covariance and geometrical invariance in quantization several notions of invariance and covariance for products with respect to lie algebras and lie groups are investigated some examples including the poincare group are given the passage from the lie algebra invariance to the lie group covariance is performed the compact and nilpotent cases are treated

w covariance of the weyl wigner groenewold moyal quantization the differential structure of operator bases used in various forms of the weyl wigner groenewold moyal wwgm quantization is analyzed and a derivative based approach alternative to the conventional integral based one is developed thus the fundamental quantum relations follow in a simpler and unified manner an explicit formula for the ordered products of the heisenberg weyl algebra is obtained the w covariance of the wwgm quantization in its most general form is established it is shown that the group action of w that is realized in the classical phase space induces on bases operators in the corresponding hilbert space a similarity transformation generated by the corresponding quantum w which provides a projective representation of the former w explicit expressions for the algebra generators in the classical phase space and in the hilbert space are given it is made manifest that this w covariance of the wwgm quantization is a genuine property of the operator bases

second order resolvability intrinsic randomness and fixed length source coding for mixed sources information spectrum approach the second order achievable asymptotics in typical random number generation problems such as resolvability intrinsic randomness and fixed length source coding are considered in these problems several researchers have derived the first order and the second order achievability rates for general sources using the information spectrum methods although these formulas are general their computations are quite hard hence an attempt to address explicit computation problems of achievable rates is meaningful in particular for i i d sources the second order achievable rates have earlier been determined simply by using the asymptotic normality in this paper we consider mixed sources of two i i d sources the mixed source is a typical case of nonergodic sources and whose self information does not have the asymptotic normality nonetheless we can explicitly compute the second order achievable rates for these sources on the basis of two peak asymptotic normality in addition extensions of our results to more general mixed sources such as a mixture of countably infinite i i d sources or markov sources and a continuous mixture of i i d sources are considered

free vibration of axially loaded rotating timoshenko shaft systems by the wave train closure principle a systematic approach for the free vibration analysis of a rotating timoshenko shaft system subjected to axial forces is presented in this paper the system has multiple point discontinuities such as elastic supports rotor masses and cross sectional changes wave reflection and transmission matrices are employed to characterize the wave motions between the sub spans of the shaft system these matrices are combined with the field transfer matrices expressed in wave forms to obtain the characteristic equation in a straightforward manner the solutions are exact since effects of attenuating wave components are included in the formulation the wave propagation based matrix algebra leads to recursive algorithms which are suitable for computer coding three examples are presented to illustrate the numerical procedure

uniform random number generation from markov chains non asymptotic and asymptotic analyses in this paper we derive non asymptotic achievability and converse bounds on the random number generation with without side information our bounds are efficiently computable in the sense that the computational complexity does not depend on the block length we also characterize the asymptotic behaviors of the large deviation regime and the moderate deviation regime by using our bounds which implies that our bounds are asymptotically tight in those regimes we also show the second order rates of those problems and derive single letter forms of the variances characterizing the second order rates furthermore we address the relative entropy rate and the modified mutual information rate for these problems

influence of centerline extensibility on the in plane free vibrations of loaded circular arches free vibrations of circular arches about a prestressed static equilibrium state are investigated the equations of motion for the small amplitude free vibrations about the initial equilibrium state attained under distributed tangential and normal loading derived in a previous paper and specialized to constant curvature are used particular attention is given to the influence of centerline stretching during the vibratory motion the vanishing of the loaded free vibration frequencies signals static buckling and the load intensities at which the frequencies go to zero correspond to the static buckling loads free vibrations with no initial loading is treated as a special case of the problem considered it is shown that exact numerical values for the frequencies can be obtained in this case in general the presence of distributed initial loading precludes the possibility of obtaining closed form analytical solutions barring a few simple loading situations such as uniform constant directional pressure as the governing differential equations have variable coefficients in the present work numerical results are obtained for uniform arches subjected to gravity loading the galerkin method with polynomial trial functions that satisfy the geometric boundary conditions is employed in obtaining accurate values of free vibration frequencies convergence of the method with increasing number of terms in the assumed expansion representing the true solution is demonstrated arches with pinned and clamped end support conditions are considered considerably different frequencies are found depending upon whether one includes or ignores the influence of centerline stretching during the vibratory motion

