the statistical distribution function of the q deformed harmonic oscillator by using the double time green function technique the authors derive explicitly the exact statistical distribution function of the q deformed harmonic oscillator and find that it is highly different from the usual bose and fermi functions for q not 1

direct method for yau filtering system with nonlinear observations for all known finite dimensional filters one always assumes that the observation terms be degree one polynomials however in practice the observation terms may be nonlinear e g tracking proble

mitter conjecture for low dimensional estimation algebras in non linear filtering it is well known that a systematical way to construct finite dimensional filter is to classify all finite dimensional estimation algebras mitter conjecture which states that all functions in any finite dimensional estimation algebra are necessarily degree one polynomial plays a crucial role in classifying all finite dimensional estimation algebras the purpose of this paper is to prove the mitter conjecture for estimation algebra of dimension at most 5 with arbitrary state space dimension dedicated to professor han fu chen on the occasion of his 70th birthday

a note on estimation algebras on nonlinear filtering theory abstract the idea of using estimation algebras to construct finite dimensional nonlinear filters was first proposed by brockett and mitter independently it turns out that the concept of estimation algebra plays a crucial role in the investigation of finite dimensional nonlinear filters in his talk at the international congress of mathematicians in 1983 brockett proposed to classify all finite dimensional estimation algebras in this paper we consider some filtering systems in a special filtering system 1 we have some structure results 2 for any arbitrary finite dimensional state space under the condition that the drift term is a linear vector field plus a gradient vector field we classify all finite dimensional estimation algebras with maximal rank 3 we classify all finite dimensional estimation algebras with maximal rank if the dimension of the state space is less than or equal to three a more general filtering system is considered the above three results can be used locally therefore from the algebraic point of view we have now understood generically some finite dimensional filters

on a necessary and sufficient condition for finite dimensionality of estimation ever since the technique of the kalman bucy filter was popularized there has been an intense interest in finding new classes of finite dimensional recursive filters in the late seventies the concept of the estimation algebra of a filtering system was introduced it has proven to be an invaluable tool in the study of nonlinear filtering problems in this paper a simple algebraic necessary and sufficient condition is established for an estimation algebra of a special class of filtering systems to be finite dimensional also presented is a rigorous proof of the wei norman program which allows one to construct finite dimensional recursive filters from finite dimensional estimation algebras

finite dimensional filters with nonlinear drift ii brockett s problem on classification of finite dimensional estimation algebras the idea of using estimation algebras to construct finite dimensional nonlinear filters was first proposed by brockett and mitter independently it turns out that the concept of estimation algebra plays a crucial role in the investigation of finite dimensional nonlinear filters in his talk at the international congress of mathematics in 1983 brockett proposed classifying all finite dimensional estimation algebras in this paper all finite dimensional algebras with maximal rank are classified if the dimension of the state space is less than or equal to two therefore from the lie algebraic point of view all finite dimensional filters are understood generically in the case where the dimension of state space is less than three

mitter conjecture and structure theorem for six dimensional estimation algebras the problem of classification of finite dimensional estimation algebras was formally proposed by brockett in his lecture at international congress of mathematicians in 1983 due to the difficulty of the problem in the early 1990s brockett suggested that one should understand the low dimensional estimation algebras first in this article we extend yau and his coauthors work of the mitter conjecture for low dimensional estimation algebras in nonlinear filtering problem and we apply the results to give classification of estimation algebras of dimension six

a comparison of simulated annealing cooling strategies using computer experiments on a simple three state system and an np complete system of permanents we compare different proposed simulated annealing schedules in order to find the cooling strategy which has the least total entropy production during the annealing process for given initial and final states and fixed number of iterations the schedules considered are constant thermodynamic speed exponential logarithmic and linear cooling schedules the constant thermodynamic speed schedule is shown to be the best we are actually considering two different schedules with constant thermodynamic speed the original one valid for near equilibrium processes and a version based on the natural timescale valid also at higher speeds the latter one delivers better results especially in case of fast cooling or when the system is far from equilibrium also with the lowest energy encountered during the entire optimization the best so far energy as the indicator of merit constant thermodynamic speed is superior finally we have compared two different estimators of the relaxation time one estimator is using the second largest eigenvalue of the thermalized form of the transition probability matrix and the other is using a simpler approximation for small deviations from equilibrium these two different expressions only agree at high temperatures

