discrete laguerre gaussian transforms and their applications laguerre gaussian functions serve as a complete and orthonormal basis for a variety of physical problems such as 2d isotropic quantum harmonic oscillators and circularly symmetric laser modes in this paper we propose discrete laguerre gaussian functions which are defined such that some elegant physical properties are preserved and a fast computation algorithm of complexity o n log n is available discrete laguerre gaussian transforms as introduced in this paper inherit nice properties from discrete laguerre gaussian functions and admit signal analysis over circularly symmetric patterns it is demonstrated through examples that discrete laguerre gaussian transforms find applications in circular pattern keypoints selection object detection image compression rotational invariance feature for pattern recognition and rotational angle estimation

combinatorial approach to generalized bell and stirling numbers and boson normal ordering problem we consider the numbers arising in the problem of normal ordering of expressions in boson creation a and annihilation a operators a a 1 we treat a general form of a boson string a rnasn a r2as2 a r1as1 which is shown to be associated with generalizations of stirling and bell numbers the recurrence relations and closed form expressions dobinski type formulas are obtained for these quantities by both algebraic and combinatorial methods by extensive use of methods of combinatorial analysis we prove the equivalence of the aforementioned problem to the enumeration of special families of graphs this link provides a combinatorial interpretation of the numbers arising in this normal ordering problem

an extension of pointwise circumscription abstract in this paper we generalize lifschitz s pointwise circumscription ander the first order framework the generalized version has the ability for simultaneously minimizing several predicates at finitely many pinpoints in a pointwise manner we show that if an anderlying first order theory is almost existential then the extended pointwise circumscription is complete with respect to minimal model semantics almost existential formulas are in the dual form of almost universal formulas which was proposed by lifschitz to investigate the satisfiability of circumscription this completeness result is a generalization of the result by kolaitis and papadimitriou who regarded the case of existential formulas we also give a partial answer to the question for exponential growth of the size of first order formulas equivalent to circumscription moreover we clarify that lifschitz s pointwise circumscription is complete in a slightly wider class of positive formulas

redundancy in logic i cnf propositional formulae a knowledge base is redundant if it contains parts that can be inferred from the rest of it we study some problems related to the redundancy of a cnf formula in particular any cnf formula can be made irredundant by deleting some of its clauses what results is an irredundant equivalent subset we study the complexity of problems related to irredundant equivalent subsets verification checking existence of an irredundant equivalent subset with a given size checking necessary and possible presence of clauses in irredundant equivalent subsets and uniqueness we also consider the problem of redundancy with different definitions of equivalence

laguerre type derivatives dobinski relations and combinatorial identities we consider properties of the operators d r m ar a a m which we call generalized laguerre type derivatives with r 1 2 m 0 1 where a and a are boson annihilation and creation operators respectively satisfying a a 1 we obtain explicit formulas for the normally ordered form of arbitrary taylor expandable functions of d r m with the help of an operator relation that generalizes the dobinski formula coherent state expectation values of certain operator functions of d r m turn out to be generating functions of combinatorial numbers in many cases the corresponding combinatorial structures can be explicitly identified

compiling propositional weighted bases in this paper we investigate the extent to which knowledge compilation can be used to improve model checking and inference from propositional weighted bases we first focus on the compilability issue for both problems deriving mainly non compilability results in the case preferences are subject to change then we present a general notion of c normal weighted base that is parametrized by a tractable class c for the clausal entailment problem we show how every weighted base can be turned compiled into a query equivalent c normal base whenever c is a complete class for propositional logic both negative and positive results are presented on the one hand complexity results are identified showing that the inference problem from a c normal weighted base is as difficult as in the general case when the prime implicates horn cover or renamable horn cover classes are targeted on the other hand we show that both the model checking and the clausal inference problem become tractable whenever dnnf normal bases are considered moreover we show that the set of all preferred models of a dnnf normal weighted base can be computed in time polynomial in the output size and as a consequence model checking is also tractable for such bases finally we sketch how our results can be used in model based diagnosis in order to compute the most likely diagnoses of a system

a robust adaptive control of a parallel robot the work presented in this article deals with the robust adaptive control tracking of a 6 degree of freedom parallel robot called c5 parallel robot the proposed approach is based on the coupling of sliding modes and multi layers perceptron neural networks mlp nns it does not require the inverse dynamic model for deriving the control law the mlp nn is added in the control scheme to estimate the gravitational and frictional forces along with the non modelled dynamic effects the nonlinearity problem present in neural networks is resolved using taylor series expansion the proposed approach allows to adjust the parameters of neural network and sliding mode control terms by taking into account a reference model and the closed loop stability in the lyapunov sense we implemented our approach on the c5 parallel robot of lissi laboratory and performed experiments to observe its effectiveness and the robust behaviour of the controller against external disturbances

