on resolving the multiplicity of arbitrary tensor products of the u n groups representations of u n are realised as right translations on holomorphic hilbert bargmann spaces of n n complex variables r fold tensor product spaces of irreducible representations of u n are shown to be isomorphic to subspaces of the holomorphic hilbert spaces maps are exhibited which carry an irreducible representation of u n into these subspaces the algebra of operators commuting with these maps is constructed and it is shown how eigenvalues of certain of these operators can be used to resolve the multiplicity several examples from u 3 are explicitly worked out

vector coherent state constructions of u 3 symmetric tensors and their su 3 su 2 u 1 wigner coefficients generalized vector coherent state constructions of totally symmetric u 3 tensors are used to gain new expressions for the su 3 su 2 u 1 wigner coefficients for the coupling 1 1 20 3 3 these expressions show how the extremely simple formulas of le blanc and biedenharn involving a single 9 j coefficient arise as special cases of a general result that involves 12 j coefficients a simpler general result involving only 9 j coefficients and k normalization factors is derived in a way that can in principle be generalized to the generic coupling with multiplicity

from canonical tensor operators of su 3 and 3 to bi orthogonal coupling coefficients explicit expansion expansion of the matrix elements of su 3 and canonical tensor operators in terms of the bi orthogonal coupling coefficients and overlaps of the draayer akiyama construction are considered special bi orthogonal extremal isoscalar factors with subscripts as multiplicity labels and proportional to q racah q 6j coefficients or the generalized wilson rahman rational bi orthogonal functions in terms of balanced or hypergeometric series are used as a natural basis for extremal matrix elements of the highest weight component of the canonical tensor operators of su 3 in the generating function approach of biedenharn lohe and louck the expansion that is obtained triple sum together with previously derived asymmetric seed isofactors and elementary overlaps gives the explicit overlap coefficients and can be used to derive su 3 and canonical tensor operators as well as new explicit normalized seed isofactors with regge type symmetry specified for the minimal null space case

analysis and design of impulsive control systems some sufficient conditions for asymptotic stability of impulsive control systems with impulses at fixed times have recently been presented in this paper we derive some less conservative conditions for asymptotic stability of such impulsive control systems and the results are used to design impulsive control for a class of nonlinear systems the class of nonlinear systems considered is also extended

canonical orthonormal wigner supermultiplet basis the explicit construction of an orthonormal basis for states of good spin isospin and su 4 wigner supermultiplet symmetry is given in a bargmann representation space a complete set of quantum labels is provided by a sp 3 r contains implies u 3 complementary symmetry

young diagrams as kronecker products of symmetric or antisymmetric components a general relation is presented for expressing any young diagram as an operator polynomial acting on the kronecker product formed from either the rows or columns of the original diagram this relation is used to derive branching rules gh for compact groups g and h of gl n which are well suited for numerical computations the examples chosen are the su 3 contains implies so 3 and su 4 contains implies su 2 su 2 reductions employed in studies of nuclear structure and the su 8 contains implies su 3 decomposition employed in studies of particle physics

clebsch gordan coefficients of su 3 with simple symmetry properties using an appropriate labelling operator constructed from representation generators su 3 clebsch gordan coefficients are introduced whose symmetry properties are similar to those of their su 2 counterparts an algebraic algorithm for computing the coefficients is presented

some special su 3 r 3 wigner coefficients and their application bargmann space expansions of oscillator functions are used to derive analytic expressions for su 3 r 3 wigner coefficients for the couplings 10 0 2 3 3 l3 0 and 10 20 3 3 l3 0 with arbitrary 3 3 these lead to expansions useful in nuclear cluster problems and are used to give a simple form for the su 3 irreducible tensor expansion of a scalar two body interaction an application which motivated this investigation

impulsive control of lurie systems in this paper the impulsive control scheme of lurie systems is represented using lyapunov s direct method and comparison technique we present novel conditions under which impulsively controlled lurie systems are asymptotically stable and give the estimate of the upper bound of impulse interval in particular globally exponential stability of impulsive control of lurie systems is presented impulsive controller design with examples is provided to show the feasibility and effectiveness of our method finally

