low firing rates in a compartmental model neuron a nonlinear relationship is obtained between the membrane potential of a compartmental model neuron as a function of input stimulation this is used to show how shunting effects can lead to low output firing rates in associative memory networks

interval and linear matrix inequality techniques for reliable control of linear continuous time cooperative systems with applications to heat transfer lower and upper state bounds can be computed independently for cooperative ordinary differential equations odes with interval valued initial conditions then all reachable states are enclosed by

applications and generalizations of fisher hartwig asymptotics fisher hartwig asymptotics refers to the large n form of a class of toeplitz determinants with singular generating functions this class of toeplitz determinants occurs in the study of the spin spin correlations for the two dimensional ising model and the ground state density matrix of the impenetrable bose gas amongst other problems in mathematical physics we give a new application of the original fisher hartwig formula to the asymptotic decay of the ising correlations above tc while the study of the bose gas density matrix leads us to generalize the fisher hartwig formula to the asymptotic form of random matrix averages over the classical groups and the gaussian and laguerre unitary matrix ensembles another viewpoint of our generalizations is that they extend to hankel determinants the fisher hartwig asymptotic form known for toeplitz determinants

interval estimation for lpv systems applying high order sliding mode techniques in this paper the problem of design of interval observers for linear parameter varying lpv systems containing non detectable or non strongly observable parts is addressed firstly a high order sliding mode hosm method is applied to the strongly observable subsystem obtained by an appropriate change of coordinates to estimate the state and its derivative secondly this information is used to decrease the level of uncertainty in the rest of the system which leads to improvement of accuracy of the set membership estimates generated by an interval observer moreover it is shown that hosm techniques allows us to relax the applicability conditions of standard interval observer design methods the efficiency of the proposed approach is demonstrated through simulation examples

brief paper interval observer design for consistency checks of nonlinear continuous time systems this paper deals with fault detection for nonlinear continuous time systems a procedure based on interval analysis is proposed to build a guaranteed qlpv quasi linear parameter varying approximation of the nonlinear model the interval qlpv approximation makes it possible to derive two point observers which estimate respectively the lower and the upper bound of the state vector using cooperativity theory a set guaranteed to contain the actual value of the residual is then designed the modelling uncertainties and measurement errors are taken into account at the design stage the proposed methodology is illustrated through numerical simulations

dynamics of a compartmental model integrate and fire neuron with somatic potential reset abstract an integral equation approach to analysing the dynamics of a compartmental model integrate and fire neuron with partial reset is presented the neuron is taken to consist of a somatic compartment coupled to a single dendritic compartment only the former resets when the neuron fires the compartmental model equations are shown to reduce to a scalar volterra integral equation that takes into account the feedback between the reset region and the dendrites an iterative solution to the integral equation is constructed in the form of a second order nonlinear difference equation for the firing times in the case of constant inputs this becomes a first order equation in the inter spike intervals which has a unique fixed point that is globally asymptotically stable the corresponding steady state firing frequency of the neuron is determined as a function of the coupling between soma and dendrites finally the response of the two compartment model to oscillatory inputs is studied and in particular the firing times are shown to evolve according to a map of the cylinder

spillover stabilization in finite dimensional control and observer design for dissipative evolution equations we consider the problem of global stabilization of a semilinear dissipative evolution equation by finite dimensional control with finite dimensional outputs coupling between the system modes occurs directly through the nonlinearity and also through the control influence functions similar modal coupling occurs in the infinite dimensional error dynamics through the nonlinearity and measurements for both the control and observer designs rather than decompose the original system into fourier modes we consider lyapunov functions based on the infinite dimensional dynamics of the state and error systems respectively the inner product terms of the lyapunov derivative are decomposed into fourier modes upper bounds on the terms representing control and observation spillover are obtained linear quadratic regulator lqr designs are used to stabilize the state and error systems with these upper bounds relations between system and lqr design parameters are given to ensure global stability of the state and error dynamics with robustness with respect to control and observation spillover respectively it is shown that the control and observer designs can be combined to yield a globally stabilizing compensator the control and observer designs are numerically demonstrated on the problem of controlling stall in a model of axial compressors

