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

nonuniversal coarsening and universal distributions in far from equilibrium systems anomalous coarsening in far from equilibrium one dimensional systems is investigated by applying simulation and analytic techniques to minimal hard core particle exclusion models they contain mechanisms of aggregated particle diffusion with rates 1 particle deposition into cluster gaps but suppressed for the smallest gaps and breakup of clusters that are adjacent to large gaps cluster breakup rates vary with the cluster length x as k x ensuremath alpha the domain growth law x ensuremath sim t z with z 1 2 ensuremath alpha for ensuremath alpha g0 is explained by a simple scaling picture involving the time for two particles to coalesce and a new particle to be deposited the density of double vacancies at which deposition and cluster breakup are allowed scales as 1 t t z numerical simulations for several values of ensuremath alpha and confirm these results a fuller approach is presented which employs a mapping of cluster configurations to a column picture and an approximate factorization of the cluster configuration probability within the resulting master equation the equation for a one variable scaling function explains the above average cluster length scaling the probability distributions of cluster lengths x scale as p x 1 t z g y with y ensuremath equiv x t z which is confirmed by simulation however those distributions show a universal tail with the form g y ensuremath sim mathrm exp ensuremath y 3 2 which is explained by the connection of the vacancy dynamics with the problem of particle trapping in an infinite sea of traps the high correlation of surviving particle displacement in the latter problem explains the failure of the independent cluster approximation to represent those rare events

the electromagnetic scattering problem in the time domain for a dissipative slab and a point source using invariant imbedding a vertical magnetic dipole source above an inhomogeneous slab is considered where the permittivity e e z and conductivity z vary with the depth z using the axial symmetry of the problem a hankel transform is introduced besides physical scattering kernels nonphysical scattering kernels are introduced and the direct and inverse transformed problem is solved by means of wave splitting in an invariant imbedding approach the imbedding equations for the nonphysical scattering kernels are simpler than the corresponding equations for the physical kernels and they are solved using existing techniques for the imbedding equations for normally incident plane waves the solution for the physical kernels is obtained by establishing relations between the two sets of kernels these relations are given by volterra equations of the second kind and thus are very easy to solve numerically some applications and extensions of the results derived in the paper are discussed

coarsening in a driven ising chain with conserved dynamics we study the low temperature coarsening of an ising chain subject to spin exchange dynamics and a small driving force this dynamical system reduces to a domain diffusion process in which entire domains undergo nearest neighbor hopping except for the shortest domains dimers which undergo long range hopping this system exhibits anomalous ordering dynamics due to the existence of two characteristic length scales the average domain length l t approximately t 1 2 and the average dimer hopping distance l t approximately square root l t approximately t 1 4 as a consequence of these two scales the density of short domains decays as t 5 4 instead of the t 3 2 decay that would arise from pure domain diffusion

exact results for vicious walker models of domain walls non intersecting or vicious random walker models in one dimension can be interpreted as models of domain walls in two dimensions three problems pertaining to vicious walker models are solved the first is the exact evaluation of the partition function for the random turns model of vicious walkers on a lattice in this model at each tick of the clock a randomly chosen walker must move one step to the left or one step to the right the second problem is the calculation of the mean spacing between walls in terms of the chemical potential for a brownian motion model of continuous domain walls in a strip while the final problem solved is the calculation of the correlation between defects which occur when two domain walls meet and end without crossing the whole system

dyson s coulomb gas on a circle and intermediate eigenvalue statistics dyson s two dimensional coulomb gas on the unit circle with inverse temperature beta is investigated with the help of a metropolis algorithm theoretical predictions for energy and specific heat are verified the connection with the theory of ensembles of random unitary matrices with orthogonal unitary or symplectic symmetry corresponding to beta 1 2 4 is investigated in detail new approximation formulae for the spacing distribution and the so called delta statistics are proposed and found to be useful not only in the three cases mentioned but also for all beta between 0 and 4

an algebraic algorithm for calculating clebsch gordan coefficients application to su 2 and su 3 a recent paper gave an explicit construction for inducing shift tensors of a compact reductive lie group from shift tensors of a suitably defined subgroup the shift tensors were defined on model spaces of holomorphic vector coherent state wave functions in this paper we use these shift tensors to obtain an algorithm for computing clebsch gordan coefficients the approach reproduces the known analytical results for su 2 and gives a simple algorithm for computing su 3 coefficients the algorithm is shown to yield analytical expressions for the multiplicity free su 3 couplings of type 20 10