is intractability of nonmonotonic reasoning a real drawback abstract several studies about computational complexity of nonmonotonic reasoning nmr showed that nonmonotonic inference is significantly harder than classical monotonic inference this contrasts with the general idea that nmr can be used to make knowledge representation and reasoning simpler not harder in this paper we show that to some extent nmr fulfills the representation goal in particular we prove that nonmonotonic formalisms such as circumscription and default logic allow for a much more compact and natural representation of propositional knowledge than propositional calculus proofs are based on a suitable definition of a compilable inference problem and on non uniform complexity classes some results about intractability of circumscription and default logic can therefore be interpreted as the price one has to pay for having such an extra compact representation on the other hand intractability of inference and compactness of representation are not equivalent notions we exhibit intractable nonmonotonic formalisms whose nonmonotonic assumptions are representable by few propositional formulae finally sometimes nmr really makes reasoning simpler we present prototypical scenarios where closed world reasoning and well founded semantics account for a faster complete and unsound approximation of classical reasoning

on the groenewold van hove problem for r 2n we discuss the groenewold van hove problem for r2n and completely solve it when n 1 we rigorously show that there exists an obstruction to quantizing the poisson algebra of polynomials on r2n thereby filling a gap in groenewold s original proof moreover when n 1 we determine the largest lie subalgebras of polynomials which can be consistently quantized and explicitly construct all their possible quantizations

normal ordering and generalised stirling numbers the relation between some normal ordering forms for boson operator functions and generalised stirling numbers is shown in particular the ordering of the operator function ak ar n s n is obtained for positive integers k r n and an arbitrary integer s this is a generalisation of the recent result of katriel ibid vol 16 p 4171 3 1983 some other normal ordering formulae are presented it was shown how to obtain antinormal forms from several normal expansions given here

full order observer design for linear systems with unknown inputs in this article a full order observer without unknown inputs reconstruction is suggested in order to achieve finite time reconstruction of the state vector for a class of linear systems with unknown inputs the observer is a simple one its derivation being direct and easy it will be shown that the problem of full order observers for linear systems with unknown inputs can be reduced in this case to a standard one the unknown input vector will not interfere in the observer equations the effectiveness of the suggested design algorithm is illustrated by a numerical example aircraft longitudinal motion and for the same aircraft dynamics we make a comparison between our new observer and other already existing observers from the existence conditions and dynamic characteristics point of view the superiority of the new designed observer is demonstrated

wigner function evolution in a self kerr medium derived by entangled state representation by introducing the thermo entangled state representation we convert the calculation of wigner function wf of density operator to an overlap between two pure states in a two mode enlarged fock space furthermore we derive a new wf evolution formula of any initial state in a self kerr medium with photon loss and find that the photon number distribution for any initial state is independent of the coupling factor with the kerr medium where the number state is not affected by the kerr nonlinearity and evolves into a density operator of binomial distribution

recursive prediction error identification using the nonlinear wiener model the nonlinear wiener model consisting of a linear dynamic block in cascade with a static nonlinearity is considered a recursive prediction error identification algorithm based on the wiener model is derived the linear dynamic block is modelled as a siso transfer function operator and the static nonlinearity is approximated with a piecewise linear function a theoretical analysis of the method is carried out and conditions for local convergence to the true parameter vector are given in particular the analysis shows that the input signal should be such that there is signal energy in the whole range of the piecewise linear approximation a numerical example illustrates the performance of the algorithm further practical guidelines on how to apply the algorithm are also included in the paper

a generalization of collapsible cases of circumscription abstract circumscription is a second order formula expressing the minimality of the extension of a particular predicate or set of predicates it was fashioned to capture the concept of nonmonotonic logic of human beings in some instances circumscription is equivalent to a first order formula we show that the known cases are special instances of a more general case

recursive subspace identification of linear and non linear wiener state space models the moesp class of identification algorithms are made recursive on the basis of various updating schemes for subspace tracking

circumscription completeness reviewed abstract in this paper we demonstrate that some results on the completeness of p defining theories published earlier are incorrect we point out that by restricting the original propositions to well founded theories results somewhat weaker than the original ones can be retained we also present a theorem that provides some insight into the relation between completeness and reducibility and helps to identify the theories whose minimal models can be adequately handled with circumscription

unknown input and state estimation for unobservable systems the concept of strong detectability and its relation with the concept of invariant zeros is reviewed for strongly detectable systems which includes the strongly observable systems it is proposed a hierarchical design of a robust observer whose trajectories converge to those of the original state vector furthermore it is shown that neither left invertibility is a sufficient condition nor strong detectability is a necessary condition to estimate the unknown inputs it is shown that the necessary and sufficient condition for estimating the unknown inputs is that the set of the invariant zeros that do not belong to the set of unobservable modes be within the interior of the left half plane of the complex space this shows that the unknown inputs could be estimated even if it is impossible to estimate the entire state vector of the system two numerical examples illustrate the effectiveness of the proposed estimation schemes

on the combinatorics of normal ordering bosonic operators and deformations of it recently some combinatorial aspects for the normal ordering of powers of arbitrary monomials of boson operators were discussed in particular it was shown that the resulting formulae lead to generalizations of the usual bell and stirling numbers in this paper these considerations are generalized to the q deformed case in particular it is shown that the simplest example of this generalization leads to q deformed lah numbers the connection between generalized stirling and bell numbers and matrix elements of the above mentioned operators with respect to the usual fock space basis and coherent states is discussed

