critical statistics for non hermitian matrices we introduce a generalized ensemble of non hermitian matrices interpolating between the gaussian unitary ensemble the ginibre ensemble and the poisson ensemble the joint eigenvalue distribution of this model is obtained by means of an extension of the itzykson zuber formula to general complex matrices its correlation functions are studied both in the case of weak non hermiticity and in the case of strong non hermiticity in the weak non hermiticity limit we show that the spectral correlations in the bulk of the spectrum display critical statistics the asymptotic linear behavior of the number variance is already approached for energy differences of the order of the eigenvalue spacing to lowest order its slope does not depend on the degree of non hermiticity close the edge the spectral correlations are similar to the hermitian case in the strong non hermiticity limit the crossover behavior from the ginibre ensemble to the poisson ensemble first appears close to the surface of the spectrum our model may be relevant for the description of the spectral correlations of an open disordered system close to an anderson transition

algebras for the two sphere and the three sphere groups of compact simple lie groups the infinite dimensional lie algebras corresponding to the lie groups of smooth maps from two and three spheres to compact simple lie groups are studied the problem of their central extension is solved the problem of the existence of semidirect sum algebras containing these and the algebras of the groups of diffeomorphisms on the two and three spheres is treated

lowast sdym fields and heavenly spaces i lowast sdym equations as an integrable system it is shown that the self dual yang mills sdym equations for the bracket lie algebra on a heavenly space can be reduced to one equation the master equation two hierarchies of conservation laws for this equation are constructed then the twistor transform and a solution to the riemann hilbert problem are given

fractal structure of random matrices abstract a multifractal analysis is performed on the universality classes of random matrices and the transition ones our results indicate that the eigenvector probability distribution is a linear sum of two 2 distributions throughout the transition between the universality ensembles of random matrix theory and poisson

on the free vibration analysis of circular plates with stepped thickness over a concentric region by the differential quadrature element method it can be seen the dqem retains all advantages of the differential quadrature method extends the applicability range of the dq method and is more convenient for treating various boundary conditions

explicitly time dependent constants symmetries of the higher order kp equations for higher order kadomtsev petviashvili kp equations the existence of explicitly time dependent constants of motion is discussed generalizing the results for the ordinary kp equation constants t m n l polynomial in t are constructed for each lth order kp equation for all n m l 1 1

a new approach to the differential quadrature method for fourth order equations a generalized and more complete methodology for treating boundary conditions in the differential quadrature method dqm is presented this improved approach eliminates the deficiencies of the type grid arrangement which represents an approximation by applying the boundary conditions exactly two kinds of basis functions chebyshev and lagrange are used for concept demonstration it is found that the new approach cures most deficiencies of the current dqm 1997 by john wiley sons ltd

area preserving diffeomorphisms and supermembrane lorentz invariance the lie algebra of area preserving diffeomorphisms on closed membranes of arbitrary topology is investigated on the basis of a harmonic decomposition we define the structure constants as well as two other tensors which appear in the supermembrane lorentz generators we derive certain identities between these tensors and analyze their validity when the areapreserving diffeomorphisms are approximated bysu n one of the additional tensors can then be identified with the invariant symmetric three index tensor ofsu n while the second has no obvious analog we prove that the lorentz generators are classically conserved in the light cone gauge for arbitrary membrane topology as a consequence of these tensor identities this formulation allows a systematic study of the violations of lorentz invariance in thesu n approximation

free vibration of plates by the high accuracy quadrature element method in this paper a highly accurate and rapidly converging hybrid approach is presented for the quadrature element method qem solution of plate free vibration problems the hybrid qem essentially consists of a collocation method in conjunction with a galerkin finite element technique to combine the high accuracy of the differential quadrature method dqm for the efficient solution of differential equations with the generality of the finite element formulation this results in superior accuracy with fewer degrees of freedom than conventional fem or fdm a series of numerical tests is conducted to assess the performance of the quadrature plate element in free vibration problems anisotropic and stepped thickness plates are investigated as well as mixed boundary conditions and point supports at the edges in all cases the results obtained are quite accurate