lie algebraic methods in optimal control of stochastic systems with exponential of integral cost abstract the purpose of this paper is to formulate and study the optimal control of partially observed stochastic systems with exponential of integral sample cost known as risk sensitive problems using lie algebraic tools this leads to the introduction of the sufficient statistic algebra l s through which one can determine a priori the maximum order of the controller when dim l s the construction of the control laws is addressed through extensions of the wei norman method as in nonlinear filtering problems aside from specific known finite dimensional examples which are studied in order to delineate the application of the lie algebraic tools new classes of finite dimensional controllers are identified as well in addition relations with minimax dynamic games are explored to best assess the importance and generality of the finite dimensional control systems

optimal filter reduction via a double projection a double projection is introduced to approximate a given digital filter by a reduced order filter so that the integral squared impulse response error between the two filters is minimized convergent algorithms are constructed for performing optimal order reduction

wei norman equations for a unitary evolution the wei norman technique allows one to express the solution of a system of linear non autonomous differential equations in terms of product of exponentials with time dependent exponents being solutions of a system of nonlinear differential equations we show that in the unitary case i e when the solution of the linear system is given by a unitary evolution operator the nonlinear system by an appropriate choice of ordering can be reduced to a hierarchy of matrix riccati equations to this end we consider a general linear non autonomous dynamical system on the special linear group the unitary case of particular significance for quantum optimal control problems is then obtained by restriction to anti hermitian generators we also point to the connections of the obtained results with the theory of the so called lie systems

new exact nonlinear filters with large lie algebras the ideas previously used stochastics vol 5 pp 65 92 1981 to construct some finite dimensional nonlinear filters also yield related new filters of finite dimension with arbitrarily large bases this is because the finite dimensionality is not destroyed by insertion of noiseless linear differential operations on the observations in engineering language the new filters are obtained from the old by smoothing the output through an n pole linear system before adding observation noise in the usual way this adds 2n to the lie algebra dimension in the simplest case drift tanh x observation x we put x through a one pole described by a new variable and observe noise instead of x noise the new lie algebra has additional generators and besides the four from the oscillator algebra to give dimension 6 the filter which gives a recursive construction of the conditional density can be derived by any of three here equivalent methods i direct integration of the kallianpur striebel formula as a gaussian integral ii solution of a parabolic pde with quadratic potential and iii the wei norman procedure

generalized commutators and deformation of strong coupling superconductivity we consider quantum deformation of a strong coupling superconductivity model based on creation annihilation operators which satisfy generalized commutator relations it is found that the nature of the superconducting phase transition can be changed from the usual second order to a first order transition if the deformation parameter exceeds a certain critical value metastable normal and superconducting states can exist when the transition is of the first order

comment on the q analogues of the harmonic oscillator the heisenberg relation for the q analogues of the quantum harmonic oscillator introduced independently by macfarlane and biedenharn 1989 for the quantum group su 2 q is derived by a method analogous to that used by schwinger 1968 for the su 2 case the author also speculates on the possible use of the quantum group as a generalisation of quantum mechanics

internal positivity preserved model reduction this article studies model reduction of continuous time stable positive linear systems under the hankel norm h norm and h 2 norm performance the reduced order systems preserve the stability as well as the positivity of the original systems this is achieved by developing new necessary and sufficient conditions of the model reduction performances in which the lyapunov matrices are decoupled with the system matrices in this way the positivity constraints in the reduced order model can be imposed in a natural way as the model reduction performances are expressed in linear matrix inequalities with equality constraints the desired reduced order positive models can be obtained by using the cone complementarity linearisation iterative algorithm a numerical example is presented to illustrate the effectiveness of the given methods

