normalisers in limit groups let gamma be a limit group s subset gamma a non trivial subgroup and n the normaliser of s if h 1 s mathbb q has finite mathbb q dimension then s is finitely generated and either n s is finite or n is abelian this result has applications to the study of subdirect products of limit groups

subgroup separability in residually free groups we prove that the finitely presentable subgroups of residually free groups are separable and that the subgroups of type mathrm fp infty are virtual retracts we describe a uniform solution to the membership problem for finitely presentable subgroups of residually free groups

energy decay problems in the design of a point stabilizer for coupled string vibrating systems this paper solves completely the following problem posed by chen coleman and west siam j appl math 47 pp 751 780 when can we achieve the desirable uniform exponential decay property of the vibration energy for two coupled vibrating strings with a stabilizer or damper installed at the coupling point an approach using abstract semigroups is shown the paper proves the following for the cases when the stabilizers are symmetrically placed the system s energy does not decay to zero with respect to time for some initial states for all the other cases if the proportion of the wave speeds on the two vibrating strings c 2 c 1 is a rational number applying the formula of the growth order of a c 0 semigroup on a hilbgrt space derived by huang 2 proves that the semigroup satisfies the spectrum determined growth assumption so the uniform exponential decay property depends completely on the representative form of the ratio c 2 c 1 finally the paper proves that if

statistical analysis of tls based prony techniques abstract we present an analysis of parameter variance statistics for the tls prony method applied to damped exponential signals we derive the covariance matrix of the estimated parameters for this method the parameters include the magnitudes and angles of the poles and the magnitudes and angles of the amplitude coefficients we verify the theoretical results using monte carlo simulations studies we also compare the variance results to the corresponding cramer rao bounds for several cases

riesz basis property of evolution equations in hilbert spaces and application to a coupled string equation suppose that lambda n is the set of zeros of a sine type generating function of the exponential system e i lambda n t in l2 0 t and is separated levin and golovin s classical theorem claims that e i lambda n t forms a riesz basis for l2 0 t in this article we relate this result with riesz basis generation of eigenvectors of the system operator of the linear time invariant evolution equation in hilbert spaces through its spectrum a practically favorable necessary and sufficient condition for the separability of zeros of function of sine type is derived the result is applied to get riesz basis generation of a coupled string equation with joint dissipative feedback control

statistical analysis of music and subspace rotation estimates of sinusoidal frequencies consideration is given to the analysis of the large sample second order properties of multiple signal classification music and subspace rotation sur methods such as esprit for sinusoidal frequency estimation explicit expressions for the covariance elements of the estimation errors associated with either method are derived these expressions of covariances are then used to analyze and compare the statistical performances of the music and sur estimation sure methods both music and sure are based on the eigendecomposition of a sample data covariance matrix the expressions for the estimation error variances derived are used to study the dependence of music and sure performances on the dimension of the data covariance matrix used

the weak commutativity construction for lie algebras abstract we study the analogue of sidki s weak commutativity construction defined originally for groups in the category of lie algebras this is the quotient g of the lie algebra freely generated by two isomorphic copies g and g of a fixed lie algebra by the ideal generated by the brackets x x for all x we exhibit an abelian ideal of g whose associated quotient is a subdirect sum in g g g and we give conditions for this ideal to be finite dimensional we show that g has a subquotient that is isomorphic to the schur multiplier of g we prove that g is finitely presentable or of homological type f p 2 if and only if g has the same property but f is not of type f p 3 if f is a non abelian free lie algebra

fast orthogonalization algorithm and parallel architecture for ar spectral estimation based on forward backward linear prediction truncated qr methods have been shown to be comparable to svd based methods for the sinusoidal frequency estimation based on the forward backward linear prediction fblp model however without exploiting the special structure of the fblp matrix the qr decomposition qrd of the fblp matrix has a computational complexity on the order of 2 6m n n sup 2 3 o n sup 2 for a 2m n fblp matrix a fast algorithm to perform the qrd of the fblp matrix by exploiting its special toeplitz hankel form is proposed the computational complexity is reduced to 10n sup 2 4mn o n the fast algorithm can also be easily implemented by a linear systolic array reducing the number of time steps required to 2m 5n 4

