a new scheme to determine the weight distributions of binary extended quadratic residue codes this letter proposes a novel scheme which consists of a weight counting algorithm the combinatorial designs of the assmus mattson theorem and the weight polynomial of gleason s theorem to determine the weight distributions of binary extended quadratic residue codes as a consequence the weight distributions of binary 138 69 22 and 168 84 24 extended quadratic residue codes are given

the probability distribution of the partition function of the random energy model the authors give the expression for both integer and non integer moments of the partition function z of the random energy model in the thermodynamic limit they find that the probability distribution p z can be decomposed into two parts for log z log z finite the distribution is independent of n the size of the system whereas for log z log z positive and of order n the distribution is gaussian these two parts match in the region 1 log z log z n where the distribution is exponential

inverse branching rules a method is given for inverting branching rules which is based on a technique for computing kronecker products due to king 1981 this approach simplifies the calculation of plethysms and branching rules of representations of exceptional groups it may also be applied to basic spin plethysms

on the resolution of ordering ambiguities associated with the path integral representation of stochastic processes simple path integral approaches to multiplicative stochastic processes are severely hampered by an inherent ambiguity in the underlying lagrangian associated with operator ordering problems the author shows how given the fokker planck equation the ambiguity can be resolved direct consequences for noise induced transitions reaction diffusion models and polymer dynamics are briefly discussed

position space renormalisation group for directed diffusion limited aggregation the author uses a position space renormalisation group transformation to show that directed diffusion limited aggregation and directed animals are in different universality classes

duadic codes a new family of binary cyclic n n 1 2 and n n 1 2 codes are introduced which include quadratic residue qr codes when n is prime these codes are defined in terms of their idempotent generators and they exist for all odd n p 1 a 1 p 2 a 2 cdots p r a r where each p i is a prime equiv pm 1 pmod 8 dual codes are identified the minimum odd weight of a duadic n n 1 2 code satisfies a square root bound when equality holds in the sharper form of this bound vectors of minimum weight hold a projective plane the unique projective plane of order 8 is held by the minimum weight vectors in two inequivalent 73 37 9 duadic codes all duadic codes of length less than 127 are identified and the minimum weights of their extensions are given one of the duadic codes of length 113 has greater minimum weight than the qr code of that length

a hopf laboratory for symmetric functions an analysis of symmetric function theory is given from the perspective of the underlying hopf and bi algebraic structures these are presented explicitly in terms of standard symmetric function operations particular attention is focused on laplace pairing sweedler cohomology for 1 and 2 cochains and twisted products rota cliffordizations induced by branching operators in the symmetric function context the latter are shown to include the algebras of symmetric functions of orthogonal and symplectic type a commentary on related issues in the combinatorial approach to quantum field theory is given

a solution to the su n external state labelling problem based upon a u n 1 n 1 group i general theory the state labelling problem arising in the reduction of the direct product of a p positive row u n irreducible representation h1 hp0 with a q negative row one 0 h q h 1 into a sum of mixed u n irreducible representations k1 kp0 k q k 1 is solved by using the complementarity between u n and u p q within some positive discrete series irreducible representations of u pn qn this complementarity allows analysis of the problem in terms of the group chain u p q contains implies u p u q instead of u n u n contains implies u n for the most general su n irreducible representations corresponding to p q n 1 the relevant group chain is therefore u n 1 n 1 contains implies u n 1 u n 1 in such a case the additional labels include those of an intermediate u n 1 irreducible representation h1s hn 1s as well as the additional labels solving the state labelling problems for the products k1 kn 1 h1s hn 1s and k 1 k n 1 h1s hn 1s of u n 1 irreducible representations hence the proposed solution reflects in a direct way the operation of king s branching rule for the chain u n u n contains implies u n supplemented whenever necessary with king s modification rule

exact macroscopic dynamics in non equilibrium chemical systems non equilibrium reaction diffusion models show an exciting array of critical phenomena ranging from the continuous transitions reminiscent of equilibrium systems to the spectacular chemical oscillators transforming the underlying stochastic master equations using poisson techniques the author obtains for the first time a comprehensive description of the dynamics including in particular the problematical multitime correlation functions the formalism is ideally adapted for the use of scaling and renormalisation group ideas