on the denominator function for canonical su 3 tensor operators the definition of a canonical unit su 3 tensor operator is given in terms of its characteristic null space as determined by group theoretic properties of the intertwining number this definition is shown to imply the canonical splitting conditions used in earlier work for the explicit and unique up to phases construction of all su 3 wcg coefficients wigner clebsch gordan using this construction an explicit su 3 invariant denominator function characterizing completely the canonically defined wcg coefficients is obtained it is shown that this denominator function squared is a product of linear factors which may be obtained explicitly from the characteristic null space times a ratio of polynomials these polynomials denoted gtq are defined over three shift parameters and three barycentric coordinates the properties of these polynomials hence of the corresponding invariant denominator function are developed in detail these include a derivation of their degree symmetries and zeros the

decomposition of the so 8 enveloping algebra under u 4 u 3 the existence of a complete set of su 3 tensor operators in the enveloping algebra of so 8 is demonstrated the analysis recasts a parallel analysis by biedenharn and flath commun math phys 93 143 1984 concerning an so 6 2 model for su 3 in the isomorphic but simpler framework of an so 8 model

prepotential formulation of su 3 lattice gauge theory the su 3 lattice gauge theory is reformulated in terms of su 3 prepotential harmonic oscillators this reformulation has enlarged su 3 u 1 u 1 gauge invariance under which the prepotential operators transform like matter fields the hilbert space of su 3 lattice gauge theory is shown to be equivalent to the hilbert space of the prepotential formulation satisfying certain color invariant sp 2 r constraints the su 3 irreducible prepotential operators which solve these sp 2 r constraints are used to construct su 3 gauge invariant hilbert spaces at every lattice site in terms of su 3 gauge invariant vertex operators the electric fields and the link operators are reconstructed in terms of these su 3 irreducible prepotential operators we show that all the su 3 mandelstam constraints become local and take a very simple form within this approach we also discuss the construction of all possible linearly independent su 3 loop states which solve the mandelstam constraints the techniques can be easily generalized to su n

algebraic criteria for absolute stability abstract algebraic criteria for absolute stability of lure systems whose linear part has a diagonal system matrix are derived the conditions for absolute stability are expressed in the form of inequalities which contain no variable other than system parameters and therefore can be checked readily

the state space extension method in the theory of absolute stability this paper shows how the state space extension method can be used to derive frequency domain criteria for stability of systems with different kinds of uncertainties the main result is illustrated by a number of examples

brief paper robust stability and h control of uncertain impulsive systems with time delay this paper investigates the problems of robust stability stabilization and h control for uncertain impulsive systems with time delay the parametric uncertainties are assumed to be time varying and norm bounded three classes of impulsive systems with time delay are considered the systems with stable stabilizable continuous dynamics and unstable unstabilizable discrete dynamics the systems with unstable unstabilizable continuous dynamics and stable stabilizable discrete dynamics and the systems where both the continuous time dynamics and the discrete time dynamics are stable stabilizable for each class of system by using the lyapunov function and razumikhin type techniques sufficient conditions for robust stability stabilization and h control are developed in terms of linear matrix inequalities numerical examples are given which illustrate the applicability of the theoretical results

on resolving the multiplicity of tensor products of irreducible representations of symplectic groups the multiplicity problem of r fold tensor products of irreducible representations of sp 2k c are considered the arbitrary r fold tensor product is shown to be isomorphic to a subspace of the holomorphic hilbert bargmann space of n 2k complex variables maps are constructed which carry an irreducible representation of sp 2k c into this subspace an algebra of commuting operators is constructed and it is shown how eigenvalues and eigenvectors of certain of these operators can be used to resolve the multiplicity

new realizations of the dual space of su 3 the logic of constructing and interrelating classical realizations of the dual space of so 3 is exhibited analogies with different methods of quantization of gauge theories are pointed out the analysis is applied to su 3 to obtain existing realizations and to construct new ones the gelfand zetlyn basis for the irreducible representations of su 3 is explicitly realized using polynomials in four variables and positive or negative integral powers of a fifth variable another realization uses a spinor of so 6 so 3 1 these are the analogues of schwinger bargmann construction for su 2