structure and classification theorems of finite dimensional exact estimation algebras estimation algebra turns out to be a crucial concept in the investigation of finite dimensional nonlinear filters in an earlier paper by the authors a necessary and sufficient algebraic condition was derived for an exact estimation algebra to be finite dimensional in this paper the investigation of the properties of finite dimensional exact estimation algebras is continued and some structure and partial classification theorems for such algebras are proved

hankel norm approximation of linear systems with time varying delay continuous and discrete cases this paper investigates the problem of hankel norm model reduction for linear systems with time varying delay in the state for a given stable system our attention is focused on the construction of reduced order model which guarantees the corresponding error system to be asymptotically stable and has a specified hankel norm error performance two different approaches are proposed to solve this problem one casts the model reduction into a convex optimization problem by using a linearization procedure and the other is based on the cone complementarity linearization idea which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints both continuous and discrete time cases are considered a numerical example is provided to show the effectiveness of the proposed theory

finite dimensional filters with nonlinear drift viii classification of finite dimensional estimation algebras of maximal rank with state space dimension 4 the idea of using estimation algebras to construct finite dimensional nonlinear filters was first proposed by brockett and mitter independently it turns out that the concept of estimation algebra plays a crucial role in the investigation of finite dimensional nonlinear filters in his talk at the international congress of mathematics in 1983 brockett proposed a classification of all finite dimensional estimation algebras chiou and yau classify all finite dimensional estimation algebras of maximal rank with dimension of the state space less than or equal to two in this paper we succeed in classifying all finite dimensional estimation algebras of maximal rank with state space dimension equal to three thus from the lie algebraic point of view we have now understood generically all finite dimensional filters with state space dimension less than four

classification of finite dimensional estimation algebras of maximal rank with arbitrary state space dimension and mitter conjecture in the late seventies the concept of the estimation algebra of a filtering system was introduced it was proven to be an invaluable tool in the study of non linear filtering problems in the early eighties brockett proposed to classify finite dimensional estimation algebras and mitter conjectured that all functions in finite dimensional estimation algebras are necessarily polynomials of total degree at most one despite the massive effort in understanding the finite dimensional estimation algebras the 20 year old problem of brockett and mitter conjecture remains open in this paper we give a classification of finite dimensional estimation algebras of maximal rank and solve the mitter conjecture affirmatively for finite dimensional estimation algebras of maximal rank in particular for an estimation algebra e of maximal rank we give a necessary and sufficient conditions for e to be finite dimensional in terms of the drift fi x and observation hj x as an important corollary we show that the numb

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

finite dimensional filters with non linear drift ix construction of finite dimensional estimation algebras of non maximal rank the idea of using estimation algebra to construct finite dimensional nonlinear filters was first proposed by brockett and mitter independently it has proven to be an invaluable tool in the study of nonlinear filtering problem in 1983 brockett proposed to classify all finite dimensional estimation algebras in this paper we give the construction of finite dimensional estimation algebras of non maximal rank these non maximal rank finite dimensional estimation algebras play an important role in brockett s classification problem

realizability of a model in infinite statistics following greenberg and others we study a space with a collection of operatorsa k satisfying the q mutator relations a l a k a l k l corresponding forq 1 to classical bose and fermi statistics we show that then n matrixa n q representing the scalar products ofn particle states is positive definite for alln ifq lies between 1 and 1 so that the commutator relations have a hilbert space representation in this case this has also been proved by fivel and by bozejko and speicher we also give an explicit factorization ofa n q as a product of matrices of the form 1 q jt 1 with 1 j n andt a permutation matrix in particular a n q is singular if and only ifq m 1 for some integerm of the formk 2 k 2 k n

optimal time weighted h 2 model reduction for markovian jump systems this article addresses the optimal time weighted h 2 model reduction problem for markovian jump linear systems that is for a given mean square stable markovian jump system our aim is to find a mean square stable jump system of lower order such that the time weighted h 2 norm of the corresponding error system is minimised the time weighted h 2 norm of the system is first defined and then a computational method is constructed the computation requires the solution of two sets of recursive lyapunov type linear matrix equations associated with the markovian jump system to solve the optimal time weighted h 2 model reduction problem we propose a gradient flow method for its solution a necessary condition for minimality is derived and a computational procedure is provided to obtain the minimising reduced order model the necessary condition generalises the standard result for systems when markov jumps and the time weighting term do not appear finally two numerical examples are given to demonstrate the