representing elements of the weyl algebra by labeled trees it is shown how arbitrary elements of the weyl algebra can be represented by labeled plane trees using normal ordering several examples are treated and combinatorial aspects are discussed also possible avenues for future research are described

the suprem architecture a new intelligent paradigm abstract we investigate the model theory of the notion of circumscription and find completeness theorems that provide a partial converse to a result of mccarthy we show that the circumscriptive theorems are precisely the truths of the minimal models in the case of various classes of theories and for various versions of circumscription we also present an example of commonsense reasoning in which first order circumscription does not achieve the intuitive and desired minimization

brief paper output feedback adaptive control of a class of nonlinear discrete time systems with unknown control directions in this paper output feedback adaptive control is investigated for a class of nonlinear systems in output feedback form with unknown control gains to construct output feedback control the system is transformed into the form of the narma nonlinear auto regressive moving average model based on which future output prediction is carried out with employment of the predicted future output a constructive output feedback adaptive control is given with the discrete nussbaum gain exploited to overcome the difficulty due to unknown control directions under the global lipschitz condition of the system functions the boundedness of all the closed loop signals and asymptotical output tracking are achieved by the proposed control simulation results are presented to show the effectiveness of the proposed approach

reducing belief revision to circumscription and vice versa nonmonotonic formalisms and belief revision operators have been introduced as useful tools to describe and reason about evolving scenarios both approaches have been proven effective in a number of different situations however little is known about their relationship previous work by winslett has shown some correlations between a specific operator and circumscription in this paper we greatly extend winslett s work by establishing new relations between circumscription and a large number of belief revision operators this highlights similarities and differences between these formalisms furthermore these connections provide us with the possibility of importing results in one field into the other one

on the matrix equation xa ax xp abstract we study the matrix equation xa ax x p in m n k for 1 p n it is shown that every matrix solution x is nilpotent and that the generalized eigenspaces of a are x invariant for a being a full jordan block we describe how to compute all matrix solutions combinatorial formulas for a m x l x l a m and ax l are given the case p 2 is a special case of the algebraic riccati equation

adaptive discrete time sliding mode control of nonlinear systems described by wiener models abstractin this paper we propose an adaptive control scheme that can be applied to nonlinear systems with unknown parameters the considered class of nonlinear systems is described by the block oriented models specifically the wiener models these models consist of dynamic linear blocks in series with static nonlinear blocks the proposed adaptive control method is based on the inverse of the nonlinear function block and on the discrete time sliding mode controller the parameters adaptation are performed using a new recursive parametric estimation algorithm this algorithm is developed using the adjustable model method and the least squares technique a recursive least squares rls algorithm is used to estimate the inverse nonlinear function a time varying gain is proposed in the discrete time sliding mode controller to reduce the chattering problem the stability of the closed loop nonlinear system with the proposed adaptive control scheme has been proved an application to a ph neutralisation

laguerre 2d functions and their application in quantum optics a set of orthonormalized and complete functions of two real variables in complex representation involving laguerre polynomials as a substantial part is introduced and is referred to as the set of laguerre two dimensional 2d functions the properties of the set of laguerre 2d functions are discussed and the fourier and radon transforms of these functions are calculated the laguerre 2d functions form a basis for a realization of the five dimensional lie algebra to the heisenberg weyl group for a two mode system real representation of this set of functions by a sum over products of hermite functions involving jacobi polynomials at the zero argument as coefficients is derived and it leads to new connections between laguerre and hermite polynomials in both directions the set of laguerre 2d functions is the most appropriate set of functions for the fock state representation of quasi probabilities in quantum optics the wigner quasi probability in fock state representation is up to a factor and an argument scaling directly given for each matrix element by a corresponding laguerre 2d function the properties of orthonormality and completeness of the laguerre 2d functions provide the fock state matrix elements of the density operator directly from the quasi probabilities the perina mista representation of the glauber sudarshan quasi probability can be represented with advantage by the laguerre 2d functions the fock state matrix elements of the displacement operator and the scalar product of displaced fock states are closely related to laguerre 2d functions

ordering relations for q boson operators continued fraction techniques and the q cbh enigma ordering properties of boson operators have been very extensively studied and q analogues of many of the relevant techniques have been derived these relations have far reaching physical applications and at the same time provide a rich and interesting source of combinatorial identities and of their g analogues an interesting exception involves the transformation from symmetric to normal ordering which for conventional boson operators can most simply be effected using a special case of the campbell baker hausdorff cbh formula to circumvent the lack of a suitable q analogue of the cbh formula two alternative procedures are proposed based on a recurrence relation and on a double continued fraction respectively these procedures enrich the repertoire of techniques available in this field for conventional bosons they result in an expression that coincides with that derived using the cbh formula