general properties of solutions to inhomogeneous black scholes equations with discontinuous maturity payoffs abstract we provide representations of solutions to terminal value problems of inhomogeneous black scholes equations and study such general properties as min max estimates gradient estimates monotonicity and convexity of the solutions with respect to the stock price variable which are important for financial security pricing in particular we focus on finding representation of the gradient with respect to the stock price variable of solutions to the terminal value problems with discontinuous terminal payoffs or inhomogeneous terms such terminal value problems are often encountered in pricing problems of compound like options such as bermudan options or defaultable bonds with discrete default barrier default intensity and endogenous default recovery our results can be used in pricing real defaultable bonds under consideration of existence of discrete coupons or taxes on coupons

eigenvalues of hermitian toeplitz matrices with smooth simple loop symbols abstract the paper presents higher order asymptotic formulas for the eigenvalues of large hermitian toeplitz matrices with moderately smooth symbols which trace out a simple loop on the real line the formulas are established not only for the extreme eigenvalues but also for the inner eigenvalues the results extend and make more precise existing results which so far pertain to banded matrices or to matrices with infinitely differentiable symbols also given is a fixed point equation for the eigenvalues which may be solved numerically by an iteration method

toeplitz determinants with perturbations in the corners abstract the paper is devoted to exact and asymptotic formulas for the determinants of toeplitz matrices with perturbations by blocks of fixed size in the four corners if the norms of the inverses of the unperturbed matrices remain bounded as the matrix dimension goes to infinity then standard perturbation theory yields asymptotic expressions for the perturbed determinants this premise is not satisfied for matrices generated by so called fisher hartwig symbols in that case we establish formulas for pure single fisher hartwig singularities and for hermitian matrices induced by general fisher hartwig symbols

boundary observer design for hyperbolic pde ode cascade systems the paper presents an observer design for a class of hyperbolic pde ode cascade systems with a boundary measurement the cascade systems consist of coupled pdes featuring one rightward and one leftward convecting first order transport pdes and a set of odes which enter the pdes through the left boundary of the systems the design which is based on the volterra integral transformation relies only on a single sensor at the right boundary of the system the observer consists of a copy of the plant plus output injection terms both in the pdes and the odes the observer is constructed in a collocated setup which means both sensing and actuation are located at the same boundary the observer gains are computed analytically by solving goursat type pdes in terms of bessel function of the first kind the observer design is tested against a field scale flow loop test experiment in stavanger by statoil oil company the results show that the observer converges to the actual values and that the design can be used as a process monitoring tool in oil well drilling

compensating actuator and sensor dynamics governed by diffusion pdes for possibly unstable ode systems with actuator delay predictor based infinite dimensional feedback can compensate for actuator delay of arbitrary length and achieve stabilization we extend this concept to another class of pde ode cascades where the infinite dimensional part of the plant is of diffusive rather than convective type we derive predictor like feedback laws and observers with explicit gain kernels the gain kernels involve second order matrix exponentials of the system matrix of the ode plant which is the result of the second order in space character of the actuator sensor dynamics the construction of the kernel functions is performed using the continuum version of the backstepping method robustness to small perturbations in the diffusion coefficient is proved

random matrix theory and entanglement in quantum spin chains we compute the entropy of entanglement in the ground states of a general class of quantum spin chain hamiltonians those that are related to quadratic forms of fermi operators between the first n spins and the rest of the system in the limit of infinite total chain length we show that the entropy can be expressed in terms of averages over the classical compact groups and establish an explicit correspondence between the symmetries of a given hamiltonian and those characterizing the haar measure of the associated group these averages are either toeplitz determinants or determinants of combinations of toeplitz and hankel matrices recent generalizations of the fisher hartwig conjecture are used to compute the leading order asymptotics of the entropy as n this is shown to grow logarithmically with n the constant of proportionality is determined explicitly as is the next constant term in the asymptotic expansion the logarithmic growth of the entropy was previously predicted on the basis of numerical computations and conformal field theoretic calculations in these calculations the constant of proportionality was determined in terms of the central charge of the virasoro algebra our results therefore lead to an explicit formula for this charge we also show that the entropy is related to solutions of ordinary differential equations of painleve type in some cases these solutions can be evaluated to all orders using recurrence relations