field theoretic formulation of an epidemic process with immunisation the author describes a model of the spread of an epidemic on a lattice in which sites may be infected by their neighbours after which they recover and are subsequently immune it corresponds to a modification of the directed percolation problem and also to a growth model of clusters the model is analysed using a continuum field theory both within a self consistent approximation and using an epsilon expansion below six transverse dimensions

trunk density profile estimates from dual x ray absorptiometry accurate body segment parameters are necessary to estimate joint loads when using biomechanical models geometric methods can provide individualized data for these models but the accuracy of the geometric methods depends on accurate segment density estimates the trunk which is important in many biomechanical models has the largest variability in density along its length therefore the objectives of this study were to 1 develop a new method for modeling trunk density profiles based on dual x ray absorptiometry dxa and 2 develop a trunk density function for college aged females and males that can be used in geometric methods to this end the density profiles of 25 females and 24 males were determined by combining the measurements from a photogrammetric method and dxa readings a discrete fourier transformation was then used to develop the density functions for each sex the individual density and average density profiles compare well with the literature there were distinct differences between the profiles of two of participants one female and one male and the average for their sex it is believed that the variations in these two participants density profiles were a result of the amount and distribution of fat they possessed further studies are needed to support this possibility the new density functions eliminate the uniform density assumption associated with some geometric models thus providing more accurate trunk segment parameter estimates in turn more accurate moments and forces can be estimated for the kinetic analyses of certain human movements

dual bases and some coupling coefficients for su4 su2 su2 sun son and sp4 u2 general analytical expressions for isoscalar factors reduced wigner coefficients for the couplings p0 0q to 0 and p10 p20 to 0 in the chains su4 su2 su2 and sun son n 3 are derived by using the algebra of complementary groups and methods of analytical continuation a review of alternative approaches to the problem grounded on the concept of biorthogonal systems of non canonical bases is given it is demonstrated that the construction of dual bases polynomial and stretched or related ones is associated with the use of certain bilinear combinations of isoscalar factors and solutions of the boundary value problem for isoscalar factors overlaps are given for different non canonical basis states of the two parametric irreducible representations for the chains su4 su2 su2 sun son and sp4 u2 as well as the expansions of the projected basis states for sp4 u2 in terms of canonical basis states a new expression for some special su2 clebsch gordan coefficients is also given

equivalence between poisson representation and fock space formalism for birth death processes the equivalence between the poisson representation and the fock space formalism both used to derive coarse grained equations from the master equation for non equilibrium systems is explicitly demonstrated

a generalised self avoiding walk the authors study a generalised self avoiding walk on a lattice in which each vertex may be visited less than k time turban 1983 has argued that for this model the critical exponents should change continuously with k from the standard self avoiding walk exponents k 2 to mean field exponents by generating series expansions for both two and three dimensional lattices the authors find strong support for the conventional and opposing view that the critical exponents remain unchanged for finite k only taking on their mean field values in the limit k to infinity

holomorphic discrete series and harmonic series unitary irreducible representations of non compact lie groups sp 2n r u p q and so 2n generalised characters of the infinite dimensional holomorphic discrete series unitary irreducible representations of the non compact groups u p q sp 2n r and so 2n are explicitly expressed in terms of characters of finite dimensional unitary group representations these formulae are remarkably succinct despite involving certain infinite series of schur functions similar formulae are derived for harmonic series unitary representation of both u p q and sp 2n r consideration of the branching rules from u p q to u q p and from sp 2n r to u n enables holomorphic representations to be identified as a subset of the harmonic representations the branching rules are established in full generality and are then used in the evaluation of tensor products of both holomorphic and harmonic representations in the case of the former a known result is recast in terms of closed formulae involving schur functions and for the latter various generalisations of these formulae are given a conjecture is also made regarding what might be the simplest possible formulae covering all holomorphic and harmonic representations of sp 2n r and u p q illustrative examples are presented

fluctuations in the random link matching problem using the replica approach and the cavity method we study the fluctuations of the optimal cost in the random link matching problem by means of replica arguments we derive the exact expression of its variance moreover we study the large deviation function deriving its expression in two different ways namely using both the replica method and the cavity method