clebsch gordan coefficients in the asymptotic limit we investigate the graded structure of the tensor product space v 2 v 1 which arises in the coupling of two irreducible representations 1 and 2 of a semisimple lie algebra g in the limit in which one of the highest weights becomes asymptotically large the construction of asymptotic coupling coefficients is considered

diffusion limited coalescence with finite reaction rates in one dimension we study the diffusion limited process a a to a in one dimension with finite reaction rates we develop an approximation scheme based on the method of inter particle distribution functions ipdf which was used formerly for the exact solution of the same process with an infinite reaction rate the approximation becomes exact in the very early time regime or the reaction controlled limit and in the long time diffusion controlled asymptotic limit for the intermediate time regime we obtain a simple interpolative behaviour between these two limits we also study the coalescence process with finite reaction rates with the back reaction a to a a and in the presence of particle input in each of these cases the system reaches a non trivial steady state with a finite concentration of particles theoretical predictions for the concentration time dependence and for the ipdf are compared with computer simulations

tensor operators iii some fundamental tensor operator identities let s 2 and let a1 a2 as where s ai z and a1 a2 as 1 let 1 t s the method of undetermined coefficients was used to investigate natural transformations a1 a2 as and t a1 at as at necessary and sufficient conditions were found on the coefficients defining and sufficient conditions on the coefficients defining t explicit formulas for 1 and s are given herein

domain growth in a one dimensional driven diffusive system the low temperature coarsening dynamics of a one dimensional ising model with conserved magnetisation and subject to a small external driving force is studied analytically in the limit where the volume fraction mu of the minority phase is small and numerically for general mu the mean domain size l t grows as t 1 2 in all cases and the domain size distribution for domains of one sign is very well described by the form p l l propto l l 3 exp lambda mu l 2 l 2 which is exact for small mu and possibly for all mu the persistence exponent for the minority phase has the value 3 2 for mu to 0

domain number distribution in the nonequilibrium ising model we study domain distributions in the one dimensional ising model subject to zero temperature glauber and kawasaki dynamics the survival probability of a domain s t t and an unreacted domain q1 t t are characterized by two independent nontrivial exponents we develop an independent interval approximation that provides close estimates for many characteristics of the domain length and number distributions including the scaling exponents

a class of n body problems with nearest and next to nearest neighbour interactions we obtain the exact ground state and part of the excitation spectrum in one dimension on a line and the exact ground state on a circle in the case where the n particles are interacting via nearest and next to nearest neighbour interactions furthermore using the exact ground state we establish a mapping between these n body problems and the short range dyson models introduced recently to model intermediate spectral statistics using this mapping we compute the one and two point functions of a related many body theory in the thermodynamic limit and show the absence of long range order however quite remarkably we prove the existence of an off diagonal long range order in the symmetrized version of the related many body theory generalization of the models to other root systems is also considered besides we also generalize the model on the full line to higher dimensions finally we consider a model in two dimensions in which all the states exhibit novel correlations

factorization of the wave equation in higher dimensions the factorization of the wave equation into a coupled system involving up and down going wave components is obtained for the case where the field quantities are multivariate functions of spatial variables but the velocity c is a function of the z variable only the form of the reflection operator is derived and the quadratic differential integral equation satisfied by its kernel is obtained

cluster growth and dynamic scaling in a two lane driven diffusive system using high precision monte carlo simulations and a mean field theory we explore coarsening phenomena in a simple driven diffusive system the model is reminiscent of vehicular traffic on a two lane ring road at sufficiently high density the system develops jams clusters which coarsen with time a key parameter is the passing probability for small values of the growing clusters display dynamic scaling with a growth exponent of 2 3 for larger values of the growth exponent must be adjusted suggesting the ordered jammed state is not a genuine phase but rather a finite size effect

vector coherent state representation theory a vector coherent state theory is formulated as a natural extension of standard coherent state theory it is shown that the godement representations and the coherent state representations of the sp n r groups of rowe and of deenen and quesne are special cases of this more general theory