robust interval observers and stabilization design for discrete time systems with input and output for a family of nonlinear discrete time systems with input output and uncertain terms a new interval observer is designed its main feature is that it is composed of two copies of classical observers this interval observer applies in the presence of unknown bounded nonlinear terms and additive disturbances and is used to achieve asymptotic stability through an appropriate choice of dynamic output feedback an illustrative example completes the presentation

the onsager formula the fisher hartwig conjecture and their influence on research into toeplitz operators this is not primarily a paper about applications of mathematics to statistical physics but rather a report on how a particular problem of statistical physics has resulted in an extensive mathematical theory the problem alluded to is the computation of the spontaneous magnetizationm o t of the two dimensional ising model with nearest neighbor interactions whose solution for temperaturest below the curie pointt c was given by the famous formula of lars onsager in 1948 the theory grown out of this formula is the edifice of toeplitz determinants matrices and operators

an estimator for a class of non linear distributed systems the on line estimation of unmeasured states in non linear distributed systems faces considerable computational and implementation difficulties in the present work an estimator is developed for a distributed system coupled through a highly non linear term the available secondary measurements and their time derivatives are used to preestimate the non linear function then the non linearity is regarded as a known time dependent forcing term the resulting estimation problem becomes linear with a significant reduction of the computational scheme the application of the method is illustrated with an example taken from the chemical industry a tubular chemical reactor

the fisher hartwig conjecture and toeplitz eigenvalues abstract the conjecture of fisher and hartwig published in 1968 describes the asymptotic expansion of toeplitz determinants with singular generating functions for more than twenty years progress was made in extending the validity of the conjecture but recent computer experiments led to counterexamples that show the limits of the original conjecture and pointed the way to a revised conjecture this paper describes the history of the problem several numerical examples and the revised conjecture

asymptotics of toeplitz determinants and the emptiness formation probability for the xy spin chain we study an asymptotic behaviour of a special correlator known as the emptiness formation probability efp for the one dimensional anisotropic xy spin 1 2 chain in a transverse magnetic field this correlator is essentially the probability of formation of a ferromagnetic string of length n in the antiferromagnetic ground state of the chain and plays an important role in the theory of integrable models for the xy spin chain the correlator can be expressed as the determinant of a toeplitz matrix and its asymptotical behaviours for n throughout the phase diagram are obtained using known theorems and conjectures on toeplitz determinants we find that the decay is exponential everywhere in the phase diagram of the xy model except on the critical lines i e where the spectrum is gapless in these cases a power law prefactor with a universal exponent arises in addition to an exponential or gaussian decay the latter gaussian behaviour holds on the critical line corresponding to the isotropic xy model while at the critical value of the magnetic field the efp decays exponentially at small anisotropy one has a crossover from the gaussian to the exponential behaviour we study this crossover using the bosonization approach

natural second order observers for second order distributed parameter systems the aim of this manuscript is to present an alternative method for designing state observers for second order distributed parameter systems without resorting to a first order formulation this method has the advantage of utilizing the algebraic structure that second order systems enjoy with the obvious computational savings in observer gain calculations the proposed scheme ensures that the derivative of the estimated position is indeed the estimate of the velocity component and to achieve such a result a parameter dependent lyapunov function was utilized to ensure the asymptotic convergence of the state estimation error

brief paper near optimal interval observers bundle for uncertain bioreactors in this paper we design an interval observer for the estimation of unmeasured variables of uncertain bioreactors the observer is based on a bounded error observer as proposed in lemesle v gouze j l 2005 hybrid bounded error observers for uncertain bioreactor models bioprocess and biosystems engineering 27 311 318 that makes use of a loose approximation of the bacterial kinetics we first show how to generate guaranteed upper and lower bounds on the state provided that known intervals for the initial condition and the uncertainties are available these so called framers depend on a tuning gain they can be run in parallel and the envelope provides the best estimate an optimality criterion is introduced leading to the definition of an optimal observer we show that this criterion provides directly a gain set containing the best framers the method is applied to the estimation of the total biomass of an industrial wastewater treatment plant demonstrating its efficiency