family of solvable generalized random matrix ensembles with unitary symmetry we construct a very general family of characteristic functions describing random matrix ensembles rme having a global unitary invariance and containing an arbitrary one variable probability measure which we characterize by a spread function various choices of the spread function lead to a variety of possible generalized rmes which show deviations from the well known gaussian rme originally proposed by wigner we obtain the correlation functions of such generalized ensembles exactly and show examples of how particular choices of the spread function can describe ensembles with arbitrary eigenvalue densities as well as critical ensembles with multifractality

impact of localization on dyson s circular ensemble a wide variety of complex physical systems described by unitary matrices have been shown numerically to satisfy level statistics predicted by dyson s circular ensemble we argue that the impact of localization in such systems is to impose certain restrictions on the eigenvalues we consider a solvable model which takes into account such restrictions qualitatively and find that within the model a gap is created in the spectrum and there is a transition from the universal wigner distribution towards a poisson distribution with increasing localization

the moyal bracket and the dispersionless limit of the kp hierarchy a new lax equation is introduced for the kp hierarchy which avoids the use of pseudo differential operators as used in the sate approach this lax equation is closer to that used in the study of the dispersionless kp hierarchy and is obtained by replacing the poisson bracket with the moyal bracket the dispersionless limit under which the moyal bracket collapses to the poisson bracket is particularly simple

random matrix ensembles from nonextensive entropy the classical gaussian ensembles of random matrices can be constructed by maximizing boltzmann gibbs shannon s entropy s text bgs ensuremath ensuremath int d mathbf h p mathbf h mathrm ln p mathbf h with suitable constraints here we construct and analyze random matrix ensembles arising from the generalized entropy s q 1 ensuremath ensuremath int d mathbf h p mathbf h q q ensuremath 1 thus s 1 s text bgs the resulting ensembles are characterized by a parameter q measuring the degree of nonextensivity of the entropic form making q ensuremath rightarrow 1 recovers the gaussian ensembles if q ensuremath ne 1 the joint probability distributions p mathbf h cannot be factorized i e the matrix elements of mathbf h are correlated in the limit of large matrices two different regimes are observed when ql1 p mathbf h has compact support and the fluctuations tend asymptotically to those of the gaussian ensembles anomalies appear for qg1 both p mathbf h and the marginal distributions p h ij show power law tails numerical analyses reveal that the nearest neighbor spacing distribution is also long tailed not wigner dyson and after proper scaling very close to the result for the 2 ifmmode times else texttimes fi 2 case char22 a generalization of wigner s surmise we discuss connections of these nonextensive ensembles with other non gaussian ones such as the so called l evy ensembles and those arising from soft confinement

asymptotic level spacing distribution for a q deformed random matrix ensemble we obtain the asymptotic behaviour of the nearest neighbour level spacing distribution for a q deformed unitary random matrix ensemble

free vibration analysis of beams and rectangular plates with free edges by the discrete singular convolution in this paper free vibration of beams annular plates and rectangular plates with free boundaries are analyzed by using the discrete singular convolution dsc a novel method to apply the free boundary conditions is proposed detailed derivations are given to validate the proposed method eight examples including the free vibrations of beams annular plates and rectangular plates with free boundaries are analyzed two kernels the regularized shannon s kernel and the non regularized lagrange s delta sequence kernel are tested dsc results are compared with either analytical solutions or and differential quadrature dq data it is demonstrated that the proposed method to incorporate the free boundary conditions is simple to use and can yield accurate frequency data for beams with a free end and plates with free edges thus the proposed method for applying the boundary conditions extends the application range of the dsc

energy level statistics of a critical random matrix ensemble we study energy level statistics of a critical random matrix ensemble of power law banded complex hermitian matrices we compute the level compressibility via the level number variance and compare it with the analytical formula for the exactly solvable model of moshe neuberger and shapiro

the pauli matrices in n dimensions and finest gradings of simple lie algebras of type a n 1 properties of the lie algebra gl n c are described for a basis which is a generalization of the 2 2 pauli matrices the 3 3 case is described in detail the remarkable properties of that basis are the grading of the lie algebra it offers each grading subspace is one dimensional and the matrix group it generates it is a finite group with the center of sl n c as its commutator group

infinite dimensional algebras and a trigonometric basis for the classical lie algebras this paper explores features of the infinite dimensional algebras that have been previously introduced in particular it is shown that the classical simple lie algebras an bn cn dn may be expressed in an egalitarian basis with trigonometric structure constants the transformation to the standard cartan weyl basis and the particularly transparent n limit that this formulation allows is provided

