recursive calculation of transformation factors in terms of primitive factors the authors present an algorithm for recursively calculating coupling recoupling induction and similar coefficients in terms of the primitive coefficients the algorithm is shown to be complete for any compact group they use the 6 j symbol as an example for describing their algorithm but the algorithm applies to a wide class of group theoretic transformation factors

quantity of information comparison between information systems 1 non fuzzy states abstract in statistical theory experiments or probabilistic information systems are supposed to be informative since they reduce the amount of uncertainty associated with the states of nature for the case that the available information systems are vague fuzzy information systems h tanaka t okuda and k asai have proven using the measure of information as provided by entropy that the fuzzy information systems are informative too now we wish to state and to study a criterion in order to compare fuzzy information systems by the quantity of information of a fuzzy information system defined by tanaka et al in this first paper we consider the situation where we require information about the original state space non fuzzy state space the second paper will deal with the situation where we require only information on certain vague states fuzzy states

subduction coefficients of brauer algebras and racah coefficients of o n and sp 2 m ii racah coefficients irreducible representations of brauer algebras are discussed in the non standard basis a method for evaluating subduction coefficients sdcs i e the transformation coefficients between standard and non standard bases of brauer algebras is outlined non trivial sdcs of for are derived racah coefficients of o n and sp 2m can be derived from subduction coefficients of brauer algebras by using the schur weyl duality relation between and o n or sp 2m

ergodic theory for markov fibred systems and parabolic rational maps a paraboiic rational map of the riemann sphere admits a non atomic h conformal measure on its julia set where h the hausdorff dimension of the julia set and satisfies 1 2 h 2 with respect to this measure the rational map is conservative exact and there is an equivalent a finite invariant measure finiteness of the measure is characterised central limit theorems are proved in the case of a finite invariant measure and return sequences are identified in the case of an infinite one a theory of markov fibred systems is developed and parabolic rational maps are considered within this framework

explicit evaluation of coupling coefficients for the most degenerate representations of so n explicit results for particular coupling coefficients for the most degenerate representations of so n are given the isoscalar factors which allow a recursive calculation of arbitrary coupling coefficients from those of so 3 are derived 6j and 9j symbols for most degenerate representations are also briefly discussed

a fuzzy probabilistic information system comparison criterion applications and properties a phi fuzzy probabilistic information system comparison criterion is defined it is based on a nonnegative concave function considered over a fuzzy state space based on phi fuzzy probabilistic information system comparison criterion many interesting properties are studied connections with the classical criteria of lehmann and blackwell are made the function phi admits many interesting information theoretical particular cases these particular cases are divided in two parts shannon s and nonshannon s and are put in the last section

more on coupling coefficients for the most degenerate representations of so n we present explicit closed form expressions for the general group theoretical factor appearing in the topology of a high temperature expansion of so n symmetric lattice models this object which is closely related to 6j symbols for the most degenerate representation of so n is discussed in detail

the a b terminal information energy in the sequential selection of fuzzy information systems abstract on the basis of information energy for fuzzy information systems a sequential selection method of a fixed number of fuzzy information systems is presented the information energy is a measure of the quantity of information concerning the parameter space provided by a fuzzy information system ox when a prior probability distribution has been defined on the parameter space

the minimum p divergence estimates with fuzzy observations statistical applications abstract in this paper we consider statistical problems involving experiments whose observation does not provide exact information but that it may be assimilated with fuzzy information first we present the minimum o divergence estimator o for the unknown parameter on the basis of the o divergence between the fuzzy statistic and the probability vector of the fuzzy information system based on a fuzzy random sample properties of this estimator are also used to obtain the asymptotic distribution of the statistic associated to the minimum o divergence estimator this asymptotic distribution is used to give a testing procedure

a class of 6 j symbols for so 2l 1 in terms of rotation matrices for so 3 it is shown that a 6 j symbol for so 2l 1 in which four primitive spinor representations 1 21 2 1 2 appear is directly related to an so 3 rotation matrix possessing a rank of l 1 2 and characterised by the euler angles 0 1 2 pi 0 an interpretation is given in terms of a rotation operator exp 1 2i pi ty acting in the combined spin and quasispin space of an atomic l shell whose states mod t mt are defined in a quasiparticle scheme in which four coupled spinors 1 21 2 1 2 are used

phase transitions for countable markov shifts we study the analyticity of the topological pressure for some one parameter families of potentials on countable markov shifts we relate the non analyticity of the pressure to changes in the recurrence properties of the system we give sufficient conditions for such changes to exist and not to exist we apply these results to the manneville pomeau map and use them to construct examples with different critical behavior