dimensional crossover in directed percolation the authors study the dimensional crossover in directed percolation in three dimensions bonds are allowed to have different concentrations along the three cartesian axes of the lattice through a position space renormalisation group one obtains the phase diagram where nonpercolating 1d 2d and 3d percolating phases are present the authors find that contrary to what happens in undirected percolation the isotropic fixed points are unstable with respect to concentration anisotropy numerical estimates are given for the values of critical probabilities and exponents which are in fairly good agreement with other results where available

s function series revisited a systematic and readily programmable computational method is given to extract the s function content of any arbitrary symmetric polynomial function applications to the derivation of new series and the outer product or skew division of an s function by a series are shown

the weight distributions of extended binary primitive bch codes of length 128 in previous work a method was presented to compute the weight distribution of a linear block code by using its trellis diagram in this correspondence the method is improved by using the trellis structure of linear block codes another method with reduced computational complexity is also proposed which uses the invariant property of a code with these methods the weight distributions of all extended binary primitive bch codes of length 128 are computed except for those for which the formulas of the weight distribution are known it turns out that 128 64 22 extended binary primitive bch code is formally self dual the probability of an undetectable error for each code is computed and its monotonicity is examined

extended poincare supersymmetry rotation groups and branching rules the decomposition of the basic spin irreps of the special orthogonal group so2k into irreps of sod 2 k where d is the spacetime dimension of the extended d dimensional poincare supersymmetry and k is the appropriate automorphism group is determined general results for d 10 several new branching rules for subgroups of so2k are developed a number of specific results are tabulated

spectrum generating functions for strings and superstrings the spectrum generating functions for a variety of strings and superstrings are derived these are expressed in terms of characters of irreducible representations of the appropriate transverse spacetime symmetry group and in the case of heterotic strings the relevant gauge group e8 e8 or spin 32 z2 the expansions involve principal specialisations of characters of both gl n and gl m n in the limit as m and n tend to infinity by using schur function methods modification rules and various theta function identities a number of spectrum generating functions are derived and tabulated the equivalence of the gso projected neveu schwarz ramond superstring and the green schwarz superstring is proved and the connection between the lattice formulation and the gso projected neveu schwarz ramond formulation of heterotic strings is spelled out

geometric and inertial data of the trunk in adult males in this study investigations on geometric and inertial quantities of 15 male patients trunks are described layers of 8 mm were scanned using computerized tomography thorax abdomen pelvis and two shoulders and their unchangeable and changeable muscle fat and skin tissues were investigated the trunk was also divided into portions and subportions according to anthropological landmarks by comparing subportions to right non circular frusta the volume of the trunk is obtained volume mass and density of trunk s segments and their tissues are given the location of the centers of mass of the segments is also provided regression equations are presented for the calculation of volume of tissues and of subportions application of the data for locating the center of mass of the body for building anthropometric dummies and for calculating the load acting on any level of a spine are presented

upper bounds for multiplicities in a tensor product of representations and in a restriction of group representations to a subgroup upper bounds for multiplicities of irreducible representations of a semisimple compact lie group in the tensor product of representations and multiplicities of irreducible representations of a subgroup in an irreducible representation of a group are derived pairs of groups and subgroups appear from the representation theory of non compact groups

vertex operators and composite supersymmetric s functions the s function basis for the fock space of vertex operator constructions is considered where states are associated with partitions mod lambda the authors show that the matrix element lambda mod valpha z mod mu is essentially given by the composite s function slambda mu z where the argument z identical to z 1 is replicated mod alpha mod times matrix elements of products of vertex operators lambda mod valpha z v beta w mod mu are given up to functions of z w independent of lambda and mu by the composite supersymmetric s function slambda mu z w where the z w are replicated mod alpha mod mod beta mod times the supersymmetric arguments being those associated with negative roots

a note on extended quadratic residue codes over gf 9 and their ternary images corresp we discuss 2 p 1 p 1 double circulant codes which are the ternary images of the p 1 p 1 2 extended quadratic residue codes over gf 9 here p is a prime of the form p 12k pm 5 as a special result we obtain a 64 32 18 ternary self dual code which is the largest known code meeting the bound of mallows and sloane

symmetric and unitary group representations i duality theory an extension of the schur weyl duality connecting the representations of the symmetric and unitary groups is given the schur weyl basis is constructed using annihilation and creation operators three factorisation lemmas are derived their importance lies in the fact that they relate the phase freedoms within the racah wigner algebra of the symmetric groups and the unitary groups extensions of the regge symmetries are also given these are expressed in five duality relations