static analysis of structures by the quadrature element method qem abstract the differential quadrature method dqm is an alternative discrete approach to solving directly the governing equations of engineering and mathematical physics since the dqm does not require the derivation of the weak forms of the governing equations like the fem it can greatly reduce formulation efforts in higher order approximation the dqm has been applied in the past to the analyses of various single structural components such as bars beams membranes and plates all of the component analyses yielded good to excellent results however previous studies were limited to simple geometries and simple boundary conditions due to the limitation of using global basis functions in the present study a domain decomposition technique for the dqm is proposed to analyse truss and frame structures where the whole structural domain is represented by a collection of simple element subdomains connected together at specific nodal points this method is named the quadrature element method qem

variations on a theme of heisenberg pauli and weyl the parentage between weyl pairs the generalized pauli group and the unitary group is investigated in detail we start from an abstract definition of the heisenberg weyl group on the field and then switch to the discrete heisenberg weyl group or generalized pauli group on a finite ring the main characteristics of the latter group an abstract group of order d3 noted pd are given conjugacy classes and irreducible representation classes or equivalently lie algebra of dimension d3 associated with pd leaving the abstract sector a set of weyl pairs in dimension d is derived from a polar decomposition of su 2 closely connected to angular momentum theory then a realization of the generalized pauli group pd and the construction of generalized pauli matrices in dimension d are revisited in terms of weyl pairs finally the lie algebra of the unitary group u d is obtained as a subalgebra of the lie algebra associated with pd this leads to a development of the lie algebra of u d in a basis consisting of d2 generalized pauli matrices in the case where d is a power of a prime integer the lie algebra of su d can be decomposed into d 1 cartan subalgebras

some examples of the algebra of flows the algebra of the group of smooth maps from a manifold m to a compact simple lie group g is studied for two cases the first is when m is the double coset so d r so d 1 r so d r the corresponding maps are those from a d sphere to g that are invariant under left translations by elements from so d r in the second example m is a two dimensional torus the problem of central extension of these algebras is solved for the first example no central extension is possible for the second the number of independent central extensions is infinite

on invariant 2 2 β ensembles of random matrices abstract we introduce and solve exactly a family of invariant 2 2 random matrices depending on one parameter and we show that rotational invariance and real dyson index are not incompatible properties the probability density for the entries contains a weight function and a multiple trace trace interaction term which corresponds to the representation of the vandermonde squared coupling on the basis of power sums as a result the effective dyson index eff of the ensemble can take any real value in an interval two weight functions gaussian and non gaussian are explored in detail and the connections with ensembles of dumitriu edelman and the so called poisson wigner crossover for the level spacing are respectively highlighted a curious spectral twinning between ensembles of different symmetry classes is unveiled as a consequence the identification between symmetry group orthogonal unitary or symplectic and the exponent of the vandermonde 1 2 4 is shown to be potentially deceptive the proposed technical tool more generically allows for designing actual matrix models which i are rotationally invariant ii have a real dyson index eff iii have a pre assigned confining potential or alternatively level spacing profile the analytical results have been checked through numerical simulations with an excellent agreement eventually we discuss possible generalizations and further directions of research

new family of unitary random matrices we consider an exactly solvable random matrix model related to the random transfer matrix model for disordered conductors in the conventional random matrix models the spacing distribution of nearest neighbor eigenvalues when expressed in units of average spacing has a universal behavior known generally as the wigner distribution in contrast our model has a single parameter as a function of which the spacing distribution crosses over from a wigner to a distribution which is increasingly more poisson like a feature common to a wide variety of physical systems including disorder and chaos

eigenvalue spacing statistics of a four matrix model of some four by four random matrices a simple four matrix model consisting of some 4 4 real and imaginary random matrices and three parameters is introduced it is shown that the eigenvalue spacing statistics of an ensemble of such matrices can be used to describe transitions between all the wigner surmises of random matrix theory formulae for the nearest neighbour spacing distributions of the ensemble are given for various parameter values