on the relation between one species diffusion limited coalescence and annihilation in one dimension the close similarity between the hierarchies of multiple point correlation functions for the diffusion limited coalescence and annihilation processes has caused some recent confusion raising doubts as to whether such hierarchies uniquely determine an infinite particle system we elucidate the precise relations between the two processes arriving at the conclusion that the hierarchy of correlation functions does provide a complete representation of a particle system on the line we also introduce a new hierarchy of probability density functions for finding particles at specified locations and none in between this hierarchy is computable for coalescence through the method of empty intervals and is naturally suited for questions concerning the ordering of particles on the line

vector coherent state theory as a theory of induced representations a general definition is given of vector coherent state vcs representation theory it is shown that the theory is more general than suggested by previous applications and that it incorporates the standard theories of induced representations as special cases the associated k matrix theory is also given a fuller treatment than hitherto and shown to provide a rather general algorithm both for projecting vcs representations from larger representations in which they are embedded and for determining the hermitian form with respect to which an isometric equivalent representation is in fact isometric

inverse methods in electromagnetic imaging this nato advanced research workshop on inverse methods in electro magnetic imaging has come at a time of greatly increased interest in using electromagnetic imaging methods as tools for remote sens ing material testing and medical diagnosis spurred by a combina tion of recent advances in sensor and device technology spanning the entire m to sub mm wavelengths the infra red optical ultraviolet and x ray regions of the electromagnetic spectrum the rapid devel opment of radar polarimetry including the deployment of active pas sive sensors on spacecraft platforms it has become evident that these advanced imaging techniques can only then become useful when supported by well developed inverse scattering theories for proper consistent and efficient data interpretation however these data interpretative techniques which are urgently needed in several mil itary and civilian areas are in many aspects not yet completely de veloped thus the main purpose of this nato arw imei 1983 was to bring together internationally renowned key experts of this new scientific discipline of inverse methods in electromagnetic imaging and have them prepare well written overviews treatises on new areas papers on special topics have them deliberate on still unre sovled problems in worki g discussion groups and then report back on their important findings to the entire nato scientific community in dealing with these exciting current developments

wigner surmise for domain systems in random matrix theory the spacing distribution functions p n s are well fitted by the wigner surmise and its generalizations in this approximation the spacing functions are completely described by the behavior of the exact functions in the limits s 0 and s most non equilibrium systems do not have analytical solutions for the spacing distribution and correlation functions because of that we explore the possibility to use the wigner surmise approximation in these systems we found that this approximation provides a first approach to the statistical behavior of complex systems in particular we use it to find an analytical approximation to the nearest neighbor distribution of the annihilation random walk

mean field approximation for spacing distribution functions in classical systems we propose a mean field method to calculate approximately the spacing distribution functions p n s in one dimensional classical many particle systems we compare our method with two other commonly used methods the independent interval approximation and the extended wigner surmise in our mean field approach p n s is calculated from a set of langevin equations which are decoupled by using a mean field approximation we find that in spite of its simplicity the mean field approximation provides good results in several systems we offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system the physical interpretation of each method is also discussed

voronoi cell patterns theoretical model and applications we use a simple fragmentation model to describe the statistical behavior of the voronoi cell patterns generated by a homogeneous and isotropic set of points in 1d and in 2d in particular we are interested in the distribution of sizes of these voronoi cells our model is completely defined by two probability distributions in 1d and again in 2d the probability to add a new point inside an existing cell and the probability that this new point is at a particular position relative to the preexisting point inside this cell in 1d the first distribution depends on a single parameter while the second distribution is defined through a fragmentation kernel in 2d both distributions depend on a single parameter the fragmentation kernel and the control parameters are closely related to the physical properties of the specific system under study we use our model to describe the voronoi cell patterns of several systems specifically we study the island nucleation with irreversible attachment the 1d car parking problem the formation of second level administrative divisions and the pattern formed by the paris metro stations

asymptotic clebsch gordan coefficients we present derivations of su 2 and su 3 so 3 clebsch gordan coefficients in the limit of large quantum numbers for su 3 we derive simple analytic expressions for the asymptotic coefficients needed for the decomposition of the product 1 0 2 0 in the limit of 1 in an so 3 basis