synchronization based approach for parameters identification in delayed chaotic neural networks abstract in this paper an adaptive procedure to the problem of synchronization and parameters identification for chaotic neural networks with time varying delay is introduced by combining the adaptive control and linear feedback with appropriate update law based on the invariance principle of functional differential equations all the connection weight matrices can be efficiently estimated according to a simple rigorous and systematic technique this approach is also able to track the changes in the operating parameters of the experimental neural networks rapidly the speed of synchronization and parameters estimation can be adjusted under the adaptive gain properly chosen in addition the method is simple to implement in practice and it is quite robust against the effect of slight noise in the given time series and the estimated value of a parameter fluctuates around the correct value

brief converting chaos into periodic motion by state feedback control a simple control method is presented to convert chaos into periodic motion by using linear state feedback of an available system variable the low periodic orbits can be derived from the chaotic attractor with slight change of the dynamical structure in the original dynamics melnikov s perturbation method in generalized hamiltonian systems is introduced to explain the control mechanism of directing chaotic motion towards low periodic motion in the lorenz equations moreover the existence of periodic orbits is examined in the perturbed lorenz system simulation results verify the effectiveness of melnikov s analysis

explicit canonical tensor operators and orthonormal coupling coefficients of su 3 the canonical unit su 3 tensor operators are constructed by means of the stretched coupling of the auxiliary maximal and minimal null space tensor operators with the renormalization factors expressed in terms of the denominator functions of biedenharn gustafson lohe louck and milne the matrix elements of the maximal null space tensor operators are expressed with the help of the modified projection operators of asherova and smirnov the self conjugate minimal null space tensor operators are expressed in terms of the group generators with the help of the weight lowering operator technique the corresponding extreme isoscalar factors of the clebsch gordan wigner coefficients are used as constructive elements of the explicit recursive expression for the general orthonormal isoscalar factors of su 3 with its considerable simplication for the boundary values of parameters the general isofactors are also expanded in the different ways in terms of their boundary values the new classes of the generaliz

two body homogeneous rational gaudin models and the missing label problem for the n 2 rational gaudin hamiltonians based on it is shown that the spectral invariants of the lax matrix correspond to linear combinations of the labelling operators associated with the embedding of lie algebras the diagonalized spectral invariants are applied to the degeneracy separation in the clebsch gordan series of

canonical solution of the state labelling problem for su n so n and littlewood s branching rule i general formulation the internal state labelling problem for the d row irreducible representations of su n where 2d or n when reduced with respect to so n is shown to amount to the external state labelling problem for u d the canonical solution of the latter due to biedenharn et al 1967 provides a canonical solution of the former which reflects the operation of littlewood s branching rule for u n contains implies o n in a very simple way

symmetry properties of matrix elements of canonical su 3 tensor operators the symmetries of the su 3 3 j symbols which are defined as symmetrized matrix elements of the canonical su 3 tensor operators are investigated the symmetries considered are those which in su 2 correspond to the interchange of columns of the 3 j symbol as well as the symmetry under conjugation it is found that for each tensor operator in a multiplicity set the matrix elements for a fixed operator pattern carry a one dimensional representation of the symmetric group s3

canonical solution of the state labelling problem for su n so n and littlewood s branching rule iii su 3 so 3 case for pt ii see ibid vol 17 no 4 p 777 89 1984 parts i and ii discussed in general terms a new solution to the state labelling problem for the d row irreducible representations irreps of su n when reduced with respect to so n this solution was termed canonical because it reflects the operation of littlewood s branching rule for u n o n in a straightforward way the su 3 so 3 case is now worked out in detail explicit expressions of the canonical basis states of so 3 irreps l belonging to an su 3 irrep h1h2 are obtained the matrix of the transformation from the bargmann moshinsky basis to the canonical one is also calculated it is shown that in both cases the extra label necessary to completely specify the states can be chosen as the label js characterising an intermediate su 2 irrep in the reduction of the produce representation jl js into su 2 irreps j where j 1 2 h1 h2 and jl 1 2l or 1 2 l 1 whenever h1 h2 l is even or odd