source resolvability and intrinsic randomness two random number generation problems with respect to a subclass of f divergences this paper deals with two typical random number generation problems in information theory one is the source resolvability problem resolvability problem for short and the other is the intrinsic randomness problem in the literature optimum achievable rates in these two problems with respect to the variational distance as well as the kullback leibler kl divergence have already been analyzed on the other hand in this study we consider these two problems with respect to f divergences the f divergence is a general non negative measure between two probabilistic distributions on the basis of a convex function f the class of f divergences includes several important measures such as the variational distance the kl divergence the hellinger distance and so on hence it is meaningful to consider the random number generation problems with respect to f divergences in this paper we impose some conditions on the function f so as to simplify the analysis that is we consider a subclass of f divergences then we first derive general formulas of the first order optimum achievable rates with respect to f divergences next we particularize our general formulas to several specified functions f as a result we reveal that it is easy to derive optimum achievable rates for several important measures from our general formulas the second order optimum achievable rates and optimistic optimum achievable rates have also been investigated

security analysis of varepsilon almost dual universal 2 hash functions smoothing of min entropy versus smoothing of renyi entropy of order 2 recently varepsilon almost dual universal2 hash functions have been proposed as a new and wider class of hash functions using this class of hash functions several efficient hash functions were proposed this paper evaluates the security performance when we apply this kind of hash functions we evaluate the security in several kinds of setting based on the l 1 distinguishability criterion and the modified mutual information criterion the obtained evaluation is based on smoothing of renyi entropy of order 2 and or min entropy we clarify the difference between these two methods

phase space functions and correspondence rules it is shown that positive quantum joint distributions in phase space lead to quantum mechanical operators depending on the state to be considered it is also shown that a simple requirement of canonical invariance leads to the weyl correspondence rule as the only allowed one

separation of random number generation and resolvability we consider the problem of determining when a given source can be used to approximate the output due to any input to a given channel we provide achievability and converse results for a general source and channel for the special case of a full rank discrete memoryless channel we give a stronger converse result than we can give for a general channel

mode localization phenomena in large space structures the possibility of localization or confinement of vibratory modes in large space structures is investigated theoretically and numerically these structures belong to a class of periodic structures that have recently been shown to be sensitive to periodicity b reaking disorder or imperfections when localization occurs the modal amplitude of a global mode becomes confined to a local region of the structure with serious implications for the control problem the results of this study indicate that mode localization is most likely to occur in structures consisting of a large number of weakly coupled substructures certain large space structures with high modal densities fall in this category and it is therefore important to include the effect of structural imperfections and disorder when designing control systems for shape or directional control of such structures k kh kw ku k k m m m n n p qi qt t u v w uf 8fj e 6

performance analysis of the interval algorithm for random number generation based on number systems in this paper we analyze the interval algorithm for random number generation proposed by han and hoshi using the expression of real numbers on the interval we first establish an explicit representation of the interval algorithm with the representation of real numbers on the interval based on number systems next using the expression of the interval algorithm we give a rigorous analysis of the interval algorithm we discuss the difference between the expected number of the coin tosses in the interval algorithm and their upper bound derived by han and hoshi and show that it can be characterized explicitly with the established expression of the interval algorithm

interval algorithm for random number generation the problem of generating a random number with an arbitrary probability distribution by using a general biased m coin is studied an efficient and very simple algorithm based on the successive refinement of partitions of the unit interval 0 1 which we call the interval algorithm is proposed a fairly tight evaluation on the efficiency is given generalizations of the interval algorithm to the following cases are investigated 1 output sequence is independent and identically distributed i i d 2 output sequence is markov 3 input sequence is markov 4 input sequence and output sequence are both subject to arbitrary stochastic processes

free vibration analysis of planar curved beams by wave propagation in this paper a systematic approach for the free vibration analysis of a planar circular curved beam system is presented the system considered includes multiple point discontinuities such as elastic supports attached masses and curvature changes neglecting transverse shear and rotary inertia harmonic wave solutions are found for both extensional and inextensional curved beam models dispersion equations are obtained and cut off frequencies are determined wave reflection and transmission matrices are formulated accounting for general support conditions these matrices are combined with the aid of field transfer matrices to provide a concise and efficient method for the free vibration problem of multi span planar circular curved beams with general boundary conditions and supports the solutions are exact since the effects of attenuating wave components are included in the formulation several examples are presented and compared with other methods