parametric identification methodology using sliding modes observer this paper deals with a new methodology concerning parametric identification designed for non linear uncertain systems non measurable states of the model are restored through a variable structure observer which converges in a finite time thanks to this latter property it is possible to derive equations of the model in order to obtain a parametric estimation law which converges in finite time to the nominal values of the parameters without the use of the classical persistent excitation for the input signal the main interest of the approach is its robustness with respect to parameter uncertainties and additive measurement noise this method will be compared to some classical ones finally simulation results will illustrate the use of the algorithm with an application to a synchronous machine

observer and output feedback stabilisation for a class of nonlinear systems the objective of the work is twofold first we investigate the problem of observer design for a class of systems in cascade form we suppose that an observer exists for each subsystem and then prove that this interconnection is an observer for the overall system one of both nonlinear functions is assumed to be not lipschitz e g to satisfy a quadratic constraint on the unmeasured part of the state this first main result may be viewed as an improvement of besancon and hammouri besancon g and hammouri h 1998 on observers design for interconnected systems journal of mathematical systems estimation and control 8 377 380 in which the authors discussed the problem of the synthesis of interconnected observers the second part is a generalisation of ammar mabrouk and vivalda ammar s mabrouk m and vivalda j c 2009 observer and global output feedback stabilisation for some mechanical systems international journal of control 82 1070 1081 in which the authors study the proble

orthogonal polynomials and operator orderings an alternative and combinatorial proof is given for a connection between a system of hahn polynomials and identities for symmetric elements in the heisenberg algebra which was first observed by bender et al resolution of the operator ordering problem by the method of finite elements phys rev lett 56 2445 1986 continuous hahn polynomials and the heisenberg algebra j math phys 28 509 1987 and proven by koornwinder meixner pollaczek polynomials and the heisenberg algebra j math phys 30 767 1989 in the same vein two results announced by bender and dunne polynomials and operator orderings j math phys 29 1727 1988 connecting a special one parameter class of hermitian operator orderings and the continuous hahn polynomials are also proven

asymptotic formulae for two variable hermite polynomials new asymptotic formulae for the two dimensional hermite polynomials with large values of indices are found the applications to the photon distribution functions in squeezed one mode mixed quantum states are considered

continuous robust control design for nonlinear uncertain systems without a priori knowledge of control direction in this paper a robust control scheme is proposed for a class of nonlinear systems that have not only additive nonlinear uncertainties but also unknown multiplicative signs these signs are called control directions since they represent effectively the direction of motion under any given control except for the unknown control directions the class of systems satisfy the generalized matching conditions nonlinear robust control is designed to identify on line unknown control directions and to guarantee global stability of uniform ultimate boundedness without the knowledge of nonlinear dynamics except their size bounding functions it is also shown that the proposed robust control can be made continuous through utilizing the so called shifting laws that change smoothly and accordingly the signs of robust controls and that no matter what time constants and gains of the shifting laws are global stability is always ensured the analysis and design is done using lyapunov s direct method

wick s theorem for q deformed boson operators in this paper combinatorial aspects of normal ordering of arbitrary words in the creation and annihilation operators of the q deformed boson are discussed in particular it is shown how by introducing appropriate q weights for the associated feynman diagrams the normally ordered form of a general expression in the creation and annihilation operators can be written as a sum over all q weighted feynman diagrams representing wick s theorem in the present context

generalized weyl transform for operator ordering polynomial functions in phase space the generalized weyl transforms were developed from the hermiticity condition and the ordering rules were represented by characteristic real valued functions the integral transforms give rise to transformation equations between weyl quantization and differently ordered operators the transforms also simplify evaluation of commutator and anticommutator of a set of operators following the same ordering rule

generating relations of tricomi and hermite tricomi functions using lie algebra representation abstract this paper is an attempt to stress the usefulness of the multi variable special functions in this paper we derive generating relations involving multi variable tricomi and hermite tricomi functions by using lie algebraic method further we derive certain new and known generating relations involving other forms of tricomi hermite tricomi and bessel functions as applications

propositional circumscription and extended closed world reasoning are p p 2 complete abstract circumscription and the closed world assumption with its variants are well known nonmonotonic techniques for reasoning with incomplete knowledge their complexity in the propositional case has been studied in detail for fragments of propositional logic one open problem is whether the deduction problem for arbitrary propositional theories under the extended closed world assumption or under circumscription is p 2 complete i e complete for a class of the second level of the polynomial hierarchy we answer this question by proving these problems p 2 complete and we show how this result applies to other variants of closed world reasoning

on the satisfiability of circumscription abstract etherington mercer and reiter showed on the basis of ideas of bossu and siegel that circumscription cannot lead to inconsistency for universal formulas we extend this result in three directions to formulas of a more general syntactic form to circumscription with some predicate symbols allowed to vary and to prioritized circumscription

observer design for nonlinear triangular systems with unobservable linearisation the article deals with the observer design problem for a wide class of triangular time varying nonlinear systems with unobservable linearisation sufficient conditions are derived for the existence of a luenberger type observer when it is a priori known that the initial state of the system belongs to a given nonempty bounded subset of the state space for the general case the state estimation is exhibited by means of a switching sequence of time varying dynamics