classical diffusion anderson localization and spectral statistics in billiard chains we study spectral properties of quasi one dimensional extended systems that show deterministic diffusion on the classical level and anderson localization in the quantal description using semi classical arguments we relate universal aspects of the spectral fluctuations to features of the set of classical periodic orbits expressed in terms of the probability to perform periodic motion which are likewise universal this allows us to derive an analytical expression for the spectral form factor which reflects the diffusive nature of the corresponding classical dynamics it defines a novel spectral universality class which covers the transition between goe statistics in the limit of a small ratio of the system size to the localization length corresponding to the ballistic regime of disordered systems to poissonian level fluctuations in the opposite limit our semi classical predictions are illustrated and confirmed by a numerical investigation of aperiodic chains of chaotic billiards

universal scaling of lyapunov exponents we prove numerically for the first time that the lower part of the spectrum of the transfer matrix of the quasi one dimensional disordered system is strongly correlated in the neighbourhood of the critical point of the metal insulator transition in particular the disorder and the system size dependence of the spectrum is governed only by one parameter which we identify with the scaling parameter of mackinnon and kramer the strong correlation of the spectrum supports the idea of the universality of the random matrix like theory of the metal insulator transition and provides us with a new way of calculation of the critical parameters of this transition

static analysis of frame structures by the differential quadrature element method in this paper a new version of differential quadrature method dqm is proposed and then extended to analyse frame structures the new method called the differential quadrature element method dqem retains all advantages of the earlier version of the differential quadrature method and overcomes some critical shortcomings existing in the original dqm the proposed method is however different from the quadrature element method qem proposed earlier by striz et al the methodology is explained in details herein via a differential quadrature beam element and some numerical examples are given to show the efficiency of the present method 1997 by john wiley sons ltd

symmetries and tau function of higher dimensional dispersionless integrable hierarchies a higher dimensional analogue of the dispersionless kp hierarchy is introduced in addition to the two dimensional phase space variables k x of the dispersionless kp hierarchy this hierarchy has extra spatial dimensions compactified to a two or any even dimensional torus integrability of this hierarchy and the existence of an infinite dimensional of additional symmetries are ensured by an underlying twistor theoretical structure or a nonlinear riemann hilbert problem an analogue of the tau function whose logarithm gives the f function free energy or prepotential in the context of matrix models and topological conformal field theories is constructed the infinite dimensional symmetries can be extended to this tau or f function the extended symmetries just like those of the dispersionless kp hierarchy obey an anomalous commutation relations

random matrix theory models of electric grid topology abstract the random matrix theory is useful in the study of large systems such as electric grids these transmission systems can be modeled as complex networks with high voltage lines the edges that connect nodes representing power plants and substations we draw upon established literature of complex systems theory and introduce methods from nuclear and statistical physics to identify new characteristics of these networks we show that most grids can be characterized by the gaussian orthogonal ensemble an indicator of chaos in many complex systems under certain circumstances however grids may be described by poisson statistics an indicator of regularity we use the random matrix formalism to describe the interconnection of multiple grids and construct a simple model of a distributed grid

description of chaos order transition with random matrices within the maximum entropy principle the deformed gaussian orthogonal ensemble introduced earlier is developed here for large dimensional matrices both the spacing and eigenvector distributions are studied and compared to other ones suggested for the chaos order transition problem the concept of a universal lower entropy with respect to the gaussian orthogonal ensemble entropy is proved very useful

central extensions of sphere groups closed forms for the central extensions of the infinite dimensional lie algebras of smooth maps from two and three spheres to compact lie groups are given

effective plasma model for the level correlations at the mobility edge we consider the mapping of the energy level statistics for a d dimensional disordered electron system at the mobility edge between metallic and insulating phases onto the model of a classical one dimensional plasma of fictitious particles we deduce the effective pairwise interaction in the plasma that is consistent with the known universal two level correlation function at the mobility edge and show that for level separation epsilon delta it decreases as delta epsilon gamma where delta is the mean level spacing and gamma is the critical exponent related to the known critical exponent v of the correlation length as gamma 1 vd 1 we apply the plasma model to generalize wigner s semicircle law and to derive the large energy asymptotic form of the nearest level distribution in the limit gamma to 0 which corresponds to the original dyson mapping onto the plasma with logarithmic repulsion we recover the classical results of wigner dyson random matrix theory