explicit wei norman formulae for matrix lie groups via putzer s method abstract the wei norman formula locally relates the magnus solution of a system of linear time varying odes with the solution expressed in terms of products of exponentials by means of a set of nonlinear differential equations in the parameters of the two types of solutions a closed form expression of such formula is proposed based on the use of putzer s method

on a new class of finite dimensional estimation algebras abstract we introduce a new class of solvable finite dimensional estimation algebras that contains both the linear and the benes cases the condition for finite dimensionality is expressed in terms of two matrices they play an important role in understanding the structure of estimation algebras

new classes of finite dimensional nonlinear filters abstract we derive sufficient conditions for the estimation algebras of two special classes of nonlinear estimation systems to be finite dimensional by carrying out the brockett wei norman program new classes of finite dimensional filters are obtained these systems can be regarded respectively as extensions of the kalman bucy filters and the benes filters

q fermionic operators and quantum exceptional algebras using a q deformation of the usual clifford algebra one constructs a realization of the quantum exceptional algebras e6 e7 e8 and f4 in terms of q fermionic operators

asymptotic expansions and lie algebras for some nonlinear filtering problems state estimation problems for systems involving small parameters are treated by both analytical and lie algebraic approximation techniques an asymptotic expansion for the unnormalized conditional density corresponding to the case of observations of a gauss markov process through a weak polynomial nonlinearity is computed and a convergence result is derived the expansion is related to certain approximations of the associated estimation lie algebra the convergence result is based on arguments used recently to prove existence and uniqueness and to estimate the tail behavior of solutions to nonlinear filtering problems with unbounded coefficients these arguments are in turn adapted from the analytical theory of parabolic pde s simulation results are presented to further assess the performance of the resulting approximate filters

the novel classes of finite dimensional filters with non maximal rank estimation algebra on state dimension four and rank of one ever since the technique of kalman bucy filter was popularised finding new classes of finite dimensional recursive filters has drawn much concern the idea of using estimation algebra to construct

q analogues of clifford and weyl algebras spinor and oscillator representations of quantum enveloping algebras we introduceq analogues of clifford and weyl algebras using these we construct spinor and oscillator representations of quantum enveloping algebras of typean 1 bn cn dn andan 1 1 also we discuss the irreducibility and the unitarity of these representations

relations for clebsch gordan and racah coefficients in suq 2 and yang baxter equations relations are exploited among clebsch gordan cg and racah coefficients in the algebra suq 2 known as a deformation of su 2 these are used to show that the yang baxter yb relation for the irf interaction round a face model results from one of the symmetry relations for the 9 j symbol specific to suq 2 and that in an asymptotic limit this yb relation becomes the yb relation for the two dimensional vertex model the racah coefficient which has a particularly simple dependence on q is efficiently used such that an asymptotic limit of the racah coefficient is the cg coefficient and another limit gives the factorized s matrix of the vertex model

structure theorem for five dimensional estimation algebras abstract the problem of classification of finite dimensional estimation algebras was formally proposed by brockett in his lecture at international congress of mathematicians in 1983 due to the difficulty of the problem in the early 1990s brockett suggested that one should understand the low dimensional estimation algebras first in this paper we give classification of estimation algebras of dimension at most five although the classification of finite dimensional estimation algebra of maximal rank was completed by yau and his coworkers chen chiou hu wong and wu the problem of classification of non maximal rank finite dimensional estimation algebra is still wide open except for the case of state space dimension 2 hopefully the result of this paper will shed some light on the non maximal rank estimation algebras