heisenberg weyl algebra revisited combinatorics of words and paths the heisenberg weyl algebra which underlies virtually all physical representations of quantum theory is considered from the combinatorial point of view we provide a concrete model of the algebra in terms of paths on a lattice with some decomposition rules we also discuss the rook problem on the associated ferrers board this is related to the calculus in the normally ordered basis from this starting point we explore combinatorial underpinning of the heisenberg weyl algebra which offers novel perspectives methods and applications

some computational aspects of circumscription the effects of circumscribing first order formulas are explored from a computational standpoint first extending work of v lifschitz it is shown that the circumscription of any existential first order formula is equivalent to a first order formula after this it is established that a set of universal horn clauses has a first order circumscription if and only if it is bounded when considered as a logic program thus it is undecidable to tell whether such formulas have first order circumscription finally it is shown that there arefirst order formulas whode circumscription has a conp complete model checking problem

computing circumscriptive databases i theory and algorithms abstract though circumscription was introduced by mccarthy over a decade ago there has been relatively little work on algorithms for computing circumscriptive databases in this paper we develop algorithms to compute the preferred models of circumscriptive databases at compile time using mixed integer linear programming techniques two advantages of this bottom up approach are that it makes efficient re use of previous computations and it provides much faster run time performance some other advantages of using linear programming to automate deduction at compile time are that its re optimization facilities elegantly accommodate database updates and also that it leads to a completely declarative formulation in which ordering of rules and literals in rule bodies plays no real role finally we plan to use a standard relational database system as our run time environment this should yield relatively fast run time processing and provide a more expressive query language in which aggregates and the like can be expressed easily

a simple nonlinear observer for a class of uncertain mechanical systems a simple nonlinear observer is proposed for a class of uncertain nonlinear multiple input multiple output mimo mechanical systems whose dynamics are first order differentiable the global asymptotic observation of the proposed observer is proved thus the observer can be designed independently of the controller furthermore the proposed observer is formulated without any detailed model knowledge of the system these advantages make it easy to implement numerical simulations are included to illustrate the effectiveness of the proposed observer

fock expansion of multimode pure gaussian states the fock expansion of multimode pure gaussian states is derived starting from their representation as displaced and squeezed multimode vacuum states the approach is new and appears to be simpler and more general than previous ones starting from the phase space representation given by the characteristic or wigner function fock expansion is performed in terms of easily evaluable two variable hermite kampe de feriet polynomials a relatively simple and compact expression for the joint statistical distribution of the photon numbers in the different modes is obtained in particular this result enables one to give a simple characterization of separable and entangled states as shown for two mode and three mode gaussian states

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

an efficient method for eliminating varying predicates from a circumscription abstract circumscription appears to be the most powerful and well studied technique used in formalizing common sense reasoning the general form of predicate circumscription allows for fixed and varying floating predicates we show that the inference problem under this form of circumscription is efficiently reducible to inferencing under circumscription without varying predicates in fact we transform this problem even into circumscription without fixed and varying predicates that is where all predicates are minimized thus any theorem prover or algorithm for inferencing under circumscription without fixed and varying predicates is able to handle inferencing under the general form of predicate circumscription as a consequence algorithms that compute circumscription for an inference task can be simplified

on the dimensions of oscillator algebras induced by orthogonal polynomials there is a generalized oscillator algebra associated with every class of orthogonal polynomials n x n 0 on the real line satisfying a three term recurrence relation x n x bn n 1 x bn 1 n 1 x 0 x 1 b 1 0 this note presents necessary and sufficient conditions on bn for such algebras to be of finite dimension as examples we discuss the dimensions of oscillator algebras associated with hermite legendre and gegenbauer polynomials some remarks on the dimensions of oscillator algebras associated with multi boson systems are also presented

discrete spherical harmonic oscillator transforms on the cartesian grids using transformation coefficients the analog harmonic oscillators are well studied in quantum physics including their energy states wavefunctions orthogonal properties and eigenfunctions of the fourier transform in addition the continuous solutions in different dimension and coordinate systems are known some discrete equivalents of the 1d wavefunctions were also studied however in the 3d spherical coordinate system the discrete equivalents of the 3d wavefunctions are not established in this paper we focus on the spherical harmonic oscillator wavefunctions shows the spherical harmonic oscillator transforms shots and their discrete implementation the shows can be synthesized by linear combinations of the hermite gaussian functions with proper transformation coefficients we find that computing the coefficients can be speeded up using the fast fourier transforms or some recursive relations these coefficients relate the hermite transforms with the shots some applications of the discrete shows and the discrete shots are introduced first the shows are exactly the eigenfunctions of the 3d dft also the shots can be used to derive the spherical harmonic oscillator descriptor shod which is a rotational invariant descriptor we find that the shod is not only compatible with the existing rotational descriptors for the spherically sampled data but also outperforms the existing rotational descriptors for 3d cartesian sampled bandlimited input data besides the shots can be used to decompose 3d signals into spherical components hence 3d signal reconstruction is done using partially chosen spherical component and 3d data compression for mri data is demonstrated using shots for medical applications