the racah wigner algebra and coherent tensors we present a set of tensors which are shift tensors wigner tensors in accordance with the definitions of biedenharn and louck and satisfy the coherence conditions of flath and towber our tensors are defined for all connected compact lie groups and for finite dimensional representations of connected reductive lie groups thus we have a realization of the coherent tensors in a rather general setting moreover this realization enables us to confirm most of the conjectures of flath and towber concerning the properties of coherent tensors

spacing distribution functions for the one dimensional point island model with irreversible attachment we study the configurational structure of the point island model for epitaxial growth in one dimension in particular we calculate the island gap and capture zone distributions our model is based on an approximate description of nucleation inside the gaps nucleation is described by the joint probability density p xy n x y which represents the probability density to have nucleation at position x within a gap of size y our proposed functional form for p xy x y describes excellently the statistical behavior of the system we compare our analytical model with extensive numerical simulations our model retains the most relevant physical properties of the system

analysis of the green s function approach to one dimensional inverse problems i one parameter reconstruction an analysis of a green s function approach based on wave splitting to the one dimensional electromagnetic inverse problem is given the green s functions refer to split components of the fundamental solution the linear system of equations for the green s functions is shown to be well posed for the inverse problem and stability estimates theorems on existence uniqueness local correctness and convergence are given

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

a time domain technique for mechanism extraction the properties of scattered fields from a structure can be better evaluated from the characteristics of the individual scatterers decomposition techniques can be classified either as a matrix or an integral formulation with either formulation aspect pattern or frequency information of a scattering center can be obtained emphasis will be placed on an integral time domain isolation extraction technique to obtain the frequency characteristics of scattering mechanisms this technique has its origins in the time domain interpretation of scattered fields

a geometric description of tensor product decompositions in su 3 the direct sum decomposition of tensor products for su 3 has many applications in physics and the problem has been studied extensively this has resulted in many decomposition methods each with its advantages and disadvantages the description given here is geometric in nature and it describes both the constituents of the direct sum and their multiplicities in addition to providing decompositions of specific tensor products this approach is very well suited to studying tensor products as the parameters vary and helping draw general conclusions after a description and proof of the method several consequences are discussed and proved in particular questions regarding multiplicities are considered

the use of the linear sampling method for obtaining super resolution effects in born approximation a two step reconstruction scheme is introduced to solve fixed frequency inverse scattering problems in born approximation conditions the aim of the approach is to achieve super resolution effects by constraining the inversion method to exploit some a priori knowledge on the scatterer therefore the first step is to apply the linear sampling method to the far field data in order to obtain an estimate of the support of the inhomogeneity the second step is to apply the projected landweber method to the linearized scattering equation in order to obtain super resolution effects via out of band extrapolation the effectiveness of the approach which has a rather wide applicability power is tested in the case of a two dimensional problem for some scatterers of simple geometry

a rotor expansion of the su 3 lie algebra vector coherent state vcs theory is used to give a rotor expansion of the su 3 lie algebra in a way that parallels the boson expansions that have been made for other lie algebras the construction provides a systematic procedure for calculating hermitian matrix elements of su 3 in an so 3 coupled basis and represents a new development in vcs theory and in the theory of induced representations

statistical behavior of domain systems we study the statistical behavior of two out of equilibrium systems the first one is a quasi one dimensional gas with two species of particles under the action of an external field which drives each species in opposite directions the second one is a one dimensional spin system with nearest neighbor interactions also under the influence of an external driving force both systems show a dynamical scaling with domain formation the statistical behavior of these domains is compared with models based on the coalescing random walk and the interacting random walk we find that the scaling domain size distribution of the gas and the spin systems is well fitted by the wigner surmise which lead us to explore a possible connection between these systems and the circular orthogonal ensemble of random matrices however the study of the correlation function of the domain edges shows that the statistical behavior of the domains in both gas and spin systems is not completely well described by a circular orthogonal ensemble nor it is by other models proposed such as the coalescing random walk and the interacting random walk nevertheless we find that a simple model of independent intervals describes more closely the statistical behavior of the domains formed in these systems

exact solution of the lock step model of vicious walkers the lock step model of vicious walkers on a one dimensional lattice allows each walker at the tick of a clock to move either one lattice site to the left or one lattice site to the right the only restriction is that no two walkers may arrive at the same lattice site or pass one another in periodic boundary conditions the partition function and correlation function for this model are calculated exactly taking the continuum limit gives an exactly solvable model of vicious walkers undergoing brownian motion