6j symbols for symmetric representations of so n as the double series the corrected triple sum expression of alisauskas 1987 j phys a math gen 20 35 for the recoupling racah coefficients 6j symbols of the symmetric most degenerate representations of the orthogonal groups so n previously derived from the fourfold sum expression of alisauskas also related to the result of hormes and junker 1999 j phys a math gen 32 4249 is rearranged into three new different double sum expressions related to the hypergeometric kampe de feriet type series and a new triple sum expression with preferable summation condition the regge type symmetry of special 6j symbols of the orthogonal groups so n in terms of special kampe de feriet f1 41 3 series is revealed the recoupling coefficients for antisymmetric representations of symplectic group sp 2n are derived using their relation with the recoupling coefficients of the formal orthogonal group so 2n

statistical properties of dynamical systems with some hyperbolicity this paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts though not necessarily all of their phase spaces the main results are for discrete time systems to put this work into context recall that for axiom a attractors the picture has been fairly complete since the 1970 s see s1 b r2 since then much progress has been made on two fronts there is a general nonuniform theory that deals with properties common to all diffeomorphisms with nonzero lyapunov exponents o p1 ka ly and there are detailed analyses of specific kinds of dynamical systems including for example billiards 1 dimensional and henon type maps s2 bsc hk j bc2 by1 statistical properties such as exponential decay of correlations are not enjoyed by all diffeomorphisms with nonzero lyapunov exponents the goal of this paper is a systematic understanding of these and other properties for a class of dynamical systems larger than axiom a this class will not be defined explicitly but it includes some of the much studied examples by looking at regular returns to sets with good hyperbolic properties one could give systems in this class a simple dynamical representation conditions for the existence of natural invariant measures exponential mixing and central limit theorems are given in terms of the return times these conditions can be checked in concrete situations giving a unified way of proving a number of results some new and some old among the new results are the exponential decay of correlations for a class of scattering billiards and for a positive measure set of henon type maps

some bounds on probability of error in fuzzy discrimination problems abstract in this paper we propose some bounds on the average probability of error for the fuzzy discrimination problem based on information energy information energy was introducted in information theory by onicescu 1966

statistical properties of maps with indifferent periodic points in this note we present an axiomatic approach to the decay of correlations for maps of arbitrary dimension with indifferent periodic points as applications we apply our results to the well known manneville pomeau equation and the inhomogeneous diophantine approximation algorithm

some 6 j symbols for symplectic and orthogonal groups by cerkaski s method the method devised by cerkaski 1987 has been used for the group sp 2n to find some 6 j symbols for which a single multiplicity index is required this approach possesses some advantages over that based on racah s techniques for so 3 the formulae for the 6 j symbols are comparatively simple and they automatically exhibit the symmetries of jucys 1973 elementary means are used to show that the eigenvalues of casimir s operator c2 for sp 2n are identical to those of c2 for o 2d if the authors take d n and replace the irreps of sp 2n by their transposed counterparts for o 2d where d is integral or half integral this enables the formulae for sp 2n to be used to generate expressions for some 6 j symbols for the orthogonal groups o 2d and so 2d illustrations are provided by so 2l 1 and o 4

algebraic expressions for some generalised 6 j symbols for so n and g2 a class of generalised 6 j symbols which enter naturally when a second pair of modes epsilon tau 2 is added to the octahedral jahn teller system gamma 8 epsilon tau 2 has been evaluated for the group so 5 the method involves the fictitious boson configurations dwd and can be readily generalised to lwl the resulting 6 j symbols for so 2l 1 can be used to produce others by means of generalisations of the equations satisfied by the ordinary 6 j symbols for so 3 extensions to so 2l 2 and g2 are described as well as the weight space symmetries of jucys 1973 the relation between 6 j symbols and isoscalar factors is illustrated for so 7 contains implies g2

new parametric measures of information in this paper methods are presented for obtaining parametric measures of information from the non parametric ones and from information matrices the properties of these measures are examined the one dimensional parametric measures which are derived from the non parametric are superior to fisher s information measure because they are free from regularity conditions but if we impose the regularity conditions of the fisherian theory of information these measures become linear functions of fisher s measure

subduction coefficients of birman wenzl algebras and racah coefficients of the quantum groups oq n and spq 2m i subduction coefficients irreducible representations of birman wenzl algebras cf r q in the non standard basis are discussed a procedure for evaluating subduction coefficients sdcs or the transformation coefficients between standard and non standard basis of birman wenzl algebras is formulated based on the linear equation method sdcs of cf r q with f 4 are derived racah coefficients of the quantum groups oq n and spq 2m can be obtained from sdcs of birman wenzl algebras cf r q by using the schur weyl brauer duality relation between birman wenzl algebras cf r q and the quantum groups oq n and spq 2m