su3 isoscalar factors a summary of the properties of the wigner clebsch gordan coefficients and iso scalar factors for the group su3 in the su2 u1 decomposition is presented the outer degeneracy problem is discussed in detail with a proof of a conjecture braunschweig s which has been the basis of previous work on the su3 coupling coefficients recursion relations obeyed by the su3 isoscalar factors are produced along with an algorithm which allows numerical determination of the factors from the recursion relations the algorithm produces isoscalar factors which share all the symmetry properties under permutation of states and conjugation which are familiar from the su2 case the full set of symmetry properties for the su3 wigner clebsch gordan coefficients and isoscalar factors are displayed

discrete data assimilation in the lorenz and 2d navier stokes equations consider a continuous dynamical system for which partial information about its current state is observed at a sequence of discrete times discrete data assimilation inserts these observational measurements of the reference dynamical system into an approximate solution by means of an impulsive forcing in this way the approximating solution is coupled to the reference solution at a discrete sequence of points in time this paper studies discrete data assimilation for the lorenz equations and the incompressible two dimensional navier stokes equations in both cases we obtain bounds on the time interval h between subsequent observations which guarantee the convergence of the approximating solution obtained by discrete data assimilation to the reference solution

implementation of the u n tensor operator calculus in a vector bargmann hilbert space using a vector coherent state framework and an associated vector bargmann hilbert space 1961 the structure of two classes of u n u n 1 unit projective operators is shown to be intimately related to 6 j and 9 j coefficients of the u n 1 subalgebra explicit verification of limit properties for these operators allows the unambiguous assignment of a set of canonical operator labels

a new fuzzy impulsive control of chaotic systems based on t s fuzzy model in this paper fuzzy impulsive control is used for stabilization of chaotic systems based on the takagi sugeno t s model the stability issue of the general nonlinear impulsive control system is first investigated via comparison criterion then a novel impulsive control scheme is presented for chaotic systems based on the t s fuzzy model some sufficient conditions are given to stabilize the t s fuzzy model our results are proven to be less conservative theoretically and numerically moreover we have also estimated the stable region of the impulsive interval finally the proposed fuzzy impulsive control scheme is successfully applied to stabilize rossler s system and chua s circuit the numerical simulations demonstrate the effectiveness and advantage of our main results

general approach to mathfrak su n quasi distribution functions we propose an operational form for the kernel of a mapping between an operator acting in a hilbert space of a quantum system with an symmetry group and its symbol in the corresponding classical phase space for symmetric irreps of this mapping is bijective we briefly discuss complications that will occur in the general case

parisi s mean field solution for spin glasses as an analytic continuation in the replica number parisi s replica symmetry breaking solution for spin glasses is extended to finite replica number n the free energy fp n obtained this way as well as its first two derivatives with respect to n are shown to join the corresponding values in the sherrington kirkpatrick sk solution at a characteristic value ns t where stability breaks down in the latter the continuation composed of the sk branch fsk n for n or ns t and the parisi branch fp n for 0 or n or ns t fulfils the requirements of convexity monotonicity and stability for all n

on biorthogonal and orthonormal clebsch gordan coefficients of su 3 analytical and algebraic approaches minimal biorthogonal systems of the clebsch gordan wigner coefficients of su 3 u 2 are discussed as well as the dual coupled bases the closed system of analytical expressions for the dual isofactors reduced wigner coefficients and the overlaps of coupled states is obtained with the help of analytical inversion symmetry the regge type symmetry of the overlaps and the boundary orthonormal isofactors orthogonalization coefficients is discovered the polynomial structure of the alternative complete algebraic systems of the orthonormal su 3 isofactors characterized by the null spaces symmetries and additional selection rules and obtained by means of the hecht or gram schmidt process is considered the realizations of the external missing label operators of the third and the fourth orders in the minimal coupled bases which lead to preferable algorithms to evaluate the orthonormal su 3 coupling coefficients satisfying different symmetry properties are presented with the help of the 6j coef

the so 6 2 model of su 3 and its generalisation to su n the complementarity relation between the u p q and u n lie groups enables the authors to reformulate the so 6 2 model of su 3 in terms of a u 1 1 group and to outline its generalisation to a family of n 2 models of su n for n or 3 respectively associated with u n 2 1 u n 1 2 and u 1 n 2 groups