domain statistics in coarsening systems we study the domain number and size distributions in the one dimensional ising and q state potts models subject to zero temperature glauber dynamics the survival probability of a domain s t t 2c and an unreacted domain q1 t t 2d are characterized by two independent nontrivial exponents for the ising case we find c50 126 and d51 27 using numerical simulations we develop an independent interval approximation that predicts the qualitative behavior of the domain distribution and provides good estimates for the exponents exact results for the domain distribution are also obtained in several solvable cases s1063 651x 97 00110 4

microscopic spatial correlations induced by external noise in a reaction diffusion system abstract the reversible single species reaction scheme x 2x has long served as an example of a system with nonlinear macroscopic dynamics in recent years a microscopic version of this interacting particle system namely the diffusion controlled limit has been solved exactly in one spatial dimension the effects of internal fluctuations correlations arising in nonequilibrium situations and external noise can all be studied in this model diffusion reaction system without approximation here we review some recent results focusing on an exact treatment of the effect of spatially homogeneous temporal fluctuations in the growth rate of the process the rate for the x 2x process we find that the nonequilibrium steady state possesses new microscopic length scales resulting from the nonequilibrium constraints demonstrating that spatially homogeneous external noise can introduce spatial correlations

microwave imaging based on a markov random field model a new approach to microwave imaging of 2d inhomogeneous dielectric scatterers is presented the method is developed in the space domain and markov random fields are used to obtain a model of the distributions of dielectric features in the scattering region in this way a priori knowledge can be easily inserted in the imaging scheme this stochastic approach gives rise to a functional equation that can be minimized by using a simulated annealing algorithm an iterative scheme is derived that allows one to bypass the need for storing large matrices in the computer numerical simulation results confirming the capabilities and effectiveness of the proposed method are reported solutions have generally been obtained in few steps and seem better than those obtained by other imaging techniques in the space domain the capability of the algorithm to operate in a strongly noisy environment is also proved

vector coherent state representations induced representations and geometric quantization i scalar coherent state representations coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model i classical realizations which are the starting point for geometric quantization ii induced unitary representations corresponding to prequantization and iii irreducible unitary representations obtained in geometric quantization by choice of a polarization these representations establish an intimate relation between coherent state theory and geometric quantization in the context of induced representations

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

a validation analysis of huynen s target descriptor interpretations of the mueller matrix elements in polarimetric radar returns using kennaugh s physical optics impulse response formulation by applying correction to kennaugh s impulse response formulation for smooth convex targets huynen s descriptors have been shown to relate to specular geometry at high frequencies a time gating technique has been developed to separate the specular signature from the creeping wave contribution in the total backscattered return this enables approximately equivalent high frequency data to be extracted from bandlimited scattering measurements it is shown that the validation of the target descriptor interpretations of the mueller matrix elements with the isolated specular contribution data is acceptable whereas the validation of these interpretations with the total backscattered data seems doubtful

electromagnetic imaging of two dimensional perfectly conducting cylinders with transverse electric scattered field electromagnetic imaging of two dimensional perfectly conducting cylinders using measured transverse electric scattered field is studied in this paper the contours of cylinders are denoted by local shape functions spl rho sub i f sub i spl theta sub i in local polar coordinates which are then approximated by closed cubic b splines instead of trigonometric series by using the boundary condition of vanishing tangential electric field on surfaces of perfectly conducting cylinders a set of electric field integral equations governing the scattering problem is derived the scattering problem is solved by a point matching method with pulse basis and dirac delta testing functions the inverse problem is reformulated as an optimization problem and solved by a real coded genetic algorithm with closed cubic b splines local shape function numerical examples show good agreement between the true profiles and the reconstructed results

wigner surmise for high order level spacing distributions of chaotic systems we suggest an extension of the wigner surmise for the nearest neighbor spacing distribution of energy levels of chaotic systems to include the nth order spacing distributions the main assumption is that the conditional probability density of occurrence of a level at a given distance from a fixed level provided that this distance contains n levels is expressed in terms of the n 1 th power of corresponding probability for a distance containing no levels at large spacings the nth order level distributions are assumed to have a gaussian shape as in the cases covered by the wigner surmise the expressions obtained are in good agreement with the results of numerical calculation by means of the random matrix theory for the three universal classes of symmetry