spectral fluctuations of billiards with mixed dynamics from time series to superstatistics a statistical analysis of the eigenfrequencies of two sets of superconducting microwave billiards one with mushroomlike shape and the other from the family of the limacon billiards is presented these billiards have mixed regular chaotic dynamics but different structures in their classical phase spaces the spectrum of each billiard is represented as a time series where the level order plays the role of time two most important findings follow from the time series analysis first the spectra can be characterized by two distinct relaxation lengths this is a prerequisite for the validity of the superstatistical approach which is based on the folding of two distribution functions second the shape of the resulting probability density function of the so called superstatistical parameter is reasonably approximated by an inverse chi2 distribution this distribution is used to compute nearest neighbor spacing distributions and compare them with those of the resonance frequencies of billiards with mixed dynamics within the framework of superstatistics the obtained spacing distribution is found to present a good description of the experimental ones and is of the same or even better quality as a number of other spacing distributions including the one from berry and robnik however in contrast to other approaches toward a theoretical description of spectral properties of systems with mixed dynamics superstatistics also provides a description of properties of the eigenfunctions in terms of a superstatistical generalization of the porter thomas distribution indeed the inverse chi2 parameter distribution is found suitable for the analysis of experimental resonance strengths in the limacon billiards within the framework of superstatistics

characteristic classes and hitchin systems general construction we consider topologically non trivial higgs g bundles over riemann surfaces g with marked points and the corresponding hitchin systems we show that if g is not simply connected then there exists a finite number of different sectors of the higgs bundles endowed with the hitchin hamiltonians they correspond to different characteristic classes of the underlying bundles defined as elements of h 2 sigma g mathcal z g mathcal z g is a center of g we define the conformal version cg of g an analog of gl n for sl n and relate the characteristic classes with degrees of cg bundles we describe explicitly bundles in the genus one g 1 case if 1 has one marked point and the bundles are trivial then the hitchin systems coincide with calogero moser cm systems for the nontrivial bundles we call the corresponding systems the modified calogero moser mcm systems their phase space has the same dimension as the phase space of the cm systems with spin variables but less number of particles and greater number of spin variables starting with these bundles we construct lax operators quadratic hamiltonians and define the phase spaces and the poisson structure using dynamical r matrices the latter are completion of the classification list of etingof varchenko corresponding to the trivial bundles to describe the systems we use a special basis in the lie algebras that generalizes the basis of t hooft matrices for sl n we find that the mcm systems contain the standard cm subsystems related to some unbroken subalgebras the configuration space of the cm particles is the moduli space of the stable holomorphic bundles with non trivial characteristic classes

power law eigenvalue density scaling and critical random matrix ensembles we consider a class of rotationally invariant unitary random matrix ensembles where the eigenvalue density falls off as an inverse power law under a scaling appropriate for such power law densities different from the scaling required in gaussian random matrix ensembles we calculate exactly the two level kernel that determines all eigenvalue correlations we show that such ensembles belong to the class of critical ensembles

deformations of the tracy widom distribution in random matrix theory the tracy widom tw distribution describes the behavior of the largest eigenvalue we consider here two models in which tw undergoes transformations in the first one disorder is introduced in the gaussian ensembles by superimposing an external source of randomness a competition between tw and a normal gaussian distribution results depending on the spreading of the disorder the second model consists of removing at random a fraction of correlated eigenvalues of a random matrix the usual formalism of fredholm determinants extends naturally a continuous transition from tw to the weilbull distribution characteristic of extreme values of an uncorrelated sequence is obtained

current algebras in d 1 dimensions and determinant bundles over infinite dimensional grassmannians we extend the methods of pressley and segal for constructing cocycle representations of the restricted general linear group in infinite dimensions to the case of a larger linear group modeled by schatten classes of rank 1 p an essential ingredient is the generalization of the determinant line bundle over an infinite dimensional grassmannian to the case of an arbitrary schatten rank p 1 the results are used to obtain highest weight representations of current algebras with the operator schwinger terms ind 1 dimensions when the space dimensiond is any odd number