a calculus for su 3 leading to an algebraic formula for the clebsch gordan coefficients we develop a simple computational tool for su 3 analogous to bargmann s calculus for su 2 crucial new inputs are i explicit representation of the gelfand zetlin basis in terms of polynomials in four variables and positive or negative integral powers of a fifth variable ii an auxiliary gaussian measure with respect to which the gelfand zetlin states are orthogonal but not normalized iii simple generating functions for generating all basis states and also all invariants as an illustration of our techniques an algebraic formula for the clebsch gordan coefficients is obtained for the first time this involves only gaussian integrations thus su 3 is made as accessible for computations as su 2 is

canonical orthonormal basis for su 3 so 3 i construction of the basis a canonical orthonormal basis is given for generic representations of the group chain su 3 contains implies so 3

new perspective on the u n wigner racah calculus ii elementary reduced wigner coefficients for u n for pt i see ibid vol 20 no 9 p 2241 50 1987 exploiting the powerful formalism of the vector coherent state theory expounded in part i the group theoretical content of the complementarity principle and a novel interpretation of the operator pattern of biedenharn and louck the authors rederive in a simple fashion all u n u n 1 reduced wigner coefficients for the elementary u n tensors

a resolution of the su 3 outer multiplicity problem and computation of wigner coefficients for su 3 a simple algorithm is given for the resolution of the su 3 multiplicity problem and the computation of su 3 wigner coefficients using a complete set of u 2 x u 3 bargmann tensors classified by operator patterns null space properties of these tensors are easily derived their structure is such that a direct one to one correspondence is shown to exist between the bargmann tensors and the terms in the clebsch gordan series for su 3 as derived by o reilly 1982 finally the resolution presented herein is shown to be concordant with an alternative resolution advocated long ago by hecht

numerical study of conformal invariance in rsos models the author studies conformal invariance in the rsos models of andrews et al 1985 at both the ferromagnetic and antiferromagnetic transitions using finite size scaling of the transfer matrix the author confirms the conjecture of huse 1984 concerning the conformal classification of the ferromagnetic transitions and gives evidence that the antiferromagnetic transitions lie in the universality class of zn models in addition he shows that conformal results can be applied to anisotropic systems if logarithmic corrections are taken into account

unitary representations branching rules and matrix elements for the non compact symplectic groups the complementarity of the symplectic and orthogonal groups is used to infer properties of the infinite dimensional unirreps of the former from the character theory of the latter the complete set of d series metaplectic unirreps of sp n r is identified and branching rules are given for their restrictions to the maximal compact subgroup u n developed in terms of the properties of schur functions a known algorithm for the evaluation of matrix elements of the sp 3 r lie algebra is extended to any sp n r and analytic expressions are given for important classes of unirreps and multiplicity free states

symbolic computation approach for absolute stability a criterion for absolute stability of nonlinear control systems which is equivalent to popov s criterion is given the condition for absolute stability can be tested without graphics symbolic computation is employed for the test a maple program and some examples are given

less conservative conditions for asymptotic stability of impulsive control systems this note studies the stability of impulsive control systems a new comparison theorem for asymptotic stability of impulsive differential system is presented based on the new result we derive some less conservative conditions for asymptotic stability of impulsive control systems with impulses at fixed times and the results are used to design impulsive control for a class of nonlinear systems the class of nonlinear systems considered is also enlarged

symmetry properties of s classified su 3 3j 6j and 9j symbols starting from the s classified su 3 clebsch gordan coefficients introduced previously pluhar et al 1985 the s classified su 3 3j 6j and 9j symbols are constructed and examined they satisfy simple symmetry relations similar to those valid for the su 2 case

driving and synchronizing by chaotic impulses for a class of dynamical systems driven by chaotic impulses we give conditions for the occurrence of chaos locking it is shown how the concept of time discontinuous coupling of two chaotic systems may lead to generalized synchronization the method of synchronization is interpreted as a nonlinear analog of the sampling theorem furthermore we examine the effect of amplitude quantization of the driving signal on their synchronization even though two time discontinuously coupled dynamical systems are no more exactly synchronized when the driving signal is digitized their trajectories are close enough to allow correct transmission of digital information signals between them textcopyright 1996 the american physical society