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

finiteness properties of direct products of algebraic structures we consider the preservation of properties of being finitely generated being finitely presented and being residually finite under direct products in the context of different types of algebraic structures the structures considered include mal cev algebras including groups rings and other classical algebras as well as loops idempotent algebras including lattices semigroups and algebras in congruence modular varieties we aim to identify as broad classes as possible in which the expected preservation results a b a b satisfies property p p if and only if a and b satisfy p p hold and to exhibit ways in which they may fail outside those classes

thefpm conjecture for a class of metabelian groups abstract we prove that ifa g qis a short exact sequence of groups wheregis finitely generated aandqare abelian ais a2 torsion krull dimension one3q module via conjugation then thefpm conjecture holds in general ifgis of typefpmand either the extension is split orais4 torsion we show thataism tame as5q module

subspace multiuser detection for multicarrier ds cdma a subspace based linear minimum mean squared error mmse multiuser detection scheme is proposed for a multicarrier direct sequence code division multiple access mc ds cdma system typically a mc ds cdma system employs a band limited chip waveform the band limited nature of the chip waveform causes problem in applying standard subspace techniques because no nonnull noise subspace can be formed it is shown that channel and timing information needed for the construction of the linear mmse detector can be identified by a multiple signal classification like algorithm based on a finite length truncation approximation of the chip waveform in practice since perturbed versions of the subspaces assumed in the finite length truncation approximation are actually observed and because of the band limited property of the chip waveform the accuracy of the channel estimation and hence the performance of the mmse detector are degraded this effect is investigated in this paper

on subdirect products of free pro p groups and demushkin groups of infinite depth abstract we study subdirect products of free and demushkin pro p groups of depth developing theory similar to the abstract case see bridson et al 2002 4 furthermore we classify when a subdirect product has homological type fp m for some m 2 a problem still open for abstract groups for m 3

sinusoidal frequency estimation by signal subspace approximation an efficient fourier transform based method that avoids eigenvector computation is proposed for approximating the signal subspace the resulting signal subspace estimate can be used directly to define a music type frequency estimator or as a very good initial guess in context with adaptive or iterative eigenvector computation schemes at low signal to noise ratios the approximation yields better results than exact music it is also more robust than music against overestimating the number of sinusoids some variations of the basic method are briefly discussed

homological finiteness properties of lie algebras abstract we apply the main ideas behind the group theoretic methods developed in p h kropholler bull london math soc 25 1993 558 566 j pure appl math 90 1993 55 67 to study lie algebras of type fp we show that every soluble lie algebra of type fp is finite dimensional some refinements of this result when the algebra is abelian by finite dimensional and only type fp m is assumed are obtained it is also shown using the complete cohomology of vogel and mislin that for a wide class of lie algebras including all countable soluble ones fp implies finite cohomological dimension

on the finite presentation of subdirect products and the nature of residually free groups we establish it virtual surjection to pairs vsp as a general criterion for the finite presentability of subdirect products of groups if gamma 1 ldots gamma n are finitely presented and s we use the vsp criterion to characterize the finitely presented residually free groups we prove that the class of such groups is recursively enumerable we describe an algorithm that given a finite presentation of a residually free group constructs a canonical embedding into a direct product of finitely many limit groups we solve the multiple conjugacy problem and membership problem for finitely presentable subgroups of residually free groups we also prove that there is an algorithm that given a finite generating set for such a subgroup will construct a finite presentation new families of subdirect products of free groups are constructed including the first examples of finitely presented subgroups that are neither rm fp infty nor of stallings bieri type

stabilisation of an anti stable joint string with boundary disturbance in this paper we consider the boundary stabilisation for a one dimensional joint anti stable string equation with input disturbance entering the control end a backstepping transformation is used