implicit summation formulae for hermite and related polynomials in this article we derive some implicit summation formulae for hermite and related polynomials by using different analytical means on their respective generating functions

optimization based non linear observers revisited optimization based non linear observers are those where the integrated output prediction error is used to define the dynamic of the observer s state their main advantage is genericity and the natural assumptions that are needed for the related convergence results to hold here we present some new theoretical results concerning these observers despite the title we use our observer is not based on the search for a global minimum of a cost function it is based on a descent like approach without the use of the hessian matrix a nice feature is that the resulting observer takes a classical form of in the sense that it is defined by a set of ordinary differential equations besides the theoretical results some implementation issues are discussed in particular we propose to use the post stabilization approach well known when dealing with differential systems with invariant submanifolds this enables to increase the sampling period while keeping very good precision two illustrative examples are presente

transformations of laguerre 2d polynomials with applications to quasiprobabilities laguerre 2d polynomials are defined and their properties are investigated the laguerre 2d functions introduced in 1 2 are related to the laguerre 2d polynomials in such a way that they also include the weight function for the orthonormalization of the laguerre 2d polynomials a one parameter group of transformations applicable to certain classes of polynomials and discrete sets of functions is investigated and applied in particular to hermite polynomials and to laguerre 2d polynomials these transformations allow us to represent the polynomials of the corresponding classes by superpositions of the same kind of polynomials with stretched arguments they contain limiting cases with delta functions and their derivatives and lead to regularized representations of the delta functions and their derivatives as demonstrated for hermite and laguerre 2d polynomials applications of the laguerre 2d polynomials and 2d functions and their transformations to problems of quantum optics as the representation of quasiprobabilities in the fock state basis and by normally and otherwise ordered moments are considered the inversion of these representations is obtained in all cases a restricted design of quasiprobabilities should become possible

dynamical robust adaptive tracking for uncertain nonlinear systems in this paper we propose two robust adaptive control schemes for a large class of single input single output nonlinear uncertain systems in order to track bounded and smooth trajectories the method is based on the introduction of a dynamical iterative change of coordinates dcc which is a modified version of a dynamical backstepping procedure the performances of these algorithms are illustrated on a buck boost converter

second order exponential differential operator and generalized hermite polynomials abstract both univariate and multivariate generalized hermite polynomials are defined by introducing second order exponential differential operator corresponding probabilistic expressions are given explicitly based on those expectation expressions their generating functions recursion relations and other properties are derived conveniently in connection to stein s identities in particular orthogonality are investigated and associated expressions are presented accordingly additionally some other classical identities related to hermite polynomials are proved by an alternative way and some examples and remarks are presented

autoepistemic logic autoepistemic logic is one of the principal modes of nonmonotonic reasoning it unifies several other modes of nonmonotonic reasoning and has important application in logic programming in the paper a theory of autoepistemic logic is developed this paper starts with a brief survey of some of the previously known results then the nature of nonmonotonicity is studied by investigating how membership of autoepistemic statements in autoepistemic theories depends on the underlying objective theory a notion similar to set theoretic forcing is introduced expansions of autoepistemic theories are also investigated expansions serve as sets of consequences of an autoepistemic theory and they can also be used to define semantics for logic programs with negation theories that have expansions are characterized and a normal form that allows the description of all expansions of a theory is introduced our results imply algorithms to determine whether a theory has a unique expansion sufficient conditions stratification that imply existence of a unique expansion are discussed the definition of stratified theories is extended and under some additional assumptions efficient algorithms for testing whether a theory is stratified are proposed the theorem characterizing expansions is applied to two classes of theories k1 theories and ae programs in each case simple hypergraph characterization of expansions of theories from each of these classes is given finally connections with stable model semantics for logic programs with negation is discussed in particular it is proven that the problem of existence of stable models is np complete authors abstract

a bijection between rooted trees and fermionic fock states grafting and growth operators in fock space and fermionic operators for rooted trees we show that fermionic fock states in the occupation number representation can be indexed uniquely by rooted trees our main ingredients in this construction are the matula numbers the fundamental theorem of arithmetic and a relabeling of fermionic quantum states by natural numbers as a byproduct of the correspondence mentioned above we realize the grafting and the growth operators comprising important constructions in the context of hopf algebras in the fermionic fock space also we show how to construct fermionic creation and annihilation operators in the context of rooted trees new representations of the solutions of combinatorial dyson schwinger equations and of the antipode in the connes kreimer hopf algebra of rooted trees related to the occupation number picture are presented