canonical orthonormal basis for su 3 contains implies so 3 iii complete set of su 3 tensor operators for pt ii see ibid vol 18 p 1905 1985 a complete set of tensor operators for su 3 is given in a model space generated by two bargmann vectors use is made of modified operator patterns to classify these tensors their tensorial properties are then discussed in the context of the su 3 tensor algebra developed by biedenharn and collaborators 1957 the authors also given analytical semi analytical expressions for important classes of wigner coefficients in gel fand rotational basis

canonical orthonormal basis for su 3 so 3 ii reduced matrix elements of the su 3 generators for pt i see ibid vol 18 p 1891 1985 a simple algorithm is given for the calculation of reduced matrix elements of the generators of the su 3 algebra in the canonical su 3 contains implies so 3 basis introduced in i

determination of the weyl invariants and calculation of the coupling coefficients for unitary groups the author presents a new approach for determining the weyl invariants of unitary groups such an approach is based on the generating function of the basis of the representation for unitary groups built in an earlier work hage hassan 1983 the author obtains two expressions for the weyl invariants both including the parameters involved in the generating function coupling coefficients appear in one of the expressions the comparison of the development of the two expressions allows the calculation of the coupling coefficients the application of this approach to the calculation of the coupling coefficients for the direct product lambda 10 x lambda 2 mu 2 of su 3 leads to an expression of the isoscalar factor where no summation occurs in contradistinction with the known expression for the coupling coefficients which involve five summations

su n irreducible schwinger bosons we construct su n irreducible schwinger bosons satisfying certain u n 1 constraints which implement the symmetries of su n young tableaues as a result all su n irreducible representations are simple monomials of n 1 types of su n irreducible schwinger bosons further we show that these representations are free of multiplicity problems thus all su n representations are made as simple as su 2

complementary group resolution of the su n outer multiplicity problem ii recoupling approach for su 3 u 2 reduced wigner coefficients a general procedure for the derivation of su 3 u 2 reduced wigner coefficients rwcs for the coupling 1 1 2 2 where is the outer multiplicity label required in the decomposition is proposed based on a recoupling approach that follows the complementary group technique for a resolution of the outer multiplicity of su n introduced in part i of this series rwcs of su n are not unique under a canonical resolution of the outer multiplicity the transformation from one set to another are elements of so m where m is the number of occurrences of the irrep in the decomposition 1 1 2 2 a special resolution of the multiplicity is identified that leads to a recursive procedure for the determination of rwcs new features of these special rwcs and differences from those obtained with other choices are discussed the method can be applied to the derivation of general su n wigner or rwcs algebraic expressions for another kind of rwcs the so called reduced auxiliary wigner coef

models for su 3 in terms of so n 2 and so 2n algebras mathematical and physical models for su 3 are given in terms of unirreps of the so n 2 and so 2n algebras vector coherent state representations are given for all the discrete series unirreps of so n 2 and so 2n traceless bosons are shown to arise naturally in these representations a new and elegant realisation of the so 8 approximately so 6 2 model for su 3 is given and it is shown how to perform calculations in the so 8 model using the powerful vector coherent state representations formalism

a new boson calculus for su 3 it is shown that the gelfand weyl pattern for su 3 can be uniquely expressed in terms of four non negative and one positive or negative free integers this provides an optimal albeit non linear boson calculus for su 3 in terms of four harmonic oscillators and one planar rotor by optimal it is meant that every irreducible representation is obtained once and once only our techniques can be generalized to other groups

a simplified so 6 2 model of su 3 a new realization is obtained of the representation of so 6 2 which has been shown recently by flath and biedenharn and also by bracken and macgibbon to define a model of su 3 in contrast to the realization in terms of six pairs of boson operators used previously which involved cubic expressions the new realization involves only quadratic expressions in eight pairs of boson operators and is manifestly hermitian properties of this new oscillator realization and in particular its advantages over the old realization are discussed briefly it is deduced that the representation of so 6 2 is integrable to a unitary group representation

on the structure of tensor operators in su3 a global algebraic formulation of su3 tensor operator structure is achieved a single irreducible unitary representation irrep v ofso 6 2 is constructed which contains every su3 irrep precisely once an algebra of polynomial differential operatorsa acting onv is given the algebraa is shown to consist of linear combinations of all su3 tensor operators with polynomial invariant operators as coefficients by carrying out an analysis ofa the multiplicity problem for su3 tensor operators is resolved