estimation of multiple sinusoidal frequencies using truncated least squares methods to reduce the computational complexity of resolving closely spaced frequencies three truncated qr methods are proposed 1 truncated qr without column pivoting tqr 2 truncated qr with reordered columns tqrr and 3 truncated qr with column pivoting tqrp it is demonstrated that many of the benefits of the singular value decomposition based methods are achievable under the truncated qr methods with much lower computational cost based on the forward backward linear prediction model computer simulations and comparisons are provided for different truncation methods under various snrs comparisons of asymptotic performance for large data samples are also given

on weak commutativity in groups abstract for a group g we study homological and homotopical properties of the group g g g g g 1 for g g in particular we show that the operator preserves the soluble of type f p property

analysis of coefficient quantization errors in state space digital filters in this paper we examine the sensitivity of state space digital filters to coefficient quantization errors a cost function using an l p norm criteria is used to measure the deviation in frequency response of the filter the cost function is used to indicate the connection between roundoff noise and filter sensitivity to coefficient quantization errors then based on this cost function it is shown that low roundoff noise state space digital filters filters in balanced coordinates and filters based on polynomials orthogonal on the unit circle have low sensitivity to coefficient quantization errors furthermore the sensitivity of the filters is shown to depend on the second order modes thereby exhibiting certain robustness and immunity to filter bandwidth

weak commutativity and nilpotency abstract we continue the analysis of the weak commutativity construction for lie algebras this is the lie algebra g generated by two isomorphic copies g and g of a fixed lie algebra subject to the relations x x 0 for all x g in this article we study the ideal l l g generated by x x for all x g we obtain an infinite presentation for l as a lie algebra and we show that in general it cannot be reduced to a finite one with this in hand we study the question of nilpotency we show that if g is nilpotent of class c then g is nilpotent of class at most c 2 and this bound can improved to c 1 if g is 2 generated or if c is odd we also obtain concrete descriptions of l g and thus of g if g is free nilpotent of class 2 or 3 finally using methods of grobner shirshov bases we show that the abelian ideal r g g l g is infinite dimensional if g is free of rank at least 3

projected nonlinear least squares for exponential fitting the modern ability to collect vast quantities of data provides a challenge for parameter estimation when posed as a nonlinear least squares problem fitting a model to data the cost of each iterat

finite presentations for kahler groups with arbitrary finiteness properties abstract we construct the first explicit finite presentations for a family of kahler groups with arbitrary finiteness properties answering a question of suciu

on the zeros of the linear prediction error filter for deterministic signals the zeros of a linear prediction error filter polynomial for a class of deterministic signals that are a sum of samples of m exponentially damped undamped sinusoids is studied it is assumed that n samples are available for processing and that they are uncorrupted by noise it is shown that the exponent parameters of the m signals can be determined from m zeros called signal zeros of an lth degree prediction error filter polynomial l m if l lies in between m and n m n m 2 in a special case the rest of the l m zeros of the filter polynomial switch are called extraneous zeros are shown to be approximately uniformly distributed with in the unit circle regardless of the type of exponentials in the signal if the prediction filter coefficients are chosen to have minimum euclidean length the results obtained provide insight into the estimation problem with noisy data

exponential stability analysis of xa long chain of coupled vibrating strings with dissipative linkage consider a long chain of coupled vibrating strings where a stabilizer is installed at each internal node and perhaps also at a boundary point the exponential stability of the stabilizers arrangement for this large dynamic structure will be determined through a careful transformation of the coupled wave equations for this structure into an equivalent hyperbolic system and analysis of the eigendeterminant it will be proven that the energy of the system decays uniformly exponentially if there is a stabilizer installed at a boundary point if the stabilizers are installed only at internal nodes it will be proven that the energy may decay either uniformly exponentially or nonuniformly or may not decay at all depending on the different wave speeds and the stabilizers arrangement all possible outcomes have been classified