dynamic characteristics and mode localization of elastically constrained axially moving strings and beams abstract the free vibration response of an axially moving string and euler bernoulli beam supported by an intermediate elastic constraint is studied the transfer function method is used to formulate the free response solution for the beam the elastic constraint can consist of either a transverse spring or both transverse and rotational springs the effects of both speed and tension on mode localization are studied a wave analysis is employed to further investigate the behaviour of the systems reflection and transmission coefficients are formulated to show the effects of the system parameters on the coupling of the subsystems the addition of the constraint is shown to increase the critical speed of the beam for low values of tension for the string mode localization increases as speed increases however the behaviour of the beam is shown to change significantly depending on both the system parameters and type of constraint the effects of tension and speed on the delocalization frequency of the weakly bi coupled beam are also presented

mode localization in multispan beams the finite element method is used to study localization as a function of timoshenko beam effects beam end conditions span length mass and stiffness imperfection viscous damping axial force transverse support and rotational coupling stiffness and modeling resolution three configurations are studied starting with two separate 2 span models and culminating in a 10 span configuration that resembles lattice type large space structures

ordered products w algebra and two variable definite parity orthogonal polynomials it has been shown that the cartan subalgebra of w algebra is the space of the two variable definite parity polynomials explicit expressions of these polynomials and their basic properties are presented it also has been shown that they carry the infinite dimensional irreducible representation of the su 1 1 algebra having the spectrum bounded from below a realization of this algebra in terms of difference operators is also obtained for particular values of the ordering parameter s they are identified with the classical orthogonal polynomials of a discrete variable such as the meixner meixner pollaczek and askey wilson polynomials with respect to variable s they satisfy a second order eigenvalue equation of hypergeometric type exact scattering states with zero energy for a family of potentials are expressed in terms of these polynomials it has been put forward that it is the inonu wigner contraction and its inverse that form a bridge between the difference and differential calculus

the quantum normal form and its equivalents a quantum analog called the quantum normal form of the classical birkhoff gustavson normal form is presented the algebraic relationship between the quantum and birkhoff gustavson normal forms has been established by developing the latter using lie transforms it is shown that the birkhoff gustavson normal form can be obtained from the quantum normal form using an anharmonic oscillator and a henon heiles system as test cases the equivalence between the quantum normal form and the rayleigh schrodinger perturbation method is shown this equivalence provides an algebraic connection between the birkhoff gustavson normal form and the rayleigh schrodinger perturbation approach the question of weyl and torus quantizations of the birkhoff gustavson normal form is discussed in the light of the quantum normal form

quantum mechanics of non linear systems a generalisation of weyl s correspondence rule and the associated moyal bracket for systems with non linear phase spaces that admit symplectic transitive group actions is presented this provides a simple account with explicit constructions of some of the general results of bayen et al 1978

generating random bits from an arbitrary source fundamental limits suppose we are given a random source and want to use it as a random number generator at what rate can we generate fair bits from it we address this question in an information theoretic setting by allowing for some arbitrarily small but nonzero deviation from ideal random bits we prove our results with three different measures of approximation between the ideal and the obtained probability distributions the variational distance the d bar distance and the normalized divergence two different contexts are studied fixed length and variable length random number generation the fixed length results of this paper provide an operational characterization of the inf entropy rate of a source defined in han and verdu see ibid vol 39 no 3 p 752 772 1993 and the variable length results characterize the liminf of the entropy rate thereby establishing a pleasing duality with the fundamental limits of source coding a feature of our results is that we do not restrict ourselves to ergodic or to stationary sources

general formulas for fixed length quantum entanglement concentration in this paper we derive general formulas for the amount of entanglement that can be concentrated from general sequences of partially entangled bipartite pure states the formulas are obtained by using an information spectrum approach the formulas obtained express the optimal rate under constant error constraints or exponential error constraints in the asymptotic framework since the formulas treat general sequences they can be applied to i i d sequences as well as sequences with correlations