adaptive variable structure control for chaos suppression of unified chaotic systems this paper investigates the chaos suppression problem for a class of unified chaotic systems subject to uncertainties and control input with dead zone nonlinearity using the variable structure control technique a robust adaptive control law is established to suppress chaos in a class of unified chaotic systems even with unknown uncertainties and dead zone nonlinearity in input in particular a switching surface is newly proposed to simplify the task of ensuring the stability of the closed loop system in the sliding mode numerical results validate the effectiveness of the proposed adaptive control scheme

new perspective on the u n wigner racah calculus i vector coherent state theory and construction of gel fand bases using a vector coherent state theory it is shown that the construction of gel fand bases for the unitary group is particularly simple the very specific rules for construction of the states greatly facilitate the subsequent computation of matrix elements of the generators of the u n lie algebra

impulsive control of lorenz system abstract in this paper an impulsive control scheme of the lorenz system is presented first we use the theory of impulsive differential equation to find conditions under which impulsively controlled lorenz system is asymptotically stable then we give the estimate of the upper bound of impulse interval for asymptotically stable control numerical experimental results are presented

explicit orthonormal clebsch gordan coefficients of su 3 the construction of the explicit algebraic polynomial expressions for the nonmultiplicity free orthonormal clebsch gordan wigner coefficients of su 3 u 2 is completed in the case of the paracanonical coupling scheme related with the explicit minimal biorthogonal systems by means of the hecht or gram schmidt process the direct and inverse orthogonalization coefficients the first of them being equivalent to the boundary orthonormal isofactors are expressed up to explicitly given multiplicative factors in terms of the numerator and denominator polynomials related with the auxiliary a function of louck biedenharn and lohe that appears as a fragment of the denominator g functions of canonical su 3 tensor operators

creation and annihilation operators for su 3 in an so 6 2 model creation and annihilation operators are defined which are wigner operators tensor shift operators for su 3 while the annihilation operators are simply boson operators the creation operators are cubic polynomials in boson operators together they generate under commutation the lie algebra of so 6 2 the vector space generated from a vacuum vector by repeated application of the creation operators carries an irreducible representation of the so 6 2 algebra equivalent to an hermitian representation and also carries in direct sum every different irreducible representation of su 3 so 6 2 exactly once a model for su 3 in the sense of bernstein gel fand and gel fand is therefore defined the different su 3 irreducible representations appear explicitly as manifestly covariant irreducible tensors whose orthogonality and normalisation properties are examined other wigner operators for su 3 can be constructed simply as products of the new creation and annihilation operators or sums of such products

complementary group resolution of the su n outer multiplicity problem i the littlewood rules and a complementary u 2n 2 group structure a complementary group to su n is found that realizes all features of the littlewood rules for kronecker products of su n representations this is accomplished by considering a state of su n to be a special gel fand state of the complementary group u 2n 2 with labels of the latter used to distinguish multiple occurrences of irreducible representations of su n irreps in the su n su n su n decomposition that is obtained from the littlewood rules furthermore this realization also helps us to determine su n su n 1 u 1 reduced wigner coefficients rwcs frequently called isoscalar factors and clebsch gordan coefficients cgcs or full nonreduced wigner coefficients of su n using algebraic or numeric methods in either the canonical or a noncanonical basis new explicit formulas for the su 3 and su 4 multiplicities are obtained by using this technique

calculation of clebsch gordan and racah coefficients using symbolic manipulatio n programs a procedure for calculating clebsch gordan and racah coefficients arising from the decomposition of n fold tensor products of the u n groups using symbolic manipulation programs is given basic states are realized as polynomials in a space equipped with a differentiation inner product the desired coefficients are then obtained by differentiating the relevant polynomials examples from su 2 and su 3 are given copyright 1989 academic press inc

a closed formula for the product of irreducible representations of su 3 we determine a closed formula in terms of p q r and s for the decomposition of the product p q r s of finite dimensional irreducible representations of su 3 we also determine in terms of p q r s m and n necessary and sufficient conditions that a term m n appears in this decomposition and its multiplicity