exploration of np hard enumeration problems by simulated annealing the spectrum values of permanents abstract the monte carlo optimisation technique simulated annealing has been used to sample the possible values of the permanent of fully indecomposable 0 1 matrices the basic idea in simulated annealing is that a markov chain explores the space of feasible solutions each of which has an associated energy here minus the permanent of the matrix the control parameter temperature is gradually reduced in order to focus the search on the low energy region of state space and eventually reaching the minimum although the minimum energy per se largest permanent is known the spectrum above the minimum is not so this importance sampling technique is quite efficient interest in permanents is based on the fact that it is complete for the class p of enumeration problems that is as hard as counting the number of accepting computations of any nondeterministic polynomial time turing machine the spectrum of possible values for the permanent of a 0 1 matrix with given topological dimension d is quite interesting but only partially understood the present work is an experimental study of this spectrum using the handle basis representation of directed graphs and simulated annealing to sample the possible values the results show that gaps exist in the spectrum of values of the permanent but also show the existence of values for d 8 and 9 not hitherto observed the new values in the spectrum of the permanent for d 8 is 72 and for d 9 are 119 132 136 138 and 140 further we found that the density of states grows exponentially with the permanent values the larger the value of the permanent the larger the number of neighbours and the larger the energy barriers between the permanent values of the neighbours

the many body problem for q oscillators the correct hamiltonian for the n body problem of free q oscillators is found which promotes the symmetries of the standard q 1 oscillator systems to q symmetries the spectrum of the system is found to be rich exhibiting interactions between the levels of the individual oscillators

complete classification of finite dimensional estimation algebras of maximal rank the idea of using estimation algebras to construct finite dimensional non linear filters was first proposed by brockett and clark and mitter independently in his famous talk at the international congress of mathematics in 1983 brockett proposed to classify all finite dimensional estimation algebras in this paper we explain why the theory of estimation algebras plays an important role in non linear filtering we show how to use the wei norman approach to construct finite dimensional filters from finite dimensional estimation algebras we survey some results in estimation algebras after 1984 we give a self contained proof of complete classification of finite dimensional estimation algebras of maximal rank in one place the proof given here is simpler than those proofs scattered in several papers this provides the readers with a complete coherent view of the important topic of the classification of finite dimensional estimation algebras

finite dimensional filters with nonlinear drift xi explicit solution of the generalized kolmogorov equation in brockett mitter program abstract ever since the technique of the kalman bucy filter was popularized there has been an intense interest in finding new classes of finite dimensional recursive filters in the late 1970s the concept of the estimation algebra of a filtering system was introduced brockett clark and mitter proposed to use the wei norman approach to solve the nonlinear filtering problem in 1990 tam wong and yau presented a rigorous proof of the brocket mitter program which allows one to construct finite dimensional recursive filters from finite dimensional estimation algebras later yau wrote down explicitly a system of ordinary differential equations and generalized kolmogorov equation to which the robust duncan mortenser zakai equation can be reduced thus there remains three fundamental problems in brockett mitter program the first is the problem of finding explicit solution to the generalized kolmogorov equation the second is the problem of finding real time solution of a system of odes the third is the brockett s problem of classification of finite dimensional estimation algebras in this paper we solve the first problem

projection properties of the l 2 optimal reduced order model the paper investigates the optimal l 2 reduced order model in the context of reduced order models obtained by projection it deals first with the general case of such systems and shows that the existence and uniqueness of a projection that relates two models of different orders can be inferred from the kronecker canonical form of a certain linear pencil combining the l 2 optimality conditions into that framework gives a different point of view on the optimal reduced order model it is shown that the zeros of the optimal approximation error transfer function are the mirror image of the reduced model poles with the same multiplicity in non square systems and doubled multiplicity in square systems the latter case enhances an existing result for siso systems that the multiplicity of the error zeros exceeds that of the optimal reduced model poles by one it is also shown that the optimal projection which is obtained in some solutions of the problem is discontinuous at the optimal solution if the reduced

theorems on the structure of finite dimensional estimation algebras abstract in this paper we proved several theorems concerning the structure of finite dimensional estimation algebras in particular under proper technical assumptions we proved the following 1 the observation of a filtering system must be linear if the estimation algebra is finite dimensional 2 all elements of a finite dimensional estimation algebra belong to a special class of polynomial differential operators 3 all finite dimensional estimation algebras are solvable