wigner quantisation of arrival time and oscillator phase by means of the wigner distribution function an expression is derived for the quasiprobability that a free particle in one dimension arrives at the origin during a given time interval and also for the quasiprobability that the phase of a one dimensional harmonic oscillator lies in a given segment of the circle it is shown that the best bounds on these quasiprobabilities p are 0 1559 or p or 1 0077 independent of the size of the interval it is shown that on disjoint unions of infinitely many intervals the quasiprobabilities may add up to any positive or negative real value it is briefly indicated how negative probabilities can be avoided altogether in an alternative approach to the quantisation of arrival time and oscillator phase

tight exponential analysis of universally composable privacy amplification and its applications motivated by the desirability of universal composability we analyze in terms of l1 distinguishability the task of secret key generation from a joint random variable under this secrecy criterion using the renyi entropy of order 1 s for s 0 1 we derive a new upper bound of eve s distinguishability under the application of the universal2 hash functions it is also shown that this bound gives the tight exponential rate of decrease in the case of independent and identical distributions the result is applied to the wiretap channel model and to secret key generation distillation by public discussion

the proper quantum analogue of the birkhoff gustavson method of normal forms a deformation approach resolves problems concerning the ordering of operators and the commutation of quantization with canonical transformation this completes the programme of robnik 1984 to develop a purely algebraic method for the quantization of non integrable hamiltonian systems about a point of stable equilibrium

energy momentum tensor in phase space a connection between schrodinger energy momentum tensor and terletsky distribution function schrodinger energy momentum tensor for a matter field interacting with an external electromagnetic field is represented in phase space by means of terletsky distribution function the explicit form of this distribution function in the case of a hydrogen type atom is found the structure of the schrodinger energy momentum tensor in phase space is compared with the structure of a real fluid and its local pressure and local energy are presented in the fundamental state of a hydrogen type atom the negative values of the terletsky distribution function are not rejected in view of their participation in the phase space energy momentum tensor the negative part of the quantum distribution function could be interpreted as phase space density for anti constituents in a hypothetical sub quantum level of the matter

folklore in source coding information spectrum approach information theory has several traditional folklore problems about data compression or channel coding with reference to random number generation problems here we focus on and reasonably formulate one of them from the viewpoint of information spectra specifically we verify the validity of the folklore that the output from any source encoder working at the optimal coding rate with asymptotically vanishing probability of error looks like almost completely random

random number conversion and locc conversion via restricted storage we consider random number conversion rnc through random number storage with restricted size we clarify the relation between the performance of rnc and the size of storage in the framework of the first and second order asymptotics and derive their rate regions then we show that the results for rnc with restricted storage recover those for conventional rnc without storage in the limit of storage size to treat rnc via restricted storage we introduce a new kind of probability distributions named generalized rayleigh normal distributions using the generalized rayleigh normal distributions we can describe the second order asymptotic behavior of rnc via restricted storage in a unified manner as an application to quantum information theory we analyze locc conversion via entanglement storage with restricted size moreover we derive the optimal locc compression rate under a constraint of conversion accuracy

birkhoff gustavson normal form in classical and quantum mechanics a quantum analogue of the classical transformations to the birkhoff gustavson normal form is derived with unitary transformations taking over the role of canonical transformations the author finds a striking similarity to lie transformations in the classical case the author suggests that the quantum normal form is identical to the rayleigh schrodinger perturbation series and thus usually only asymptotic to the eigenvalues the convergence question of both classical and quantum normal forms is discussed in some detail

strong secrecy from channel resolvability we analyze physical layer security based on the premise that the coding mechanism for secrecy over noisy channels is tied to the notion of channel resolvability instead of considering capacity based constructions which associate to each message a subcode that operates just below the capacity of the eavesdropper s channel we consider channel resolvability based constructions which associate to each message a subcode that operates just above the resolvability of the eavesdropper s channel building upon the work of csiszar and hayashi we provide further evidence that channel resolvability is a powerful and versatile coding mechanism for secrecy by developing results that hold for strong secrecy metrics and arbitrary channels specifically we show that at least for symmetric wiretap channels random capacity based constructions fail to achieve the strong secrecy capacity while channel resolvability based constructions achieve it we then leverage channel resolvability to establish the secrecy capacity region of arbitrary broadcast channels with confidential messages and a cost constraint for strong secrecy metrics finally we specialize our results to study the secrecy capacity of wireless channels with perfect channel state information csi mixed channels and compound channels with receiver csi as well as the secret key capacity of source models for secret key agreement by tying secrecy to channel resolvability we obtain achievable rates for strong secrecy metrics with simple proofs