a numerical algorithm for the explicit calculation of su n and sl n c clebsch gordan coefficients we present an algorithm for the explicit numerical calculation of su n and sl n c clebsch gordan coefficients based on the gelfand tsetlin pattern calculus our algorithm is well suited for numerical implementation we include a computer code in an appendix our exposition presumes only familiarity with the representation theory of su 2

comments with reply on a generalization of van den berg s integral square error computational technique for scattering by a j mackay and a mccowen the commenters note that if the conjugate gradient method were used in the above named work ibid vol ap 35 p 213 20 feb 1987 its use automatically enforces the orthogonality of the authors functions without requiring any additional storage in replying the authors agree that it was perhaps an oversight not to compare van den berg s method with the conjugate gradient method however they note that it was not their aim to provide such a comparison but only to show how improvements could be made to the spectral iteration technique sit

large distance asymptotic behavior of the emptiness formation probability of the xxz spin 1 2 heisenberg chain using its multiple integral representation we compute the large distance asymptotic behaviour of the emptiness formation probability of the xxz spin 1 2 heisenberg chain in the massless regime

distribution of domain sizes in the zero temperature glauber dynamics of the one dimensional potts model for the zero temperature glauber dynamics of the q state potts model we calculate the exact distribution of domain sizes by mapping the problem on an exactly soluble one species coagulation model a1a a in the long time limit this distribution is universal and from its complicated exact expression we extract its behavior in various regimes our results are tested in a simulation and compared to the predictions of a simple approximation proposed recently considering the dynamics of domain walls as a reaction diffusion model a1a a with probability q22 q21 and a1a f with probability 1 q21 we calculate the pair correlation function in the long time regime s1063 651x 96 12809 9

capture zone areas in submonolayer nucleation effects of dimensionality and short range interactions simulation results for the asymptotic scaled capture zone distribution czd for the case of irreversible nucleation and growth of point islands are presented for substrate dimension d 1 2 3 and 4 and compared with a recent conjecture based on the wigner distribution poor agreement is found between the predicted wigner distributions and the asymptotic czd in the limit of infinite df corresponding to the ratio of monomer hopping rate d to deposition rate f our results also indicate that for d 2 and 3 the asymptotic czd for point islands is independent of model details and dimension however for d 1 and d 4 the resulting distribution is significantly more sharply peaked we also find that in contrast to the island size distribution for which mean field like behavior is observed in d 3 and above the asymptotic czd is significantly broadened by fluctuations even in d 4

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

em plane wave diffraction by a a planar junction of two thin material half planes oblique incidence a uniform geometrical theory of diffraction utd solution is developed for analyzing the high frequency diffraction of an obliquely incident plane wave by a two part thin planar transparent material slab the solution is obtained by appropriately combining two solutions for the two related configurations involving perfectly conducting electric and magnetic ground plane bisections of the original slab the analysis is based on the wiener hopf technique and each of the grounded material half planes is assumed to be electrically thin so that it can be modeled by a generalized impedance boundary condition of 0 t where t is the corresponding slab thickness to solve the boundary value problem completely an additional condition related to the field behavior at the junction of the two material half planes is imposed this junction condition is determined by matching an approximate quasi static solution which is developed in the proximity of the discontinuity with the corresponding external wiener hopf solution in the common region of overlap the solution thus obtained automatically satisfies reciprocity

non markovian persistence and nonequilibrium critical dynamics the persistence exponent ensuremath theta for the global order parameter m t of a system quenched from the disordered phase to its critical point describes the probability p t ensuremath sim t ensuremath ensuremath theta that m t does not change sign in the time interval t following the quench we calculate ensuremath theta to o ensuremath epsilon 2 for model a of hohenberg and halperin rev mod phys 49 435 1977 and to order ensuremath epsilon for model c and show that at this order m t is a non markov process consequently to our knowledge ensuremath theta is a new exponent the calculation is performed by expanding around a markov process using a simplified version of the perturbation theory recently introduced by majumdar and sire phys rev lett 77 1420 1996