superstatistics in random matrix theory abstract using the superstatistics method we propose an extension of the random matrix theory to cover systems with mixed regular chaotic dynamics unlike most of the other works in this direction the ensembles of the proposed approach are basis invariant but the matrix elements are not statistically independent spectral characteristics of the mixed systems are expressed by averaging the corresponding quantities in the standard random matrix theory over the fluctuations of the inverse variance of the matrix elements we obtain analytical expressions for the level density and the nearest neighbor spacing distributions for four different inverse variance distributions the resulting expressions agree with each other for small departures from chaos measured by an effective non extensivity parameter our results suggest among other things that superstatistics is suited only for the initial stage of transition from chaos to regularity

high accuracy plane stress and plate elements in the quadrature element method in this paper a high accuracy and rapid convergence hybrid approach is developed for the quadrature element method qem solution of two dimensional plane stress and plate bending problems the hybrid qem essentially consists of a collocation method in conjunction with a galerkin finite element technique to combine the high accuracy of the differential quadrature method dqm with the generality of finite element formulations this results in superior accuracy with fewer degrees of freedom than conventional fem or fdm the present method also extends the general application of the collocation numerical approach to fourth order governing equation systems here the influence of collocation point location is investigated a series of numerical tests is conducted in order to assess the performance of the quadrature plane stress and plate elements in static problems

two new approximate methods for analyzing free vibration of structural components two approximate methods which have not previously been used for structural dynamics problems are applied to the free vibration analysis of various structural components the first method is a new version of the complementary energy method it is shown to be considerably more accurate than the conventional rayleigh and rayleigh schmidt methods when applied to spatially one dimensional free vibration problems prismatic and tapered bars prismatic beams and axisymmetric motion of circular membranes the second method is the differential quadrature method introduced by bellman and his associates it is applied successfully here to all of the problems mentioned plus square membranes and circular and square plates

quantum systems with finite hilbert space galois fields in quantum mechanics a galois quantum system in which the position and momentum take values in the galois field gf pl is considered it is comprised of l component systems which are coupled in a particular way and is described by a certain class of hamiltonians displacements in the gf pl gf pl phase space and the corresponding heisenberg weyl group are studied symplectic transformations are shown to form the sp 2 gf pl group wigner and weyl functions are defined and their properties are studied frobenius symmetries which are based on frobenius automorphisms in the theory of galois fields are a unique feature of these systems for l 2 if they commute with the hamiltonian there are constants of motion which are discussed an analytic representation in the l sheeted complex plane provides an elegant formalism that embodies the properties of frobenius transformations the difference between a galois quantum system and other finite quantum systems where the position and momentum take values in the ring is discussed

random matrix models with additional interactions it has been argued that despite remarkable success existing random matrix theories are not adequate at describing disordered conductors in the metallic regime due to the presence of certain two body interactions in the effective hamiltonian for the eigenvalues in addition to the standard logarithmic interaction that arises entirely from symmetry considerations we present a new method that allows exact solution of random matrix models with such additional two body interactions this should broaden the scope of random matrix models in general

from gumbel to tracy widom the tracy widom distribution that has been much studied in recent years can be thought of as an extreme value distribution we discuss interpolation between the classical extreme value distribution exp exp x the gumbel distribution and the tracy widom distribution there is a family of determinantal processes whose edge behaviour interpolates between a poisson process with density exp x and the airy kernel point process this process can be obtained as a scaling limit of a grand canonical version of a random matrix model introduced by moshe neuberger and shapiro we also consider the deformed gue ensemble m m 0 sqrt 2s v with m 0 diagonal with independent elements and v from gue here we do not see a transition from tracy widom to gumbel but rather a transition from tracy widom to gaussian

spectral analysis of deformed random networks we study spectral behavior of sparsely connected random networks under the random matrix framework subnetworks without any connection among them form a network having perfect community structure as connections among the subnetworks are introduced the spacing distribution shows a transition from the poisson statistics to the gaussian orthogonal ensemble statistics of random matrix theory the eigenvalue density distribution shows a transition to the wigner s semicircular behavior for a completely deformed network the range for which spectral rigidity measured by the dyson mehta ensuremath delta 3 statistics follows the gaussian orthogonal ensemble statistics depends upon the deformation of the network from the perfect community structure the spacing distribution is particularly useful to track very slight deformations of the network from a perfect community structure whereas the density distribution and the ensuremath delta 3 statistics remain identical to the undeformed network on the other hand the ensuremath delta 3 statistics is useful for the larger deformation strengths finally we analyze the spectrum of a protein protein interaction network for helicobacter and compare the spectral behavior with those of the model networks