equivocations exponents and second order coding rates under various renyi information measures we evaluate the asymptotics of equivocations their exponents as well as their second order coding rates under various renyi information measures specifically we consider the effect of applying a hash function on a source and we quantify the level of non uniformity and dependence of the compressed source from another correlated source when the number of copies of the sources is large unlike previous works that use shannon information measures to quantify randomness information or uniformity we define our security measures in terms of a more general class of information measures the renyi information measures and their gallager type counterparts a special case of these renyi information measure is the class of shannon information measures we prove tight asymptotic results for the security measures and their exponential rates of decay we also prove bounds on the second order asymptotics and show that these bounds match when the magnitudes of the second order coding rates are large we do so by establishing new classes non asymptotic bounds on the equivocation and evaluating these bounds using various probabilistic limit theorems asymptotically

quantum canonical invariance a moyal approach the quasiclassical generalised moyal quantisation procedure is applied to the problem of quantum canonical invariance simple new formulae for the moyal bracket corresponding to various correspondence rules are given and are used to calculate the additional potential terms arising from a point canonical transformation made on a free hamiltonian the status of canonical transformations in other equivalent quantum phase space formulations is also reviewed

coding theorems on the threshold scheme for a general source in this paper coding theorems on the t m threshold scheme for a general source are discussed where m means the number of the shares and t means a threshold the t m threshold scheme treated in this paper encrypts n source outputs xn to m shares at once and is required to satisfy the two conditions that 1 xn is reproduced from arbitrary t shares and 2 almost no information of xn is revealed from any t 1 shares it is shown that the t m threshold scheme must satisfy certain inequalities including the limit inferiors in probability one of the inequalities is closely related to the minimum length of the fair random bits needed to a dealer for realizing the t m threshold scheme in addition it is shown that a certain variation of shamir s threshold scheme meets the two conditions the same approach can be taken to the problems of shannon s cipher system with the perfect secrecy and fixed length source coding with vanishing decoding error probability it is shown that the same kind of inequalities which indicate the converse coding theorems hold in both two cases

free vibration of elastically coupled dual span curved beams the free vibration response of dual span extensional and inextensional circular curved beams constrained by an intermediate elastic support is studied the elastic constraint consists of a transverse and rotational spring as well as a tangential spring which couples the extensional motion of one span with the other wave propagation techniques are used to formulate the eigenvalue problem which result in exact eigensolutions the effects of the support type and stiffness on the transverse and tangential modes are examined in addition the influence of the curvature on the free response of the extensional curved beam is also addressed for certain support conditions the extensional and inextensional curved beams have similar behavior in general however the behavior of the system is shown to depend strongly on the type of support the modeling of the beam as extensional or inextensional and whether the natural frequencies are above or below the cut off frequency

second order asymptotics of conversions of distributions and entangled states based on rayleigh normal probability distributions we discuss the asymptotic behavior of conversions between two independent and identical distributions up to the second order conversion rate when the conversion is produced by a deterministic function from the input probability space to the output probability space to derive the second order conversion rate we introduce new probability distributions named rayleigh normal distributions the family of rayleigh normal distributions includes a rayleigh distribution and coincides with the standard normal distribution in the limit case using this family of probability distributions we represent the asymptotic second order rates for the distribution conversion as an application we also consider the asymptotic behavior of conversions between the multiple copies of two pure entangled states in quantum systems when only local operations and classical communications locc are allowed this problem contains entanglement concentration entanglement dilution and a kind of cloning problem with locc restriction as special cases

on the operator bases underlying wigner s kirkwood s and glauber s phase space functions the hermitian operators behind wigner s phase space function 1932 are recognised to be simple ordered exponentials of the dynamical variables this operator basis is highly symmetric it supplies a perfectly unbiased formulation of operator equations in terms of phase space functions which is as close to classical physics as it possibly can be the author demonstrates how the symmetry properties of the basis can be exploited to simplify the computation of wigner functions enormously the ordered operator methods are also applicable to the phase space functions of kirkwood 1933 and glauber 1963 type both kinds are briefly discussed with emphasis on how they differ from wigner s description