observers and initial state recovering for a class of hyperbolic systems via lyapunov method a b s t r a c t recently the problem of estimating the initial state of some linear infinite dimensional systems from measurements on a finite interval was solved by using the sequence of forward and backward observers ramdani tucsnak and weiss 2010 in the present paper we introduce a direct lyapunov approach to the problem and extend the results to the class of semilinear systems governed by wave and beam equations with boundary measurements from a finite interval we first design forward observers and derive linear matrix inequalities lmis for the exponential stability of the estimation errors further we obtain simple finite dimensional conditions in terms of lmis for an upper bound t on the minimal time that guarantees the convergence of the sequence of forward and backward observers on 0 t for the initial state recovering this t represents also an upper bound on the observability time for observation times bigger than t these lmis give upper bounds on the convergence rate of the iterative algorithm in the norm defined by the lyapunov functions in our approach t is found as the minimal dwelling time for the switched exponentially stable forward and backward estimation error systems with the different lyapunov functions liberzon 2003 the efficiency of the results is illustrated by numerical examples 2013 elsevier ltd all rights reserved

the fisher hartwig formula and entanglement entropy toeplitz matrices have applications to different problems of statistical mechanics recently it was used for calculation of entanglement entropy in spin chains in the paper we review these recent developments we use the fisher hartwig formula as well as the recent results concerning the asymptotics of the block toeplitz determinants to calculate entanglement entropy of large block of spins in the ground state of xy spin chain

null controllability and finite time stabilization for the heat equations with variable coefficients in space in one dimension via backstepping approach using the backstepping approach we recover the null controllability for the heat equations with variable coefficients in space in one dimension and prove that these equations can be stabilized in finite time by means of periodic time varying feedback laws to this end on the one hand we provide a new proof of the well posedness and the optimal bound with respect to damping constants for the solutions of the kernel equations this allows one to deal with variable coefficients even with a weak regularity of these coefficients on the other hand we establish the well posedness and estimates for the heat equations with a nonlocal boundary condition at one side

observer design for a class of nonlinear ode pde cascade systems abstract the problem of state observation is addressed for nonlinear systems that can be modeled by an ode pde series association the ode subsystem assumes a triangular structure while the pde element is of heat diffusion type the aim is to accurately estimate online the state vector of the ode subsystem and the distributed state of the pde element one major difficulty is that the state observation must only rely on the global system output i e the pde state at the terminal boundary in particular the connection point between the ode and the pde blocks is not accessible to measurements the observation problem is dealt with by designing a high gain type observer sufficient conditions involving the pde domain length are formally established that ensure the observer exponential convergence

on the extended luenberger type observer for semilinear distributed parameter systems the design of an extended luenberger observer is considered to solve the state observation problem for semilinear distributed parameter systems for this a backstepping based technique is proposed for the design of the output injection weights by making use of the extended linearization of the semilinear observer error system with respect to the observer state stability of both the linearized and the semilinear observer error dynamics is analyzed theoretically moreover an efficient sample and hold implementation is considered to improve the computational efficiency of the observer design simulation examples are provided for a bistable semilinear partial differential equation and the simplified model of a bioreactor with monod kinetics

average firing rate of a neural network with dynamical disorder we analyse the effects of time varying synaptic background activity on the steady state firing rate of a compartmental model neural network with shunting the background is taken to be a multi component dichotomous coloured noise process distributed randomly across the compartments of each neuron we exploit the formal similarity between the neural network model and a model of excitons moving on a lattice with random modulations of the local energy at each site in particular we use a dynamical coherent potential approximation and the method of partial cumulants to evaluate the single neuron green s function averaged over the stochastic background this is then used to determine the firing rate it is found that the firing rate increases with the variance and correlation time of the coloured noise process