extensions and contractions of the lie algebra ofq pseudodifferential symbols on the circle abstract we construct cocycles on the lie algebra of pseudo and q pseudodifferential symbols of one variable and on their close relatives the sine algebra and the poisson algebra on two torus a quantum godbillon vey cocycle on pseudo differential operators appears in this construction as a natural generalization of the gelfand fuchs 3 cocycle on periodic vector fields a nontrivial embedding of the virasoro algebra into a completion of q pseudodifferential symbols is proposed we describe q analogs of the kp and kdv hierarchies admitting an infinite number of conserved charges as well as q deformed gelfand dickey structures

the generalized differential quadrature rule for initial value differential equations abstract the generalized differential quadrature rule gdqr proposed recently by the authors is applied here to solve initial value differential equations of the 2nd to 4th order differential quadrature expressions are derived based on the gdqr for these equations the hermite interpolation functions are used as trial functions to obtain the explicit weighting coefficients for an easy and efficient implementation of the gdqr the numerical solutions for example problems demonstrate that the gdqr has high efficiency and accuracy a detailed discussion on the present method is presented by comparing with other existing methods the present method can be extended to other types of differential equation systems

critical statistics in quantum chaos and calogero sutherland model at finite temperature we investigate the spectral properties of a generalized gaussian orthogonal ensemble capable of describing critical statistics the joint distribution of eigenvalues of this model is expressed as the diagonal element of the density matrix of a gas of particles governed by the calogero sutherland cs hamiltonian taking advantage of the correspondence between cs particles and eigenvalues and utilizing a recently conjectured expression by kravtsov and tsvelik for the finite temperature density density correlations of the cs model we show that the number variance of our random matrix model is asymptotically linear with a slope depending on the parameters of the model such linear behavior is a signature of critical statistics this random matrix model may be relevant for the description of spectral correlations of complex quantum systems with a self similar or fractal poincare section of its classical counterpart this is shown in detail for two examples the anisotropic kepler problem and a kicked particle in a well potential in both cases the number variance and the delta 3 statistic are accurately described by our analytical results

area preserving diffeomorphisms of riemann surfaces a number of riemann surfaces are constructed by factoring the plane under the action of discontinuous groups expressions are found for the algebras and curvatures of the groups of area preserving diffeomorphisms of the riemann surfaces the difficulties involved in finding finite algebras which yield the diffeomorphism algebras in the infinite dimension limit are discussed

continuum analogues of contragredient lie algebras lie algebras with a cartan operator and nonlinear dynamical systems we present an axiomatic formulation of a new class of infinitedimensional lie algebras the generalizations ofz graded lie algebras with generally speaking an infinite dimensional cartan subalgebra and a contiguous set of roots we call such algebras continuum lie algebras the simple lie algebras of constant growth are encapsulated in our formulation we pay particular attention to the case when the local algebra is parametrized by a commutative algebra while the cartan operator the generalization of the cartan matrix is a linear operator special examples of these algebras are the kac moody algebras algebras of poisson brackets algebras of vector fields on a manifold current algebras and algebras with differential or integro differential cartan operator the nonlinear dynamical systems associated with the continuum contragredient lie algebras are also considered

area preserving diffeomorphisms of the tetrahedron expressions for the curvature and structure constants of the area preserving diffeomorphism group of the tetrahedron are derived finite dimensional algebras are identified that yield the diffeomorphism lie algebra in an infinite limit

large n penner matrix model and a novel asymptotic formula for the generalized laguerre polynomials the gaussian penner matrix model is re examined in the light of the results which have been found in double well matrix models the orthogonal polynomials for the gaussian penner model are shown to be the generalized laguerre polynomials l n x with and x depending on n the size of the matrix an asymptotic formula for the orthogonal polynomials is derived following closely the orthogonal polynomial method of deo 1997 nucl phys b 504 609 the universality found in the double well matrix model is extended to include non polynomial potentials an asymptotic formula is also found for the laguerre polynomial using the saddle point method by rescaling and x with n combining these results a novel asymptotic formula is found for the generalized laguerre polynomials different from that given in szego s book in a different asymptotic regime this may have applications in mathematical and physical problems in the future the density density correlators are derived and are the same as those found for the double well matrix models these correlators in the smoothed large n limit are sensitive to odd and even n where n is the size of the matrix these results for the two point density density correlation function may be useful in finding eigenvalue effects in experiments in mesoscopic systems or small metallic grains there may be applications to string theory as well as the tunnelling of an eigenvalue from one valley to the other being an important quantity there