on phase diagrams for directed percolation problems the authors propose a real space renormalisation group scheme for anisotropic directed bond percolation in two dimensions which differing from previous phenomenological or small cell real space renormalisation groups is sensitive to the existence of an infinite cluster along any lattice direction this enables them to explore new aspects of the phase diagram for the problem which were not accessible through existing treatments in particular the crossover exponent between one and two dimensional behaviour is shown to be exactly one for directed percolation numerical estimates are in agreement with known inequalities

branching rules and even dimensional rotation groups so2k unambiguous methods are developed for calculating branching rules for the classical subgroups of the even dimensional rotation group so2k complete results are given for the subgroups suk u1 so2k 2 u1 so2p so2q and so2p 1 so2q 1 a number of examples relevant to problems in supergravity and unification theories are given a complete resolution of the antisymmetric powers of the basic spinor irrep of so10 is given and the results extended to so11

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

the theory of angular momenta and higher su n symmetries the authors discuss interrelations between generating invariants gi for the reduction pi mi 1 d pi to d on 1 of the m fold tensor product of su n irreducible representations irreps d pi and polynominal bases of the su m irreps d on 1j om n 1 ok 0 0 0 k times a realisation of the su m irrep d oj om 3 bases is given in terms of gi for su 2 coupling wigner coefficients as a byproduct an expression is obtained for su 2 6 j symbols in terms of only two wigner coefficients the authors also discuss some possibilities of the analysis involved in solving the wigner biedenharn problem construction of orthonormal sets of the wigner coefficients for su n groups n or 3

some recent results on symmetries of lagrangian systems re examined hojman s results 1984 on alternative lagrangians and first integrals related to symmetries of lagrangian systems are shown to be covered by previous treatments in a more geometrical setting it is argued that the use of lagrangians linear in the accelerations for second order systems does not widen the spectrum of results

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

modification rules for orthosymplectic superalgebras modification rules are presented for finite dimensional graded tensor representations of osp m n with the representations specified by young supertableaux these rules relate non standard supertableaux to standard supertableaux via the removal of continuous boundary hooks all typical tensor representations are treated together with atypical representations which satisfy up to two atypically conditions

on the weight enumerators of duadic and quadratic residue codes in this correspondence we compute the weight enumerators of various quadratic residue codes over f sub 2 and f sub 3 together with certain codes of related families like the duadic and the quadratic double circulant codes we use a parallel algorithm to find the number of codewords of a given not too high weight from which we deduce by usual classical methods for self dual and formally self dual codes over f sub 2 and f sub 3 their associated previously unknown weight enumerators we compute weight enumerators for lengths as high as 152 for binary codes and 96 for ternary codes

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

spiral self avoiding walks self avoiding walks with a spiral constraint on the square lattice are enumerated up to 40 steps numerical evidence suggests that they belong to a new universality class

appearance of correlations and symmetry breaking in non equilibrium reaction diffusion systems using the reaction diffusion master equation of chemical kinetics the authors study fluctuations and correlation functions around non equilibrium steady states they demonstrate that the underlying lagrangian description in the poisson representation possesses in the equilibrium limit an exact symmetry which ensures that statistical mechanics is recovered and that the intrinsically non equilibrium long range correlations in these systems vanish an explicit form for the two time single particle correlation function including both the long range and short range contributions is constructed using mean field arguments

field theories for kinetic growth models field theories for kinetic growth models such as dla or the eden model are formulated using simple reaction diffusion master equations the approach based on poisson transform techniques specifies the stochastic fluctuations exactly the author studies the mean field approximations fluctuations and the renormalisation group