quantization of set theory and generalization of the fermion algebra the quantum states of a d dimensional fermion algebra are in one to one correspondence with the subsets of a d element universal set in this paper we use this set theoretical motivation to construct a one parameter deformation of the fermion algebra and extend it to a d dimensional generalization which is invariant under the group u d this discrete fermionic oscillator system is extended to the continuous case we also show that the q deformation of these systems is related to supercovariant q oscillators

finite dimensional filters with nonlinear drift vii mitter conjecture and structure of eta the concept of estimation algebra introduced independently by brockett and mitter has been playing a fundamental role in the investigation of finite dimensional nonlinear filters mitter conjectured that the observation terms h i x are polynomials of degree one if the corresponding estimation algebra is finite dimensional chiou leung and the present authors classify all finite dimensional estimation algebra of maximal rank with dimension of the state space less than or equal to three in this paper we prove the mitter conjecture for finite dimensional estimation algebra of maximal rank with arbitrary state space dimension in the course of our proof we show that the omega partial f j over partial x i partial f i over partial x j matrix where f denotes the drift term has special linear structure which generalizes our previous result in j chen and s s t yau textit math control signals systems 9 1996 to appear we also give a structure theorem for eta sum n i 1 partial f i over partial x i sum n i 1 f i 2 sum m i 1 h i 2

solution of filtering problem with nonlinear observations for all known finite dimensional filters one always needs the conditon that the observation terms are degree one polynomial on the other hand in many practical examples e g tracking problem the observation terms may be nonlinear our new method in this paper can treat filtering problems with nonlinear observation terms in the first time which includes kalman bucy filter as a special case

classification of estimation algebras with state dimension 2 this paper considers general finite dimensional estimation algebras associated with nonlinear filtering systems general considerations and approaches toward the classification of finite dimensional estimation algebras are proposed some structural results are obtained the properties of euler operator and the solutions to an underdetermined partial differential equation which inevitably arise in an estimation algebra are studied these tools and techniques are applied to the study of finite dimensional estimation algebras with state dimension 2 to obtain a complete classification result it is shown that a finite dimensional estimation algebra with state dimension 2 can only have dimension less than or equal to 6 moreover the mitter conjecture and the levine conjecture hold for finite dimensional estimation algebras with state dimension 2

nonexistence of finite dimensional filters for conditional statistics of the cubic sensor problem consider the cubic sensor dx dw dy x3dt dv where w v are two independent brownian motions given a function x of the state x let hat phi t left x right denote the conditional expection given the observations ys 0 s t this paper consists of a rather detailed discussion and outline of proof of the theorem that for nonconstant there can not exist a recursive finite dimensional filter for hat phi driven by the observations

on the q oscillator and the quantum algebra suq 1 1 the authors discuss some problems of the q deformed harmonic oscillator different q bosonisations of the quantum suq 1 1 algebra are given and the corresponding infinite dimensional representations of discrete series are analysed

real time solution of the nonlinear filtering problem without memory ii it is well known that the nonlinear filtering problem has important applications in both military and commercial industries the central problem of nonlinear filtering is to solve the duncan mortensen zakai dmz equation in real time and in a memoryless manner the purpose of this paper is to show that under very mild conditions which essentially say that the growth of the observation h is greater than the growth of the drift f the dmz equation admits a unique nonnegative weak solution u which can be approximated by a solution u r of the dmz equation on the ball b r with u r pat b r 0 the error of this approximation is bounded by a function of r which tends to zero as r goes to infinity the solution u r can in turn be approximated efficiently by an algorithm depending only on solving the observation independent kolmogorov equation on b r in theory our algorithm can solve basically all engineering problems in real time specifically we show that the solution obtained from ou

classification of four dimensional estimation algebras of central importance in nonlinear filtering theory is the classification of finite dimensional estimation algebras through which we can construct recursive filters we classify all t dimensional estimation algebras t spl les 4 for arbitrary state space dimension