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

morse theory and finiteness properties of groups we examine the finiteness properties of certain subgroups of right angled artin groups in particular we find an example of a group that is of type fp z but is not finitely presented

simple and efficient nonparametric method for estimating the number of signals without eigendecomposition inspired by the computational simplicity and numerical stability of qr decomposition a nonparametric method for estimating the number of signals without eigendecomposition mense is proposed for the coherent narrowband signals impinging on a uniform linear array ula by exploiting the array geometry and its shift invariance property to decorrelate the coherency of signals through subarray averaging the number of signals is revealed in the rank of the qr upper trapezoidal factor of the autoproduct of a combined hankel matrix formed from the cross correlations between some sensor data since the infection of additive noise is defused signal detection capability is improved a new detection criterion is then formulated in terms of the row elements of the qr upper triangular factor when finite array data are available and the number of signals is determined as a value of the running index for which this ratio criterion is maximized where the qr decomposition with column pivoting is also used to improve detection performance the statistical analysis clarifies that the mense detection criterion is asymptotically consistent furthermore the proposed mense algorithm is robust against the array uncertainties including sensor gain and phase errors and mutual coupling and against the deviations from the spatial homogeneity of noise model the effectiveness of the mense is verified through numerical examples and the simulation results show that the mense is superior in detecting closely spaced signals with a small number of snapshots and or at relatively low signal to noise ratio snr

tensor powers of modules over finitely generated abelian groups in an earlier paper 11 the authors investigated as a major component of their final result a special case of the following question let r be a commutative ring with unity g a finitely generated abelian group and a4 a finitely generated rg module consider the tensor power m as an rg module via the diagonal action of g under what conditions is m a finitely generated rg module the answer obtained in 1 was for the case when r is a field and used an invariant z m introduced by the first author and strebel in 3 we briefly describe cl firstly if n is the torsion free rank of g we can identify hom g w with w defining two elements of hom g iw to be equivalent if they differ by a positive real multiple we obtain a natural projection of hom g w o onto the sphere s i denote the equivalence class of xe hom g 1w by x and define gcxi g ge g x g 30 then z is the subset of s consisting of all those x for which m is a finitely generated rg module and cl is the complement of c in s we say that m is k tame if there do not exist x i xk in zh such that x1 xk 0 then the partial answer referred to above theorem 3 4 of l is

the statistical performance of the music and the minimum norm algorithms in resolving plane waves in noise this paper presents an asymptotic statistical analysis of the null spectra of two eigen assisted methods music 1 and minimum norm 2 for resolving independent closely spaced plane waves in noise particular attention is paid to the average deviation of the null spectra from zero at the true angles of arrival for the plane waves these deviations are expressed as functions of signal to noise ratios number of array elements angular separation of emitters and the number of snapshots in the case of music an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise this result is validated by monte carlo simulations

sensitivity considerations in state space model based harmonic retrieval methods state space models are considered for estimating the frequencies of multiple sinusoids and robust coordinate systems for frequency estimation are identified it is shown that the ideal parameter set from a parameter sensitivity point of view involves estimating a unitary state transition matrix and then computing its eigenvalues to obtain an estimate of the frequencies procedures to estimate such matrices from covariance and time series data are examined it is shown that two state space methods the toeplitz approximation method and direct data approximation estimate robust state transition matrices

ascending chains of finitely generated subgroups abstract we show that a nonempty family of n generated subgroups of a pro p group has a maximal element this suggests that noetherian induction can be used to discover new features of finitely generated subgroups of pro p groups to demonstrate this we show that in various pro p groups e g free pro p groups nonsolvable demushkin groups the commensurator of a finitely generated subgroup h 1 is the greatest subgroup of containing h as an open subgroup we also show that an ascending chain of n generated subgroups of a limit group must terminate this extends the analogous result for free groups proved by takahasi higman and kapovich myasnikov