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

critical behaviour of a probabilistic automata network sis model for the spread of an infectious disease in a population of moving individuals a probabilistic automata network sis susceptible infective susceptible model for the spread of an infectious disease in a population of moving individuals is studied the local rule consists of two subrules the first one applied synchronously models infection and recovery it is a probabilistic cellular automaton rule the second applied sequentially describes the motion of the individuals the model contains three parameters the probabilities pi to get infected and pr to recover and the average number of tentative moves per individual m depending upon the values of these parameters in the infinite time limit the system is either in the disease free state or in the endemic state it goes from one state to the other through a transcritical bifurcation similar to a second order phase transition characterized by a non negative order parameter whose role is played in this model by the stationary density of infected individuals the pi pr phase diagram and the critical behaviour of the stationary density of infectives in the neighbourhood of the phase transition are studied as a function of m according to whether the individuals perform short or long range moves it is found that the parameters characterizing the transition have a qualitatively different behaviour as m varies when m is very large the correlations created by the application of the subrule modelling infection and recovery are destroyed and as expected the behaviour of the system is then correctly predicted by a mean field type approximation which assumes a homogeneous mixing of the individuals when m is not large this assumption is no longer correct

reduction of the unitary group to its orthogonal or symplectic subgroup a unified approach based upon complementary groups a unified analysis of the state labelling problems for the d row irreducible representations of u n when reduced with respect to either its orthogonal subgroup o n or its sympletic subgroup usp n the latter in the even n case is carried out by using appropriate metrics and the complementarity relationship between the group o n and sp 2d r or usp n and so 2d in this way a recently proposed canonical solution to the u n contains implies o n state labelling problem is extended to the u n contains implies usp n chain this shows the equivalence between both these internal state labelling problems and the external state labelling problem for u d as expressed in littlewood s branching rules for u n contains implies o n and u n contains implies usp n

from random walks to spin glasses abstract the talk was a short review on systems which exhibit non self averaging effects sums of random variables when the distribution has a long tail mean field spin glasses random map models and returns of a random walk to the origin non self averaging effects are identical in the case of sums of random variables and in the spin glass problem as predicted by the replica approach also we will see that for the random map models or for the problem of the returns of a random walk to the origin the non self averaging effects coincide with the results of the replica approach when the number n of replica n 1 2 or n 1

real space renormalisation group for directed systems in arbitrary dimensions a real space renormalisation group approach to intrinsically anisotropic systems i e systems having two different correlation lengths is defined the problems of directed self avoiding walks dsaw and directed percolation in d dimensions are discussed in detail for dsaw one obtains the exact critical fugacity in all dimensions for directed percolation the percolation threshold pc obtained is very good in two dimensions asymptotically exact for large dimensions and quite good in between the parallel and perpendicular correlation length exponents nu sub and nu perpendicular to are computed for the two problems

critical fluctuations around non equilibrium steady states scaling and renormalisation group concepts are used to derive phenomenological langevin equations for non equilibrium steady states for the schlogl model the authors unambiguously identify the critical langevin equation in 4 epsilon dimensions simply by requiring that the correct mean field limit be reproduced the approach is applicable to models for which only the mean field behaviour is well established

complementarity relation between the usp 2ν and so 2d lie groups the object of this paper consists of finding a complementary group with respect to usp n within either irreducible representation 1 2 dn or 1 2 dn 13 2 of the real symplectic group sp 2dn r for such purpose the author deals with the full orthogonal group o n n 2 nu or 2 nu 1 and the unitary symplectic group usp n n 2 nu in a unified way by introducing an appropriate metric a similar treatment applied to their complementary group determination leads to the well known sp 2d r group in the o n case and to the so 2d group in the usp n case

the self avoiding walk on the honeycomb lattice the author analyses the chain generating function for the self avoiding walk problem on the honeycomb lattice she uses the exact critical point value of nienhuis and finds exponent values of gamma approximately 1 344 and delta 1 approximately 0 93 for the dominant and first confluent exponents the former value is in agreement with nienhuis exact result second and third confluent exponents delta 2 approximately 1 2 and delta 3 approximately 1 5 are also identified these exponents being consistent with monte carlo results and nienhuis exact irrelevant eigenvalue respectively

slinkies and the s function content of certain generating functions a variety of methods are described for expanding particular generating functions in terms of their s function content plethysms are used to establish conjugacy relations between s function series and the task of evaluating certain products of classical s function series introduced by littlewood 1950 is then completed slinky diagrams are introduced to represent non standard s functions and their modification to give standard s functions the role of slinkies in determining the s function content of other generating functions is then explained and exemplified