the size of a revised knowledge base abstract in this paper we address a specific computational aspect of belief revision the size of the propositional formula obtained by means of the revision of a formula with a new one in particular we focus on the size of the smallest formula which is logically equivalent to the revised knowledge base the main result of this paper is that not all formalizations of belief revision are equal from this point of view for some of them we show that the revised knowledge base can be represented by a polynomial size formula we call these results compactability results on the other hand for other ones the revised knowledge base does not always admit a polynomial space representation unless the polynomial hierarchy collapses at a sufficiently low level non compactability results we also show that the time complexity of query answering for the revised knowledge base has definitely an impact on being able to represent the result of the revision compactly nevertheless formalisms with the same complexity may have different compactability properties we also study compactability properties for a weaker form of equivalence called query equivalence which allows to introduce new propositional symbols moreover we extend our analysis to the special case in which the new formula has constant size and to the case of sequences of revisions i e iterated belief revision a complete analysis along these four coordinates is shown

preprocessing of intractable problems some computationally hard problems e g deduction in logical knowledge bases are such that part of an instance is known well before the rest of it and remains the same for several subsequent instances of the problem in these cases it is useful to preprocess off line this known part so as to simplify the remaining on line problem in this paper we investigate such a technique in the context of intractable i e np hard problems recent results in the literature show that not all np hard problems behave in the same way for some of them preprocessing yields polynomial time on line simplified problems we call them compilable while for other ones their compilability implies some consequences that are considered unlikely our primary goal is to provide a sound methodology that can be used to either prove or disprove that a problem is compilable to this end we define new models of computation complexity classes and reductions we find complete problems for such classes completeness meaning they are the less likely to be compilable we also investigate preprocessing that does not yield polynomial time on line algorithms but generically decreases complexity this leads us to define hierarchies of compilability that are the analog of the polynomial hierarchy a detailed comparison of our framework to the idea of parameterized tractability shows the differences between the two approaches

some consequences of non uniform conditions on uniform classes we obtain some results of the form if certain complexity classes satisfy a non uniform condition then some unlikely consequences follow more precisely 1 1 if the non uniform polynomial time hierarchy collapses at level i 0 i e ipoly ipoly then the meyer stockmeyer hierarchy collapses at level i 2 i e i 2 i 2 this strengthens a generalization of a result of karp and lipton 1980 2 2 if co np is conjunctively reducible to a sparse set then p np this generalizes a theorem of fortune 1979 3 3 if np is conjunctively and disjunctively reducible to a sparse np complete set then p np this is a partial generalization of a result of mahaney 1980 conjuctive and disjunctive reducibility were introduced by ladner lynch and selman 1975 4 4 if co np is reducible to a sparse set then np co np reducibility was introduced 5 by adleman and manders 1977

identification of wiener type nonlinear systems in a noisy environment wiener systems are widely encountered in engineering and science applications this paper proposes a straightforward approach to the identification of wiener systems in a noisy environment the obtained models are represented in terms of the frequency response for the linear subsystem and the inverse of the static nonlinearity a variety of input excitation signals including random binary and periodic can be used with the proposed method simulation studies using a ph neutralization continuous stirred tank reactor show that excellent results are obtained with relatively short data lengths

generalized zernike or disc polynomials we investigate generalized zernike or disc polynomials p m n z z which are orthogonal 2d polynomials in the unit disc 0 zz 1 is a free parameter these polynomials can be expressed by jacobi polynomials of transformed arguments in connection with a simple angle dependence a limiting procedure leads to laguerre 2d polynomials lm n z z furthermore we introduce the corresponding orthonormalized disc functions the disc polynomials and disc functions obey two differential equations a first order and a second order one with a certain degree of freedom and the operators of lowering and raising of the indices are found these operators can be closed to a lie algebra su 1 1 su 1 1 new generating functions are derived from an operational representation which is alternative to the rodrigues type representation the one dimensional analogue of the disc polynomials which are orthogonal polynomials in the interval 0 r 1 with weight factors 1 r2 x are ultraspherical or gegenbauer polynomials in a new standardization the lowering and raising operators to the corresponding orthonormalized functions form a simple su 1 1 lie algebra this is given in the appendix in sketched form

on compact representations of propositional circumscription we prove that unless the polynomial hierarchy collapses at the second level the size of a purely propositional representation of the circumscription circ t of a propositional formula t grows faster than any polynomial as the size of t increases we then analyze the significance of this result in the related field of closed world reasoning

applications of circumscription to formalizing common sense knowledge we present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in mccarthy 1980 and some applications to formalizing common sense knowledge the applications in this paper are mostly based on minimizing the abnormality of different aspects of various entities included are nonmonotonic treatments of is a hierarchies the unique names hypothesis and the frame problem the new circumscription may be called formula circumscription to distinguish it from the previously defined domain circumscription and predicate circumscription a still more general formalism called prioritized circumscription is briefly explored

observer based dynamic surface control for a class of nonlinear systems an lmi approach this note presents a new analysis method to design an observer based dynamic surface controller odsc for a class of nonlinear systems while the separation principle from linear system theory does not generally hold for nonlinear systems a separation principle for the odsc systems will be shown for a class of nonlinear systems thus enabling the independent design of the observer and dsc furthermore a convex optimization problem to test quadratic stability of odsc will be formulated later