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

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

structure and finiteness properties of subdirect products of groups we investigate the structure of subdirect products of groups particularly their finiteness properties we pay special attention to the subdirect products of free groups surface groups and hnn extensions we prove that a finitely presented subdirect product of free and surface groups virtually contains a term of the lower central series of the direct product or else fails to intersect one of the direct summands this leads to a characterization of the finitely presented subgroups of the direct product of 3 free or surface groups and to a solution to the conjugacy problem for arbitrary finitely presented subgroups of direct products of surface groups we obtain a formula for the first homology of a subdirect product of two free groups and use it to show there is no algorithm to determine the first homology of a finitely generated subgroup a useful structure theory for subgroups of finite direct products of groups has yet to be developed to begin to study such subgroups it is natural to assume one knows about the subgroups of the direct factors and to concentrate on subdirect products recall that g is termed a subdirect product of the groups a1 an if g a1 an is a subgroup that projects surjectively to each factor work by various authors has exposed the surprisingly rich structure to be found amongst the subdirect products of superficially tame groups for example in contrast to the fact that subdirect products of abelian or nilpotent groups are again in the specified class nonabelian free groups harbour a great diversity of subdirect products including some with unsolvable decision problems 21 this diversity has long been known but it is only as a result of more recent work by baumslag roseblade 5 and bridson howie miller short 9 that it has been understood as a phenomenon that is intimately tied to the failure of various homological finiteness conditions from this background we pick out the three strains of thought to be developed in this article the subtlety of subdirect products in general 1991 mathematics subject classification 20f05 20e07 20f67 20j05 20f10

parameter estimation of exponentially damped sinusoids using a higher order correlation based approach a very common problem in signal processing is parameter estimation of exponentially damped sinusoids from a finite subset of noisy observations when the signal is contaminated with colored noise of unknown power spectral density a cumulant based approach provides an appropriate solution to this problem we propose a new class of estimator namely a covariance type estimator which reduces the deterministic errors associated with imperfect estimation of higher order correlations from finite data length this estimator allows a higher order correlation sequence to be modeled as a damped exponential model in certain slices of the moments plane this result shows a useful link with well known linear prediction based methods such as the minimum norm principal eigenvector method of kumaresan and tufts 1982 which can be subsequently applied to extracting frequencies and damping coefficients from the 1 d correlation sequence this paper discusses the slices allowed in the moments plane the uses and limitations of this estimator using multiple realizations and a single record in a noisy environment monte carlo simulations applied to standard examples are also performed and the results are compared with the kt method and the standard biased estimator based approach the comparison shows the effectiveness of the proposed estimator in terms of bias and mean square error when the signals are contaminated with additive gaussian noise and a single data record with short data length is available

subgroups of direct products of limit groups if ti tn are limit groups and s c t x x tn is of type fp q then s contains a subgroup of finite index that is itself a direct product of at most n limit groups this answers a question of sela

on self similar lie algebras and virtual endomorphisms we introduce the notion of virtual endomorphisms of lie algebras and use it as an approach for constructing self similarity of lie algebras this is done in particular for a class of metabelian lie algebras having homological type fp n which are lie algebra analogues of lamplighter groups we establish several criteria when the existence of virtual endomorphism implies a self similar lie structure furthermore we prove that the classical lie algebra sl n k where char k does not divide n affords non trivial faithful self similarity

stabilization of a 2 2 system of hyperbolic pdes with recirculation in the unactuated channel abstract a result by guo and jin 2010 considered boundary control of a string with point damping at the exact midpoint an interpretation of the model admits a system of first order hyperbolic transport pdes with actuation at the boundary of one pde the unactuated second pde exhibits recirculation phenomena the recirculation coupling of these two pdes gives rise to a stabilization problem with nonlocal terms that prior has not been considered in this paper we consider a general class of 2 2 hyperbolic pdes where both the unactuated pde and the actuated pde have strict feedback recirculation from the outlet in the upstream direction in addition the state of the unactuated pde feeds in a non local fashion into the domain of the actuated pde we introduce a novel set of transformations through which we arrive at a simple target system with desirable exponential stability characteristics a backstepping observer and output feedback controller design are also given for this 2 2 hyperbolic pde system we then apply our control design to the string and midway antidamper application found in guo and jin and illustrate the result with simulations

finitely presented metabelian restricted lie algebras abstract we classify the finitely presented restricted lie algebras among the finitely generated restricted lie algebras l that are split extension of abelian by abelian restricted lie algebras