robust nonlinear state estimation for a class of infinite dimensional systems using reduced order models a methodology for designing robust low order observers for a class of spectral infinite dimensional nonlinear systems is presented this approach uses the low dimensional subspace explicitly in th

pointwise exponential stabilization of a linear parabolic pde system using non collocated pointwise observation this paper deals with the problem of exponential stabilization for a linear distributed parameter system dps using pointwise control and non collocated pointwise observation where the system is modeled by a parabolic partial differential equation pde the main objective of this paper is to construct an output feedback controller for pointwise exponential stabilization of the linear parabolic pde system using the non collocated pointwise observation the observer based output feedback control technique is utilized to overcome the design difficulty caused by the non collocation pointwise observation we construct a luenberger type pde state observer to exponentially track the state of the pde system a collocated pointwise feedback controller is proposed based on the estimated state a variation of poincare wirtinger inequality is derived and the spatial domain is decomposed into multiple sub domains according to the number of the actuators and sensors by using lyapunov s direct method integration by parts and the variation of poincare wirtinger inequality at each sub domain sufficient conditions for the existence of the observer based out feedback controller are developed such that the resulting closed loop system is exponentially stable and presented in terms of standard linear matrix inequalities lmis furthermore the closed loop well posedness analysis is also provided by the semigroup approach extensive numerical simulation results are presented to show the performance of the proposed output feedback controller

interval methods and contractor based branch and bound procedures for verified parameter identification of quasi linear cooperative system models abstract a large number of dynamic system models in engineering as well as computational physics chemistry or biology are described after first principle modeling approaches by sets of either discrete time difference equations or by sets of ordinary differential equations in both cases the structure of those system models results from fundamental physical system properties such as conservation laws of mass momentum and energy newton s or kirchhoff s laws as well as a structural subdivision into subsystems or individual compartments regardless of the area of application all of these system models involve parameters which are not perfectly known due to uncertainty resulting from tolerances in the construction of the respective real life systems or which are described by an inherent uncertainty coming from model simplifications or even from a lack of knowledge about detailed microscopic dynamic effects this is especially true for applications in engineering where a trade off between the model accuracy and the resulting computational complexity has to be made in order to obtain mathematical representations which can be evaluated numerically in real time this real time applicability is inevitable if tasks such as feedback control or model based state estimation on the basis of incomplete state measurements are of interest hence all aforementioned tasks depend on the reliable estimation of those parameters of the structurally predefined sets of state equations which are feasible with respect to the knowledge about selected measurable state variables under consideration of the associated measurement tolerances this paper presents computational techniques for a model based identification of system parameters under the a priori knowledge of stability of the underlying open loop dynamics and the structural constraint of cooperativity

design of interval observers and controls for pdes using finite element approximations synthesis of interval state estimators is investigated for the systems described by a class of parabolic partial differential equations pdes first a finite element approximation of a pde is constructed and the design of an interval observer for the derived ordinary differential equation is given second the interval inclusion of the state function of the pde is calculated using the error estimates of the finite element approximation finally the obtained interval estimates are used to design a dynamic output stabilizing control the results are illustrated by numerical experiments with an academic example and the black scholes model of financial market

approximate singular values of the fractional difference and summation operators abstract we obtain sharp bounds on the singular values of the fractional difference and summation operators on r n these bounds allow us to establish that the convergence rates of the distributions of the singular values of these operators are o 1 n since the fractional difference operator of order is associated with the toeplitz matrix with fisher hartwig symbol 2 2 cos u 0 we are able to obtain similar bounds on the eigenvalues of this toeplitz matrix and a similar result on the convergence rate of the distribution of its eigenvalues

toeplitz determinants with one fisher hartwig singularity letcbe a function defined on the unit circle with fourier coefficients cn n the fisher hartwig conjecture describes the asymptotic behaviour of the determinants of then ntoeplitz matricesdn c det ci j n 1i j 0for a certain class of functionsc in this paper we prove this conjecture in the case of functions with one singularity more precisely we consider functions of the formc ei b ei t ei 1 u ei 1 heret ei exp i 0 2 is a function with a jump discontinuity u ei 2 2 cos is a function which may have a zero a pole or a discontinuity of oscillating type andbis a sufficiently smooth nonvanishing function with winding number equal to zero the only restriction we impose on the parameters is that 2 is required not to be a negative integer in the case where re 1 2 i e where the corresponding functioncis not integrable we identifycin an appropriate way with a distribution