clebsch gordan coefficients for u 8 o 8 su 3 the group chain u 8 o 8 su 3 plays an important role in many particle systems whenever the fundamental particles have eight degrees of freedom as a particular example the systems of many gluons and pairs of quark antiquark are discussed which can be coupled to a flavor octet in order to determine the explicit structure of states and decay probabilities the calculation of the clebsch gordan coefficients cgc of this group chain is indispensable in this contribution the polynomial states of the u 8 chain are constructed and also the isoscalar factors of the cgc s tables of isoscalar factors are presented the method shown serves as an example for higher rank groups

computer aided stability analysis renders popov criterion obsolete a class of multipliers that can be used for producing alternative stability tests for systems having a single incrementally conic nonlinearity f x has been nearly parameterized by zames and falb 1 the present note demonstrates how linear programming can be used to compute optimal multipliers leading to a frequency domain stability criterion that is less conservative than the standard graphical criteria

general impulsive control of chaotic systems based on a ts fuzzy model in this paper a time delayed impulsive controller is constructed and the uniformly asymptotic stability of chaotic systems based on a takagi sugeno ts fuzzy model is investigated and some new and useful criteria are derived in addition the uniformly asymptotic synchronization of chaotic systems based on the ts fuzzy model is discussed using similar techniques finally some numerical simulations are presented to illustrate the effectiveness and feasibility of the derived results

canonical solution of the state labelling problem for su n so n and littlewood s branching rule ii use of modification rules for pt i see ibid vol 16 p 2095 1983 in part i it was shown that when d 1 2n case where littlewood s branching rule 1950 for u n contains implies o n has to be supplemented with newell s modification rules 1951 the explicit solution of the state labelling problem for v 1 row irreducible representations of both su 2v 1 and su 2v is given and is shown to reflect the operation of littlewood s modified branching rule in a direct way the generalisation to higher d values is then outlined

orthogonalization of the projected states and isofactors the explicit direct and inverse orthogonalization coefficients ocs are derived for the projected basis states of the two parametric covariant irreducible representations of including elliott s n 3 case and draayer with the alternative choices of the gram schmidt processes began respectively from the lowest vergados or highest absolute value of the intrinsic parameter k the different direct and inverse ocs the latter equivalent to the definite boundary isofactors or the boundary resubducing coefficients are found to be connected by the definite analytical continuation contraction procedures with mutually related ocs of the biorthogonal states and the boundary orthonormal pseudocanonical and paracanonical isofactors of the orthogonalization coefficients considered are presented as definite algebraic polynomial structures under the square root with the linear factors and numerator denominator polynomials in terms of the partition dependent functions of biedenharn and louck

the missing link operators for labelling multiplicity in the clebsch gordan series it is indicated that there are invariant operators on the direct product space of irreducible representations of lie groups which distinguish between repeating representations they complete the labelling of the clebsch gordan series

e factor of representations of classical groups abstract we let g be the isometry group of a nondegenerate symmetric or skew symmetric form h on a space v over some local or global field k i e g u v h we let lg be the l group of go the identity component of g and r be the natural representation of this group we develop here a theory of l functions and e factors attached to this r in particular we develop a theory of local and global zeta integrals for such g we use very special intertwining operators therein we require an analysis of the proper normalization of such operators with such techniques we determine the correct e factors associated to local representations the issue of the correct local l factor is discussed

induced shift tensors in vector coherent state theory it is shown that the so called shift tensors of biedenharn and louck have a natural expression within the framework of vector coherent state vcs theory vcs theory was developed to give a systematic construction of the representations of lie groups and to derive the corresponding matrices representing the elements of their lie algebras in this paper there are explicit realizations of shift tensors within the framework of vcs theory for semisimple lie groups in terms of shift tensors for suitably defined subgroups

new perspective on the u n wigner racah calculus iii applications to u 2 and u 3 for pt ii see ibid vol 20 no 14 p 4613 35 1987 using the framework introduced in parts i and ii the author derives an interesting relationship between u 3 symmetric tensors and u 2 racah coefficients closed formulae for generic u 2 wigner and racah coefficients are given in terms of alternative parametrisations for such coefficients