fully residually free pro p groups abstract we prove that the pro p completion of the orientable surface group of genus d is residually free pro p if d is even or p 2 the case when p 2 odd d 1 is still open

perturbation analysis of an svd based linear prediction method for estimating the frequencies of multiple sinusoids a linear prediction approach is studied for estimating the frequencies of sinusoids in white noise it is shown that in the first step the continuity of the generalized inverse and the concept of angle between subspaces play an important role the continuity concept helps explain the need for a low rank approximation and the quality of the approximation is appraised by using the notion of angle between subspaces for the second step the sensitivity of the zeros of the predictor polynomial becomes an important consideration and is examined it is shown that increasing the order of the predictor polynomial and computing the minimum norm solution provides a mechanism to reduce parameter sensitivity

on conjugacy separability of fibre products in this paper we study conjugacy separability of subdirect products of two free or hyperbolic groups we establish necessary and sufficient criteria and apply them to fibre products to produce a finitely presented group g1 in which all finite index subgroups are conjugacy separable but which has an index 2 overgroup that is not conjugacy separable conversely we construct a finitely presented group g2 which has a non conjugacy separable subgroup of index 2 such that every finite index normal overgroup of g2 is conjugacy separable the normality of the overgroup is essential in the last example as such a group g2 will always possess an index 3 overgroup that is not conjugacy separable finally we characterize p conjugacy separable subdirect products of two free groups where p is a prime we show that fibre products provide a natural correspondence between residually finite p groups and p conjugacy separable subdirect products of two non abelian free groups as a consequence we deduce that the open question about the existence of an infinite finitely presented residually finite p group is equivalent to the question about the existence of a finitely generated p conjugacy separable full subdirect product of infinite index in the direct product of two free groups

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

krull dimension of solvable groups in this paper we prove that free solvable groups have finite krull dimension in fact this is true for much wider class of solvable groups termed rigid groups along the way we study the algebraic structure of the limit solvable groups fully residually free solvable groups

performance analysis of root music the authors analyze the performance of root music a variation of the music algorithm for estimating the direction of arrival doa of plane waves in white noise in the case of a linear equispaced sensor array the performance of the method is analyzed by examining the perturbation in the roots of the polynomial formed in the intermediate step of root music in particular asymptotic results for the mean squared error in the estimates of the direction of arrival are derived simplified expressions are presented for the one and two source case and compared to those obtained for least squares esprit computer simulations are also presented and they are in close agreement with the theory an important outcome of this analysis is the fact that the error in the signal zeros has a largely radial component this provides an explanation as to why the root music is superior to the spectral music algorithm

high snr asymptotics for signal subspace methods in sinusoidal frequency estimation high snr limit second order properties of multiple signal classification music minimum norm mn and subspace rotation sur signal subspace methods for sinusoidal frequency estimation are discussed an alternative to large sample analysis of the methods is presented the two most important variants of these methods are considered in connection with the choice of the sample covariance matrix the simpler technique follows the principle of a linear prediction and the more complex one is based on the idea of a forward backward prediction explicit expressions for the high snr covariance elements of the estimation errors associated with all the methods are derived the expressions for the covariances are used to analyze and compare the statistical performances of music mn and sur estimation methods in both of the variants to discuss the problem of the optimal dimension of the data covariance matrix and to study the limit statistical efficiency of the methods performances of the large sample and high snr asymptotics derived using monte carlo simulations are presented

optimal boundary control of one dimensional multi span vibrating systems a class of optimal control problems of one dimensional coupled vibrating systems with control applied at the coupled points is considered a maximum principle is developed for a class of such optimal problems governed by n linear hyperbolic partial differential equations of second order in time and fourth order in space with variable coefficients the maximum principle given involves a hamiltonian which contains an adjoint variable as well as an admissible boundary control function the proof of the maximum principle is given with the help of convexity arguments the uniqueness theory of the solution of the optimal control problem is given using convexity arguments