first exit time of termites and random super normal conductor networks the resistance of a random super normal conductor network is calculated through the diffusion of a termite which performs a random walk on the normal bonds and has the same probability to exist from any point on a cluster of superconducting bonds the first time t that the termite exits at a distance r from the origin averaged over many configurations and runs is found to behave as t approximately r2k for r xi pc p s describes the divergence of the conductivity as p to pc p being the concentration of the superconductor scaling arguments are used to show that k 1 s 2 theta where 2 theta is the fractal dimension of random walks on single clusters at pc numerical simulations at two dimensions d 2 yields s 1 34 or 0 10 and k 1 34 or 0 03 in agreement with scaling the authors also show that the probability of return to the origin at time t behaves as t dk2 preliminary results at d 1 and other calculations methods are also discussed

properties of the density relaxation function in classical diffusion models with percolation transition the relation between the density relaxation function phi and the pair connectedness is shown static and dynamical scaling for phi and quantities related to it are derived from percolation scaling theory due to finite clusters phi contains a non ergodic singularity even in the conducting phase whence a green kubo identity does not hold the form factor of this singularity is discussed for d or 3 the static polarisability can be related to a diverging characteristic length also above the threshold contributions come from confinement in finite clusters and from the structure of the infinite cluster

susceptible infected recovered and susceptible exposed infected models two stochastic epidemic lattice models the susceptible infected recovered and the susceptible exposed infected models are studied on a cayley tree of coordination number k the spreading of the disease in the former is found to occur when the infection probability b is larger than bc k 2 k 1 in the latter which is equivalent to a dynamic site percolation model the spreading occurs when the infection probability p is greater than pc 1 k 1 we set up and solve the time evolution equations for both models and determine the final and time dependent properties including the epidemic curve we show that the two models are closely related by revealing that their relevant properties are exactly mapped into each other when p b k k 1 b these include the cluster size distribution and the density of individuals of each type quantities that have been determined in closed forms

covariance correlation and entanglement some new identities for quantum variance and covariance involving commutators are presented in which the density matrix and the operators are treated symmetrically a measure of entanglement is proposed for bipartite systems based upon covariance this works for two and three component systems but produces ambiguities for multicomponent systems of composite dimension its relationship to angular momentum dispersion for symmetric spin states is described

tests of hyperuniversality for self avoiding walks a universal combination of amplitudes for the end to end distance of n step self avoiding walks and for the number of n step self avoiding polygons is estimated numerically for various lattices in d 2 universality of this amplitude combination is confirmed to good accuracy while in d 3 the data are consistent with universality but the error limits are rather large for finite width square lattice strips the authors calculate universal critical point correlation amplitudes by fixed fugacity monte carlo simulations in addition these amplitudes are calculated analytically either exactly or approximately by cardy s conformal mapping approach numerical values agree well with the theoretical predictions

kronecker product of sp 2n representations using generalised young tableaux using generalised young tableaux the authors obtain an explicit formula for the reduction of the kronecker product of irreducible representations of the symplectic groups this extends a previous work devoted to the case of orthogonal groups

smoluchowski and beyond a field theoretical study of coagulation fragmentation processes adopting simple field theoretical techniques the author demonstrates how the smoluchowski approach to reaction diffusion models can be systematically corrected focusing on coagulation fragmentation processes he identifies the upper critical dimension dc 2 below which finite mobility corrections are important and full universality lattice independence etc can be achieved trends seem by direct simulation of simple lattice models for d 2 are confirmed whilst problems of interpretation exist for d 2

a new algorithm to enumerate the self avoiding random walk presents a new algorithm for enumerating the self avoiding walk and extend the existing series of 19 terms by one more term on a triangular lattice the leading correction to scaling exponent delta 1 for the mean square end to end distance of the self avoiding walk is found to be less than one

scaling in reaction diffusion systems the authors study irreversible reaction diffusion models of the form px from k1 from mx to k2 to qx sx from k3 from nx m dc 2 n m 1 n 1 which they study for d dc using the renormalisation group in conjunction with then epsilon expansion and exact techniques for m 1 and any n the transition remains continuous they present epsilon expansions for the case n 3 by contrast for m 2 and any n the system shows a fluctuation induced first order transition