transitions in spectral statistics we present long range statistical properties of a recently introduced unitary random matrix ensemble whose short range correlations were found to describe a transition from wigner to poisson type as a function of a single parameter we argue by evaluating the two level correlation function of a different solvable model that the transition is perhaps a quite general feature for a class of models our analytic results compare well with numerical studies on a variety of physical systems we discuss the possibility of observing experimentally the signature of such transitions

application of differential quadrature to static analysis of structural components the numerical technique of differential quadrature for the solution of linear and non linear partial differential equations first introduced by bellman and his associates is applied to the equations governing the deflection and buckling behaviour of one and two dimensional structural components separate transformations are used for higher order derivatives as suggested by mingle thus extending the method to treat fourth order equations and to include multiple boundary conditions in the respective co ordinate directions results are obtained for various boundary and loading conditions and are compared with existing exact and numerical solutions by other methods the application of differential quadrature to this class of problems is seen to lead to accurate results with relatively small computational effort

high accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain summary based on the differential quadrature dq rule the gauss lobatto quadrature rule and the variational principle a dq finite element method dqfem is proposed for the free vibration analysis of thin plates the dqfem is a highly accurate and rapidly converging approach and is distinct from the differential quadrature element method dqem and the quadrature element method qem by employing the function values themselves in the trial function for the title problem the dqfem without using shape functions essentially combines the high accuracy of the differential quadrature method dqm with the generality of the standard finite element formulation and has superior accuracy to the standard fem and fdm and superior efficiency to the p version fem and qem in calculating the stiffness and mass matrices by incorporating the reformulated dq rules for general curvilinear quadrilaterals domains into the dqfem a curvilinear quadrilateral dq finite plate element is also proposed the inter element compatibility conditions as well as multiple boundary conditions can be implemented simply and conveniently as in fem through modifying the nodal parameters when required at boundary grid points using the dq rules thus the dqfem is capable of constructing curvilinear quadrilateral elements with any degree of freedom and any order of inter element compatibilities a series of frequency comparisons of thin isotropic plates with irregular and regular planforms validate the performance of the dqfem copyright q 2009 john wiley sons ltd

the generalized differential quadrature rule for fourth order differential equations the generalized differential quadrature rule gdqr proposed here is aimed at solving high order differential equations the improved approach is completely exempted from the use of the existing point technique by applying multiple conditions in a rigorous manner the gdqr is used here to static and dynamic analyses of bernoulli euler beams and classical rectangular plates numerical error analysis caused by the method itself is carried out in the beam analysis independent variables for the plate are first defined the explicit weighting coefficients are derived for a fourth order differential equation with two conditions at two different points it is quite evident that the gdqr expressions and weighting coefficients for two dimensional problems are not a direct application of those for one dimensional problems the gdqr are implemented through a number of examples good results are obtained in this work copyright 2001 john wiley sons ltd

moyal nahm equations various aspects of the nahm equations in three and seven dimensions are investigated the residues of the variables at simple poles in the seven dimensional case form an algebra a large class of matrix representations of this algebra is constructed the large n limit of these equations is taken by replacing the commutators by moyal brackets and a set of nontrivial solutions in a generalized form of wigner distribution functions is obtained

rotationally invariant family of levy like random matrix ensembles we introduce a family of rotationally invariant random matrix ensembles characterized by a parameter while 1 corresponds to well known critical ensembles we show that 1 describes levy like ensembles characterized by power law eigenvalue densities for 1 the density is bounded as in gaussian ensembles but 1 describes ensembles characterized by densities with long tails in particular the model allows us to evaluate in terms of a novel family of orthogonal polynomials the eigenvalue correlations for levy like ensembles these correlations differ qualitatively from those in either the gaussian or the critical ensembles