decision problems and profinite completions of groups abstract we consider pairs of finitely presented residually finite groups p for which the induced map of profinite completions p is an isomorphism we prove that there is no algorithm that given an arbitrary such pair can determine whether or not p is isomorphic to we construct pairs for which the conjugacy problem in can be solved in quadratic time but the conjugacy problem in p is unsolvable let j be the class of super perfect groups that have a compact classifying space and no proper subgroups of finite index we prove that there does not exist an algorithm that given a finite presentation of a group and a guarantee that j can determine whether or not 1 we construct a finitely presented acyclic group h and an integer k such that there is no algorithm that can determine which k generator subgroups of h are perfect

algebraic geometry over groups i algebraic sets and ideal theory abstract the object of this paper which is the first in a series of three is to lay the foundations of the theory of ideals and algebraic sets over groups

exponential stability of two strings under joint damping with variable coefficients abstract we study the stabilization of two vibrating strings with variable physical coefficients joined by a feedback control at a common endpoint and subject to non symmetrical boundary conditions we prove that this system is exponentially stable under sufficient conditions on the physical coefficients for this result we show that the system has a sequence of the generalized eigenvectors which forms a riesz basis with parentheses for the state hilbert space and as a consequence the spectrum determined growth condition holds

volume gradients and homology in towers of residually free groups we study the asymptotic growth of homology groups and the cellular volume of classifying spaces as one passes to normal subgroups g n g of increasing finite index in a fixed finitely generated group g assuming bigcap n g n 1 we focus in particular on finitely presented residually free groups calculating their ell 2 betti numbers rank gradient and asymptotic deficiency if g is a limit group and k is any field then for all j ge 1 the limit of dim h j g n k g g n as n rightarrow infty exists and is zero except for j 1 where it equals chi g we prove a homotopical version of this theorem in which the dimension of dim h j g n k is replaced by the minimal number of j cells in a k g n 1 this includes a calculation of the rank gradient and the asymptotic deficiency of g both the homological and homotopical versions are special cases of general results about the fundamental groups of graphs of slow groups we prove that if a residually free group g is of type mathrm fp m but not of type mathrm fp infty then there exists an exhausting filtration by normal subgroups of finite index g n so that lim n dim h j g n k g g n 0 hbox for j le m if g is of type mathrm fp infty then the limit exists in all dimensions and we calculate it

an explanation to the limitation observed in the kumaresan prony algorithm in this correspondence we explain the limitation of the kumaresan prony algorithm observed in 2 it is shown that the condition number of the matrix involved with the associated least squares problem periodically degrades condition number rightarrow infin making the least squares solution ill conditioned this ill conditioning causes a degradation in the estimates obtained by the kumaresan prony algorithm

optimality of high resolution array processing using the eigensystem approach in the classical approach to underwater passive listening the medium is sampled in a convenient number of look directions from which the signals are estimated in order to build an image of the noise field in contrast a modern trend is to consider the noise field as a global entity depending on few parameters to be estimated simultaneously in a gaussian context it is worthwhile to consider the application of likelihood methods in order to derive a detection test for the number of sources and estimators for their locations and spectral levels this paper aims to compute such estimators when the wavefront shapes are not assumed known a priori this justifies results previously found using the asymptotical properties of the eigenvalue eigenvector decomposition of the estimated spectral density matrix of the sensor signals they have led to a variety of high resolution array processing methods more specifically a covariance matrix test for equality of the smallest eigenvalues is presented for source detection for source localization a best fit method and a test of orthogonality between the smallest eigenvectors and the source vectors are discussed

linear prediction approach to direction estimation of cyclostationary signals in multipath environment we investigate the estimation of the directions of arrival doa of closely spaced narrowband cyclostationary signals in the presence of multipath propagation by exploiting the spatial and temporal properties of most communication signals we propose a new cyclic forward backward linear prediction fblp approach for coherent signals impinging on a uniform linear array ula in the proposed algorithm the evaluation of the cyclic array covariance matrix is avoided and the difficulty of choosing the optimal time lag parameter is alleviated as a result the proposed approach has two advantages 1 the computational load is relatively reduced and 2 the robustness of estimation is significantly improved the performance of the proposed approach is confirmed through numerical examples and it is shown that this approach is superior in resolving the closely spaced coherent signals with a small length of array data and at relatively low signal to noise ratio snr