quantum first time of arrival operators this paper undertakes the problem of constructing first time of arrival operators for arbitrary everywhere analytic potentials in the space of operators spanned by the bender dunne basis bender and dunne 1989 phys rev d 40 3504 the operators are conjugate with their respective system hamiltonians and reduce to their corresponding classical time of arrival expressions for infinitesimal the supraquantized time of arrival operators galapon 2004 j math phys 45 3180 and the confined time of arrival operators galapon et al 2004 phys rev lett 93 180406 galapon 2006 j mod phys a 21 6351 are then shown to be two distinct representations of the time of arrival operators constructed in the bender dunne space

general ordering problem and its combinatorial roots we introduce the general method of converting a given operator function into its s ordered form we state and prove a theorem representing the fact that any ordered expansion of some operator function might be considered as the combinatorial problem of counting the number of contractions this will also unify the two essentially distinct notions of taking an operator into some ordered form and reordering or formally ordering an operator in this way we reduce the general ordering problem into a purely combinatorial one finally we show the application of the theorem through two generic examples from both quantum optics and field theory

sliding observer controller design for uncertain triangular nonlinear systems in order to achieve robust output tracking for a class of uncertain triangular systems a combination of a robust sliding observer and a backstepping procedure is introduced

multivariable orthogonal polynomials associated with tensor products of the oscillator algebra b 1 it is well known that the tensor product of n 1 lowest weight representations of a generalization of the oscillator algebra b 1 can be depicted by a binary coupling tree with each such binary coupling tree we associate a polynomial rl h x that will turn out to be an n variable hermite polynomial we prove that the polynomials rl h x associated with a fixed binary coupling tree are orthogonal over the n dimensional real space for some weight function which is independent of the shape of the considered binary coupling tree the connection coefficients expressing a polynomial associated with a given binary coupling in terms of polynomials associated with another binary coupling tree are the 3nj coefficients of b 1

new relations for two dimensional hermite polynomials the effective formulas reducing the two dimensional hermite polynomials to the classical one dimensional orthogonal polynomials by jacobi gegenbauer legendre laguerre and hermite are given new one parameter generating functions for the diagonal multidimensional hermite polynomials are derived the factorial moments and cumulants of the distribution functions related to the hermite polynomials of two variables with equal indices are expressed in terms of the legendre and chebyshev polynomials asymptotical formulas for the two dimensional polynomials with large values of indices and zero arguments are found the applications to the squeezed one mode states and to the time dependent quantum harmonic oscillator are considered

lie theoretic generating relations of hermite 2d polynomials in this paper we derive some generating relations involving hermite 2d polynomials h2dp hm n u x y of two variables with an arbitrary 2d matrix u as parameter using lie theoretic approach certain known or new generating relations for the polynomials related to h2dp are also obtained as special cases

from sequences to polynomials and back via operator orderings bender and dunne polynomials and operator orderings j math phys 29 1727 1731 1988 showed that linear combinations of words qkpnqn k where p and q are subject to the relation qp pq i may be expressed as a polynomial in the symbol z 12 qp pq relations between such polynomials and linear combinations of the transformed coefficients are explored in particular examples yielding orthogonal polynomials are provided

on the relationship between circumscription and negation as failure abstract the aim of this paper is to investigate two powerful methods of handling negative information in logic based knowledge representation systems the logical minimization in the form of circumscription and the negation as failure rule formalized by various closures or completions of original theories we suggest a new more powerful form of the negation as failure rule and describe an important class of theories for which this form of negation as failure is equivalent to particular forms of circumscription these results establish a close relationship between the two important formalizations of nonmonotonic reasoning and provide a syntactic characterization of the corresponding circumscriptive theories this allows us to apply existing methods of deduction using various negation as failure rules to answering queries in a broad class of circumscriptive theories

an algorithm to compute circumscription abstract mccarthy s theory of circumscription appears to be the most powerful among various formalizations of nonmonotonic reasoning designed to handle incomplete and negative information in knowledge representation systems in this paper we describe a query answering algorithm for circumscriptive theories the closed world assumption cwa and its generalizations the generalized closed world assumption gcwa and the extended closed world assumption ecwa can be considered as special forms of circumscription consequently our algorithm also applies to answering queries in theories using the closed world assumption and its generalizations similarly since prioritized circumscription is equivalent to a conjunction of parallel circumscriptions our algorithm can be used to answer queries in theories circumscribed by prioritized circumscription

hermite and laguerre 2d polynomials abstract we define hermite 2d polynomials hm n u x y and laguerre 2d polynomials l m n u z z as functions of two variables with an arbitrary 2d matrix u as parameter and discuss their properties and their explicit representation recursion relations and generating functions for these polynomials are derived the advantage of the introduced hermite and laguerre 2d polynomials in comparison to the related usual two variable hermite polynomials is that they satisfy orthogonality relations in a direct way whereas for the purpose of orthonormalization of the last one has to introduce two different kinds of such polynomials which are biorthogonal to each other