interval state estimation for a class of nonlinear systems the goal of this technical note is to design interval observers for a class of nonlinear continuous time systems the first part of this work shows that it is usually possible to design an interval observer for linear systems by means of linear time invariant changes of coordinates even if the system is not cooperative this result is extended to a class of nonlinear systems using partial exact linearisations the proposed observers guarantee to enclose the set of system states that is consistent with the model the disturbances and the measurement noise moreover it is only assumed that the measurement noise and the disturbances are bounded without any additional information such as stationarity uncorrelation or type of distribution the proposed observer is illustrated through numerical simulations

interval observer design and control of uncertain non homogeneous heat equations the problems of state estimation and observer based control for heat non homogeneous equations under distributed in space point measurements are considered first an interval observer is designed in the form of partial differential equations pdes without galerkin projection second conditions of boundedness of the interval observer solutions with non zero boundary conditions and measurement noise are proposed third the obtained interval estimates are used to design a dynamic output feedback stabilizing controller the advantages of the pde based interval observer over the approximation based one are clearly shown in the numerical example

a green s function approach to analysing the effects of random synaptic background activity in a model neural network the effect of randomly distributed synaptic background activity on the states of self sustained firing in a model neural network with shunting is investigated using mean field theory the steady state of the network is expressed in terms of an ensemble averaged single neuron green s function this green s function is shown to satisfy a matrix equation identical in form to that found in the tight binding alloy model of excitations on a one dimensional disordered lattice the ensemble averaging is then performed using a coherent potential approximation thus allowing the steady state firing rate of the network to be determined the firing rate is found to decrease as the mean level of background activity across the network is increased a uniform background zero variance leads to a greater reduction than a randomly distributed one non zero variance

a new correlator in quantum spin chains we propose a new correlator in one dimensional quantum spin chains the s emptiness formation probability s efp this is a generalization of the emptiness formation probability efp which is the probability that the first n spins of the chain are all aligned downwards in the s efp we let the spins in question be separated by s sites the usual efp corresponds to the special case when s 1 taking s 1 allows us to quantify non local correlations we express the s efp for the anisotropic xy model in a transverse magnetic field a system with both critical and non critical regimes in terms of a toeplitz determinant for the isotropic xy model we find that the magnetic field induces an interesting length scale

interval observers for continuous time lpv systems with l 1 l 2 performance an approach to interval observer design for linear parameter varying lpv systems is proposed it is assumed that the vector of scheduling parameters in lpv models is not available for measurement two different interval observers are constructed for nonnegative systems and for a generic case stability conditions are expressed in terms of matrix inequalities which can be solved with respect to the observer gains using standard numerical solvers applying l 1 l 2 framework the robustness and estimation accuracy with respect to model uncertainty are analyzed the efficiency of interval estimation for lpv models is demonstrated through numerical experiments for a microfluidic system and an academic example

the fisher hartwig conjecture and generalizations abstract we discuss the status of the fisher hartwig conjecture concerning the asymptotic expansion of a class of toeplitz determinants with singular generating functions a counterexample is given for a nonrational generating function and we formulate a generalized fisher hartwig conjecture

toeplitz matrices and determinants with fisher hartwig symbols abstract this paper is concerned with toeplitz matrices generated by symbols of the form a t r 1 r t t r 2 r t t r r b t t 1 where t 1 t r are pairwise distinct points on the unit circle b is sufficiently smooth b t 0 t 1 and ind b 0 t t r r is defined as exp i r arg t t r with arg t t r and r r are complex numbers satisfying re r 1 2 re r 1 2 weighted hardy spaces l 2 1 and l 2 2 are defined such that the toeplitz operator t a l 2 1 l 2 2 is bounded and invertible and that the finite section method is applicable to t a considered as acting from l 2 1 onto l 2 2 these results are then applied to prove a conjecture of fisher and hartwig adv in chem phys 15 1968 333 353 which asserts that the determinants of the n n sections of t a are asymptotically equal to g b n n q e a n where q r 2 r 2 and g b e a are certain nonzero constants under quite general conditions on the smoothness of b these constants are completely identified