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

subexponential decay of correlations we describe a method for proving subexponential lower bounds for correlations functions and apply it to study decay of correlations for maps with countable markov partitions one result is that ls young s upper estimates y2 are optimal in many situations our method is based on a general result concerning the asymptotics of renewal sequences of bounded operators acting on banach spaces which we apply to the iterates of the transfer operator

calculation of primitive 6 j symbols the 6 j symbols of a group are independent of the subgroup chain chosen to define the basis states the authors present an improved algorithm for calculating the primitive 6 j symbols for a compact group with a faithful irrep by recursive building up using only the kronecker product rules and the general properties of 6 j previously one has sometimes needed to search for the useful equations by systematically trying all equations which involve unknown 6 j the authors show that the primitive 6 j may all be easily solved in terms of a subclass the core 6 j they discuss how the core 6 j can usually be solved proving that the method is complete for so3 the authors conjecture that the algorithm is complete for all groups

equilibriums of some non holder potentials we consider one sided subshifts with some potential functions which satisfy the holder condition everywhere except at a fixed point and its preimages we prove that the systems have conformal measures and invariant measures absolutely continuous with respect to where may be finite or infinite we show that the systems are exact and are weak gibbs measures and equilibriums for we also discuss uniqueness of equilibriums and phase transition these results can be applied to some expanding dynamical systems with an indifferent fixed point

comparing location experiments in sections 1 3 the classical theory of the comparison of two experiments is reviewed with particular reference to the comparison of two location experiments it is shown that the requirement of domination of one experiment by another for all decision problems is too strong to provide a reasonable basis for comparison for one parameter problems with monotone likelihood ratio it is therefore proposed to restrict the comparison to decision problems that are monotone in the sense of karlin and rubin 1956 application of this weaker definition to the location problem is shown to give satisfactory results a scale free comparison of this type leads to a new tail ordering of distributions and this is explored in section 6

algebraic expressions for some so n racah coefficients in this paper the algebraic expressions for so n racah coefficients involving the coupling of three irreducible representations 1 0 over dot m 1 m 2 m 3 0 over dot are given by using the building up process their properties are discussed in detail c 1998 american institute of physics s0022 2488 98 01811 8

connections between some criteria to compare fuzzy information systems abstract in previous papers we have examined the extension of some methods to compare random experiments to the case in which the available experiment information is fuzzy in this paper we analyze the relationships between the criteria based on blackwell s sufficiency and some criteria based on well known information measures

a class of generalised 9 j symbols for sp 2n the symbolic method of kramers 1930 is used to obtain an expression for a 9 j symbol in terms of multiple products of spinor invariants this technique is generalised from the unitary compact symplectic group sp 2 to sp 2n and a generating function is found for a class of multiplicity free 9 sigma symbols where sigma denotes an irreducible representation of sp 2n of the form sigma 1 sigma 2 sigma n for which sigma i 0 i 1 schwinger s generating function for a 9 j symbol is recovered by setting n 1 a specialisation to 6 sigma symbols is made by setting one of the nine irreducible representations equal to the scalar 00 0 and the method is checked by working out a sample 6 sigma symbol previously obtained by an aufbau approach

a sequential selection method of a fixed number of fuzzy information systems based on the information energy gain on the basis of the information energy gain for fuzzy information systems a sequential selection method of a fixed number of fuzzy information systems is presented the information energy gain is a measure of the quantity of information concerning the state space provided by a fuzzy information system x when a prior probability distribution has been defined on the state space

sufficient fuzzy information systems in this paper we suggest and study a new selection criterion in order to compare probabilistic information systems when the available information from them is vague in the sense that it might be considered as fuzzy information tanaka okuda and asai this criterion is based on the concept of sufficient probabilistic information system established by blackwell

algebraic formulas for some nontrivial un 6j symbols and umn um un 3jm symbols we give tables of algebraic formulas for some nontrivial 6j symbols and 3jm symbols of the unitary groups the tables demonstrate that the building up method can be used successfully to obtain the rank dependence of unitary group j and jm symbols to emphasize the rank dependent nature of this calculation we have employed the composite young tableaux notation or back to back notation to label the unitary group irreps in using this notation the transpose conjugate symmetry of the corresponding composite young diagram leads to a new symmetry of the unitary group 6j and 3jm symbols the transposition of the groups um and un gives rise to a further symmetry of the 3jm symbols of umn um un

weak gibbs measures for intermittent systems and weakly gibbsian states in statistical mechanics in this paper we associate weak gibbs measures for intermittent maps with non gibbsian weakly gibbsian states in statistical mechanics in the sense of dobrushin 4 5 we show a higher dimensional intermittent map of which the sinai bowen ruelle measure is a weak gibbs equilibrium state and a weakly gibbsian state in the sense of dobrushin admitting essential discontinuities in its conditional probabilities

algebraic expressions for some multiplicity free 6j symbols and isoscalar factors for g2 generalized 6j symbols for g2 in which all four triangular conditions involve the seven dimensional irreducible representation irrep 10 are multiplicity free algebraic expressions depending on the highest weights of the accompanying irreps are found by using generalizations of the racah wigner algebra a rule is given for generalizing the so 3 phase factors the results are applied to finding algebraic expressions for a class of isoscalar factors for so 7 g2

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

some statistical applications of generalized jensen difference divergence measures for fuzzy information systems in previous papers we have compared statistical experiments by considering unified scalar parametric generalizations of the jensen difference divergence measure in this paper we first introduce generalized jensen difference divergence measures when the available information from the experiment is not exact in order to compare fuzzy information systems then we establish the relationship between extended fisher information and the generalized r s jensen difference divergence measures