source and channel simulation using arbitrary randomness necessary and sufficient conditions for approximation of a general channel by a general source are proved for the special case of a deterministic channel input which corresponds to source simulation we prove a stronger necessary condition as the approximation criteria vanishing variational distance between the original and the approximated quantity is used for both of the problems both necessary and sufficient conditions for the two problems are based on some individual properties of the sources and the channel and are relatively easy to evaluate in particular unlike prior results for this problem our results do not require solving an optimization problem to test simulatability the results are illustrated with several nonergodic examples

classical versus quantum integrability classical integrability and quantum integrability are compared for two degrees of freedom hamiltonian systems we use c number representatives for quantum operators and the moyal bracket for the commutator three different cases are found i the c number representative of the quantum mechanical second invariant is identical to the classical second invariant ii o 2 corrections are needed in the classical second invariant to obtain the quantum invariant and iii also the potential must be deformed by an o 2 term several examples from the henon heiles and holt families of integrable potentials are included

a general formula for channel capacity a formula for the capacity of arbitrary single user channels without feedback not necessarily information stable stationary etc is proved capacity is shown to equal the supremum over all input processes of the input output inf information rate defined as the liminf in probability of the normalized information density the key to this result is a new converse approach based on a simple new lower bound on the error probability of m ary hypothesis tests among equiprobable hypotheses a necessary and sufficient condition for the validity of the strong converse is given as well as general expressions for spl epsiv capacity

birkhoff gustavson normal form and the semiclassical energies of a double pendulum although the double pendulum is a well known system the literature is sparse with regard to the study of its full dynamical behaviour as a simple conservative system that displays both ordered and chaotic motion it poses an interesting problem for the study of classical quantum correspondence in this work we present its birkhoff gustavson normal form and semiclassical energies obtained from the normal form the pade summation technique is used to re sum the normal form series

on the uniqueness of the moyal structure of phase space functions uniqueness up to isomorphism of the moyal product and bracket of functions on as associative and lie deformations of the ordinary product and poisson bracket is known to follow under additional hypotheses using an integral formalism we show here that this result holds without these hypotheses

second order asymptotics in fixed length source coding and intrinsic randomness there is a difference between the optimal rates of fixed length source coding and intrinsic randomness when we care about the second order asymptotics we prove this difference for general information sources and then investigate independent and identically distributed i i d random variables and markovian variables as examples the difference is demonstrated through an investigation of the second order asymptotic behavior of the rates a universal fixed length source code attaining the second order optimal rate is also proposed the difference between the rates of fixed length source coding and intrinsic randomness proves that the outputs of fixed length source codes are not uniformly distributed

the algebraic quantisation of the birkhoff gustavson normal form the author develops an algebraic quantisation method for the birkhoff gustavson normal form for this purpose the weyl quantisation rule is used the method developed here for multidimensional systems allows one to calculate the energy levels and the transition probabilities the author gives a brief review of the normal form derives some of its general properties and finds a general analytic solution for the fourth degree normal form for hamiltonians of two degrees of freedom in particular this includes the henon heiles system the author compares the results of specific examples with other works the question of canonically invariant quantisation the relation to the quantum mechanical perturbation theory and the question of chaotic behaviour and quantum stochasticity are discussed the author shows that the operators corresponding to the formal integrals of the motion are also quantum mechanical integrals if the normal form accidentally terminates so that the classical system is integrable then this implies quantum integrability of the normal form hamiltonian

the parametrisation of quantisation rules equivalent to operator orderings and the effect of different rules on the physical spectrum the author recalls the problem of choosing an ordering for the terms in a hamiltonian of the form h p q of finite dimension in p q he demonstrates that most orderings which provide one with a hermitian operator are in fact redundant and he gives a general form for ordering rules in terms of arbitrary parameters he concludes that differences in the choice of an ordering contribute differences to the physics which are only of order 2 and higher he provides an example of a hamiltonian for which the spectrum is explicitly dependent on the choice of quantisation rule operator ordering he compares the method of characterising operator ordering rules with that of cohen 1966 1970 finally he generalises cohen s method to the case of all linear quantisation rules and shows how his rule is a special case