on the accuracy of the kumaresan tufts method for estimating complex damped exponentials recently kumaresan and tufts kt presented a method for estimating the parameters of damped exponential waveforms in additive white noise the kt method uses singular value decomposition svd of the data matrix with truncation and backward prediction to improve the accuracy of the estimates the kt method was demonstrated to have a very good performance in comparison to traditional methods used for the same problem e g prony s method kumaresan and tufts also showed by numerical simulations that the variances of the estimates obtained by their method approaches the cramer rao lower bounds for selected test cases in this correspondence we provide a quantitative accuracy analysis of the kt method the analysis is based on first order taylor series approximations of the estimated parameters around their true values no assumptions are made on the number of data points used but it is assumed that the noise level is small enough for the first order approximations to be valid results of the analysis are illustrated by some numerical examples these results confirm the good performance of the kt method and show the effect of the user chosen parameters on the accuracy of the estimates

perturbation analysis of subspace based methods in estimating a damped complex exponential we present a study of mode variance statistics for three svd based estimation methods in the case of a single mode damped exponential the methods considered are namely kumaresan tufts matrix pencil and kung s direct data approximation through first order perturbation analysis we derive closed form expressions of the variance of the complex mode frequency and damping factor estimates these expressions are used to compare the different methods and to determine the optimal prediction order for matrix pencil and direct data approximation methods application to the undamped case shows the coherence of the results with those already stated in the literature it is also found that the variances converge linearly towards the cramer rao bound finally the theoretical results are verified using monte carlo simulations

brief paper arbitrary decay rate for two connected strings with joint anti damping by boundary output feedback in this paper we are concerned with the boundary stabilization of two connected strings with middle joint anti damping for which all eigenvalues of the control free system are located on the right complex plane we first design an explicit state feedback controller to achieve exponential stability for the closed loop system consequently we design the output feedback by using infinite dimensional observer the backstepping approach is adopted in investigation it is shown that by using one boundary stabilizer only the output feedback can make the closed loop system exponentially stable with arbitrary decay rate

mse based regularization approach to direction estimation of coherent narrowband signals using linear prediction this paper addresses the problem of directions of arrival doas estimation of coherent narrowband signals impinging on a uniform linear array ula when the number of signals is unknown by using an overdetermined linear prediction lp model with a subarray scheme the doas of coherent signals can be estimated from the zeros of the corresponding prediction polynomial although the corrected least squares cls technique can be used to improve the accuracy of the lp parameters estimated from the noisy array data the inversion of the resulting matrix in the cls estimation is ill conditioned and then the cls estimation becomes unstable to combat this numerical instability we introduce multiple regularization parameters into the cls estimation and show that determining the number of coherent signals is closely related to the truncation of the eigenvalues an analytical expression of the mean square error mse of the estimated lp parameters is derived and it is clarified that the number of signals can be determined by comparing the optimal regularization parameters with the corresponding eigenvalues an iterative regularization algorithm is developed for estimating directions without any a priori knowledge where the number of coherent signals and the noise variance are estimated from the noise corrupted received data simultaneously

pointwise stabilisation of a string with time delay in the observation abstractpointwise stabilisation is proposed in this paper for a string equation where the observation signal is subject to a time delay different from the boundary control the feedback stabiliser is acting at the middle joint of the string well posedness of the open loop system and solvability of the observer are shown first an observer system is then designed to estimate the state at the time interval when the observation is available and a predictor system is designed to predict the state at the time interval when the observation is not available pointwise output feedback controller is introduced to make the closed loop system asymptotically stable for the non smooth initial values and exponentially stable for the smooth initial values respectively simulation results demonstrate that the output feedback based on the observer and predictor effectively stabilises the pointwise control system with time delay