self avoiding walks on percolation clusters the author studies self avoiding walks saws on percolation clusters a scaling function representation for r the mean end to end distance is proposed which describes a crossover from ordinary saws to saws on fractals he distinguishes between saws on a single cluster for which r approximately nx where x nu 1 and saws on all clusters for which r approximately nz where z nu 2 and n is the number of monomers in the walk he estimates nu 1 d 2 approximately 1 285 and the correction to scaling exponent omega d 2 approximately 1 3 and nu 1 d 3 approximately 1 38 two plausible generalisations of the flory 1953 approximation for nu 1 are investigated and it is argued that none of them provides a satisfactory approximation for nu 1 at all dimensions

on the apparent failure of a flory approximation for directed linear polymers the author discusses the apparent failure of a flory approximation for directed linear polymers commenting on the details implicit in this type of picture the relationship of a standard flory viewpoint to a simplified application of fractal theory is explored and a correspondence is drawn between aspects of both theories

coupling coefficients of sun son for on scalar microscopic theory of collective states boson realisations of all on scalar states which span a subspace of the hilbert space for the collective degrees of freedom of the nucleus and are labelled by irreducible representations of the chain of subgroups u3 contains implies u2 contains implies u1 of the complementary group sp 6 r are given two general expressions for isoscalar factors reduced wigner coefficients of sun contains implies son needed for constructing on scalar basis functions depending on the microscopic collective variables in the oscillator basis are derived these isoscalar factors couple three symmetric representations of sun un p10 p20 p30 to the representation h1h2h3 of sun subduced to the son on scalar representation and more generally to the son irreducible representation fff which appears in the case of the closed shells

products and symmetrized powers of irreducible representations of the calculation of branching rules tensor products and plethysms of the infinite dimensional harmonic series unitary irreducible representations of the non compact group is considered and the duality between and sp 2k exploited the branching rule for the restriction of an arbitrary harmonic series irreducible representation of to u n is derived and the decomposition is given explicitly for each of the infinite number of fundamental harmonic series irreducible representations of whose direct sum constitutes the metaplectic representation h of a concise expression for the decomposition of tensor products is derived and a complete analysis of the terms in both and is given a general formula for plethysms of arbitrary irreducible representations of is derived and its implementation illustrated both by means of a detailed generic example and by a complete determination of the symmetric and antisymmetric terms of finally relationships that arise from the embedding of the product groups and in the metaplectic group mp 4nk are discussed

non equilibrium scaling in the schlogl model from the reaction diffusion master equation formulation of the schlogl model the authors develop a comprehensive description of the non equilibrium dynamics using the poisson transformation and the dynamical renormalisation group they firstly show how the equilibrium limit is recovered and secondly describe the low frequency low momenta scaling behaviour of the concentration fluctuations the approach extends simplifies or corrects previous studies and is easily generalised to treat more complicated systems

duadic codes corresp the notion of duadic codes over gf 2 is generalized to arbitrary fields duadic codes of composite length are constructed an upper bound is given for the minimum distance of duadic codes of length a prime power

body segment inertial parameter estimation for the general population of older adults the practical determination of accurate body segment inertial parameters for the general older adult population remains a problem especially in estimating these parameters for women and accounting for variations in body type a method is presented for determining the mass and center of mass location of the body segments of individuals within the general population of older adults effects of sex and body type on older adult mass distribution are accounted for using 32 easily obtainable body measurements the method is based on existing results from different data sources and employs a combination of validated estimation approaches including body mass and segment length proportions linear and nonlinear regression equations and a mathematical model of the trunk the method was applied to a validation sample of healthy community dwelling older adults 29 men 50 women predicted body mass was 96 7 4 8 and 95 7 3 7 of measured body mass in the men and women respectively the estimates of body segment mass and trunk center of mass location for the sample population approximate those reported in the literature supporting the validity of the described method by producing practical subject specific estimates of body segment inertial parameters the method should allow more accurate biomechanical analyses of the older adult population

a new upper bound on the minimal distance of self dual codes it is shown that the minimal distance d of a binary self dual code of length n or 74 is at most 2 n 6 10 this bound is a consequence of some new conditions on the weight enumerator of a self dual code obtained by considering a particular translate of the code called its shadow these conditions also enable one to find the highest possible minimal distance of a self dual code for all n or 60 to show that self dual codes with d or 22 with d or 8 exist precisely for n 24 32 and n or 26 and with d or 10 exist precisely for n or 46 and to show that there are exactly eight self dual codes of length 32 with d 8 several of the self dual codes of length 34 have trivial group this appears to be the smallest length where this can happen