brockett s problem of classification of finite dimensional estimation algebras for nonlinear filtering systems in his talk at the international congress of mathematicians in 1982 brockett proposed to classify all finite dimensional estimation algebras arising in nonlinear filters recently chen yau and leung siam j control optim 35 1997 pp 1132 1141 claimed that they had classified all finite dimensional estimation algebras of maximal rank when the dimension of the state space is less than or equal to four in this paper we introduce a series of completely new computations about the estimation algebra and we find two sets of new equations about the omega matrix as a consequence we can prove without any dimension assumption on the state space that the omega matrix is a constant matrix and thus we succeed in classifying all finite dimensional estimation algebras of maximal rank with the state space dimension being arbitrary

a q analogue of the supersymmetric oscillator and its q superalgebra a q analogue of the supersymmetric oscillator is constructed out of q boson and q fermion creation and annihilation operators for a fixed nb nf 2n where nb and nf are q boson and q fermion occupation numbers the irreducible representations of the q superalgebra generated by the q oscillator are 2n 1 dimensional particular cases when q is a root of or 1 are discussed a realization of the quantum group suq 2 is obtained using a pair of 1 fermion creation and annihilation operators

integrable representations of the ultra commutation relations we consider representations of the unital complex algebra generated by the identity and two elements and with and one relation the ultra commutation relations ucr in general we do not impose any commutation relation between and this is a very general scheme encompassing many important physical examples inter alia the ccr car q deformed bosons and fermions the representations of interest in physics have a diagonal number operator whose spectrum is contained in the positive integers together with some other technical conditions our principal result is that every representation in this class is completely determined up to unitary equivalence by the sequence of numbers n 1 n 1 n 2 for n 0 with 0 0 here n is the normalized eigenvector of corresponding to the eigenvalue n if the dimension of that eigenspace is 1 if the carrier hilbert space is infinite dimensional this representation is irreducible if and only if n 0 for n 1 finall

example of infinite statistics i give a second quantized example of infinite statistics in which any representation of the symmetric group can occur for identical particles and discuss the properties of the example

information states in stochastic control and filtering a lie algebraic theoretic approach the purpose of the paper is two fold i to introduce the sufficient statistic algebra which is responsible for propagating the sufficient statistics or information state in the optimal control of stochastic systems and ii to apply certain lie algebraic methods and gauge transformations widely used in nonlinear control theory and quantum physics to derive new results concerning finite dimensional controllers this enhances our understanding of the role played by the sufficient statistics the sufficient statistic algebra enables us to determine a priori whether there exist finite dimensional controllers it also enables us to classify all finite dimensional controllers relations to minimax dynamic games are delineated

comment on generalized commutators and deformation of strong coupling superconductivity for original paper see ibid vol 26 p 4827 1993 it is shown that a commonly used deformation of the fermionic canonical anticommutation relations is equivalent to the undeformed relations

a graph theoretic upper bound on the permanent of a nonnegative integer matrix i abstract let a be a fully indecomposable n n matrix with nonnegative integer entries then the permanent of a is bounded above by 1 min c i 1 r i 1 where c i and r i are the column and row sums of a the inequality results from a bound on the number of disjoint cycle unions in an associated multigraph this bound can improve via contractions

reply to comment on generalized commutators and deformation of strong coupling superconductivity by a solomon and r mcdermott for original paper see ibid vol 26 p 4827 1993 we reply to the comment by solomon and mcdermott see ibid vol 27 p 2619 1994 that the q deformed fermionic oscillator is equivalent to the usual fermionic quantum oscillator noting that our many body hamiltonian is truly a deformed model of strong coupling superconductivity

a counterexample of comments on stability margin evaluation for uncertain linear systems in the original paper c gong and s thompson ibid vol 39 p 548 50 1994 there is given what is claimed to be the tightest bound for all unstructured pertubations such that a specified system keeps its asymptotic stability j h su ibid vol 39 p 2523 4 1994 showed that it is not the tightest bound and gives another bound that bound is shown by a counterexample to be incorrect

finite dimensional estimation algebras with state dimension 3 and rank 2 mitter conjecture in this paper we study the structure of finite dimensional estimation algebras with state dimension 3 and rank 2 arising from a nonlinear filtering system by using the theories of the euler operat