and the controllers obtained guarantee any desired achievable level of long term average cost for a given risk sensitivity parameter theta furthermore they lead to closed loop system trajectories that are bounded in probability and in some cases asymptotically stable in the large these results also generalize to nonlinear systems with strongly stabilizable zero dynamics a numerical example included in the paper illustrates the analytical results

sign patterns that require repeated eigenvalues abstract motivated by the question of which sign patterns allow a diagonalizable matrix we relate a number of properties to that of requiring repeated eigenvalues these are then used to make several observations about sign patterns that allow diagonalizability the only barrier to diagonalizability is a required nontrivial jordan structure associated with zero we note that the question of sign patterns that require diagonalizability is also open

doubles of groups and hyperbolic lerf 3 manifolds we show that the quasiconvex subgroups in doubles of certain negatively curved groups are closed in the profinite topology this allows us to construct the first known large family of hyperbolic 3 manifolds such that any finitely generated subgroup of the fundamental group of any member of the family is closed in the profinite topology