q deformed star products and moyal brackets the standard and antistandard ordered operators acting on two dimensional q deformed phase space are shown to satisfy algebras which can be called q w q star products and q moyal brackets corresponding to these algebras are constructed some applications like defining q classical mechanics and q path integrals are discussed

quantization on the virasoro group the quantization of the virasoro group is carried out by means of a previously established group approach to quantization we explicitly work out the two cocycles on the virasoro group as a preliminary step in our scheme the carrier space for all the virasoro representations is made out of polarized functions on the group manifold it is proved that this space does not contain null vector states even forc 1 although it is not irreducible the full reduction is achieved in a striaghtforward way by just taking a well defined invariant subspace c h the orbit of the enveloping algebra through the vacuum which is irreducible for any value ofc andh c h is a proper subspace of the space of polarized functions for those values ofc andh for which the kac determinant is zero we give the local version of these group representations as well as the associated classical phase space structures i e symplectic form and noether invariants

normal forms and quasi integrals for the hamiltonians of magnetic bottles the well known birkhoff gustavson normal form theory suffers from the restraint that the quadratic part of the hamiltonian must be of the harmonic oscillator type in this paper we describe a generalized normal form concept which can be applied to any polynomial hamiltonian thus rendering the above restriction to harmonic oscillators unnecessary as in the classical theory we can derive an asymptotic expression for a second integral of motion the truncated formal integral the quasi integral exhibits good convergence properties in regions of phase space where the dynamics is regular whereas in chaotic regions the convergence deteriorates in order to exemplify these findings we apply the theory to a hamiltonian describing a particular type of magnetic bottle which cannot be analysed using the birkhoff gustavson normal form we calculate the quasi integrals up to and including the 14th order and analyse their convergence properties

optimal algorithms for universal random number generation from finite memory sources we study random number generators rngs both in the fixed to variable length fvr and the variable to fixed length vfr regimes in a universal setting in which the input is a finite memory source of arbitrary order and unknown parameters with arbitrary input and output finite alphabet sizes applying the method of types we characterize essentially unique optimal universal rngs that maximize the expected output respectively minimize the expected input length in the fvr respectively vfr case for the fvr case the rng studied is a generalization of elias s scheme while in the vfr case the general scheme is new we precisely characterize up to an additive constant the corresponding expected lengths which include second order terms similar to those encountered in universal data compression and universal simulation furthermore in the fvr case we consider also a twice universal setting in which the markov order k of the input source is also unknown

asymptotic properties on codeword lengths of an optimal fv code for general sources this correspondence is concerned with asymptotic properties on the codeword length of a fixed to variable length code fv code for a general source x sup n sub n 1 sup spl infin with a finite or countably infinite alphabet suppose that for each n spl ges 1 x sup n is encoded to a binary codeword spl phi sub n x sup n of length l spl phi sub n x sup n letting spl epsiv sub n denote the decoding error probability we consider the following two criteria on fv codes i spl epsiv sub n 0 for all n spl ges 1 and ii lim sup sub n spl rarr spl infin spl epsiv sub n spl les spl epsiv for an arbitrarily given spl epsiv spl isin 0 1 under criterion i we show that if x sup n is encoded by an arbitrary prefix free fv code asymptotically achieving the entropy 1 nl spl phi sub n x sup n 1 nlog sub 2 1 px sup n x sup n spl rarr 0 in probability as n spl rarr spl infin under a certain condition where p sub x sup n denotes the probability distribution of x sup n under criterion ii we first determine the minimum rate achieved by fv codes next we show that 1 nl spl phi sub n x sup n of an arbitrary fv code achieving the minimum rate in a certain sense has a property similar to the lossless case

theorems on the variable length intrinsic randomness we address variable length intrinsic randomness problems in the sense of vembu and verdu 1995 for countably infinite source alphabet spl chi under the unnormalized divergence distance the normalized conditional divergence distance and the variational distance it turns out that under all three kinds of approximation measures the variable length intrinsic randomness still takes the same value called the inf entropy rate of the source