second order observers for second order distributed parameter systems in r2 this note addresses observer design for second order distributed parameter systems in r2 particularly second order distributed parameter systems without distributed damping are studied based on finite number of measurements exponentially stable observer is designed the existence uniqueness and stability of solutions of the observers are based on semigroup theory

some results on complex toeplitz eigenvalues we consider the asymptotics of the eigenvalues of toeplitz matrices generated by a complex valued symbol f which is essentially bounded we prove that if the essential range of f has empty interior and does not separate the complex plane then the corresponding toeplitz eigenvalues have the canonical distribution in the sense of widom the assumptions on the symbol only concern the topological structure of its essential range and are completely independent of its smoothness properties we also prove some clustering properties of eigenvalues and some new distribution results

emergence of a singularity for toeplitz determinants and painleve v we obtain asymptotic expansions for toeplitz determinants corresponding to a family of symbols depending on a parameter t for t positive the symbols are regular so that the determinants obey szeg s strong limit theorem if t 0 the symbol possesses a fisher hartwig singularity letting t 0 we analyze the emergence of a fisher hartwig singularity and a transition between the two different types of asymptotic behavior for toeplitz determinants this transition is described by a special painleve v transcendent a particular case of our result complements the classical description of wu mccoy tracy and barouch of the behavior of a 2 spin correlation function for a large distance between spins in the two dimensional ising model as the phase transition occurs

backstepping observers for a class of parabolic pdes in this paper we design exponentially convergent observers for a class of parabolic partial integro differential equations p i des with only boundary sensing available the problem is posed as a problem of designing an invertible coordinate transformation of the observer error system into an exponentially stable target system observer gain output injection function is shown to satisfy a well posed hyperbolic pde that is closely related to the hyperbolic pde governing backstepping control gain for the state feedback problem for several physically relevant problems the observer gains are obtained in closed form the observer gains are then used for an output feedback design in both collocated and anti collocated setting of sensor and actuator the order of the resulting compensator can be substantially lowered without affecting stability explicit solutions of a closed loop system are found in particular cases

technical communique nonlinear bounded error state estimation of continuous time systems this paper presents a first study on the application of interval analysis and consistency techniques to state estimation of continuous time systems described by nonlinear ordinary differential equations the approach is presented in a bounded error context and the resulting methodology is illustrated by an example

toeplitz and wiener hopf determinants with piecewise continuous symbols abstract the asymptotics for determinants of toeplitz and wiener hopf operators with piecewise continuous symbols are obtained in this paper if w is the wiener hopf operator defined on l2 0 with piecewise continuous symbol having a finite number of discontinuities at r then under appropriate conditions it is shown that det w g r2k where g exp log 0 r 1 2 log r r and k is a completely determined constant an analogous result is obtained for toeplitz operators the main point of the paper is to obtain a result in the wiener hopf case since the toeplitz case had been treated earlier in the toeplitz case it was discovered that one could obtain asymptotics fairly easily for symbols with several singularities if for each singularity one could find a single example of a symbol with a singularity of that kind whose associated asymptotics were known fortunately in the toeplitz case such asymptotics were known the difficulty in the wiener hopf case is that there was not a single singular case where the determinant was explicitly known this problem was overcome by using the fact that wiener hopf determinants when discretized become toeplitz determinants whose entries depend on the size of the matrix no theorem on toeplitz matrices can be applied directly but these theorems are modified to obtain the desired results

thin structure of eigenvalue clusters for non hermitian toeplitz matrices in contrast to the hermitian case the unfair behavior of non hermitian toeplitz eigenvalues is still to be unravelled we propose a general technique for this which reveals the eigenvalue clusters for symbols from l moreover we study a thin structure of those clusters in the terms of properly defined subclusters in some cases this leads to as much as the szego like formulas