asymptotics of a fredholm determinant corresponding to the first bulk critical universality class in random matrix models we study the determinant det i kpii of an integrable fredholm operator kpii acting on the interval s s whose kernel is constructed out of the function associated with the hastings mcleod solution of the second painleve equation this fredholm determinant describes the critical behavior of the eigenvalue gap probabilities of a random hermitian matrix chosen from the unitary ensemble in the bulk double scaling limit near a quadratic zero of the limiting mean eigenvalue density using the riemann hilbert method we evaluate the large s asymptotics of det i kpii

non semi regular quantum groups coming from number theory in this paper we study c algebraic quantum groups obtained through the bicrossed product construction examples using groups of adeles are given and they provide the first examples of locally compact quantum groups which are not semi regular the crossed product of the quantum group acting on itself by translations does not contain any compact operator we describe all corepresentations of these quantum groups and the associated universal c algebras on the way we provide several remarks on c algebraic properties of quantum groups and their actions

admissibility conjecture and kazhdan s property t for quantum groups abstract we give a partial solution to a long standing open problem in the theory of quantum groups namely we prove that all finite dimensional representations of a wide class of locally compact quantum groups factor through matrix quantum groups admissibility conjecture for quantum group representations we use this to study kazhdan s property t for quantum groups with non trivial scaling group strengthening and generalising some of the earlier results obtained by fima kyed and soltan chen and ng daws skalski and viselter and brannan and kerr our main results are i all finite dimensional unitary representations of locally compact quantum groups which are either unimodular or arise through a special bicrossed product construction are admissible ii a generalisation of a theorem of wang which characterises property t in terms of isolation of finite dimensional irreducible representations in the spectrum iii a very short proof of the fact that quantum groups with property t are unimodular iv a generalisation of a quantum version of a theorem of bekka valette proven earlier for quantum groups with trivial scaling group which characterises property t in terms of non existence of almost invariant vectors for weakly mixing representations v a generalisation of a quantum version of kerr pichot theorem proven earlier for quantum groups with trivial scaling group which characterises property t in terms of denseness properties of weakly mixing representations

kawada ito kelley theorem for quantum semigroups abstract idempotent states on locally compact quantum semigroups with weak cancellation properties are shown to be haar states on a certain sub object described by an operator system with comultiplication we also give a characterization of the situation when this sub object is actually a compact quantum subgroup in particular we reproduce classical results on idempotent probability measures on locally compact semigroups with cancellation

semidirect products of c quantum groups multiplicative unitaries approach c quantum groups with projection are the noncommutative analogues of semidirect products of groups radford s theorem about hopf algebras with projection suggests that any c quantum group with projection decomposes uniquely into an ordinary c quantum group and a braided c quantum group we establish this on the level of manageable multiplicative unitaries

a scattered equivalent source method for interpolation and gridding of potential field data in three dimensions potential field geophysical data observed at scattered discrete points in three dimensions can be interpolated gridded for example onto a level surface by relating the point data to a continuous function of equivalent discrete point sources the function used here is the inverse distance newtonian potential the sources located beneath some of the data points at a depth proportional to distance to the nearest neighboring data point are determined iteratively areas of no data are filled by minimum curvature for two dimensional 2 d data all data points at the same elevation grids calculated by minimum curvature and by equivalent sources are similar but the equivalent source method can be tuned to reduce aliasing gravity data in an area of high topographic relief in southwest u s a were gridded by minimum curvature a 2 d algorithm and also by equivalent sources 3 d the minimum curvature grid shows strong correlation with topography as expected because variation in gravity effect due to

tannaka krein duality for compact matrix pseudogroups twisted su n groups the notion of concrete monoidalw category is introduced and investigated a generalization of the tannaka krein duality theorem is proved it leads to new examples of compact matrix pseudogroups among them we have twistedsu n groups denoted bys u n it is shown that the representation theory fors u n is similar to that ofsu n irreducible representations are labeled by young diagrams and formulae for dimensions and multiplicity are the same as in the classical case

efficient 3d inversion of magnetic data via octree mesh discretization space filling curves and wavelets abstractairborne magnetic survey data sets can contain from hundreds of thousands to millions of observations and typically cover large areas the large number of measurements combined with a model mesh to accommodate the survey extent can render an inversion of these data intractable faced with this challenge we have developed a three step procedure to locally optimize the degree of model discretization and to compress the corresponding sensitivity matrix for the inversion of magnetic data the mesh optimization is achieved through the use of adaptive octree discretization the compression is achieved by first reordering the model cells using the hilbert space filling curve and then applying the one dimensional wavelet transform to the corresponding sensitivities the fractal property of the hilbert curve groups the spatially adjacent cells into algebraically adjacent positions in the reordered model mesh and thereby maximizes the number of zero or near zero coefficients in the one dimensional wavelet

reconciliation of the discrete and integral fourier transforms in the application of harmonic analysis to potential field geophysical studies relationships derived in terms of the continuous fourier integral transform are evaluated in terms of the discrete fourier transform the discrete transform obtained by transforming a finite number of equispaced samples of the actual aperiodic continuous function is too low at the dc level and increasingly too high in the high frequencies compared with the theoretical integral transform as a consequence overly restrictive limitations must be placed on high frequency amplifying operators such as differentiation and downward continuation also a spurious and troublesome azimuthal distortion occurs in the discrete fourier analysis of three dimensional 3 d map data represented as grids the discrete transform can be made essentially equivalent to the integral transform if before sampling the continuous aperiodic input function is made periodic by shifting the function by integer multiples of the data interval and summi

a bayesian approach to modeling 2d gravity data using polygons abstractwe apply a bayesian markov chain monte carlo formalism to the gravity inversion of a single localized 2d subsurface object the object is modeled as a polygon described by five parameters the number of vertices a density contrast a shape limiting factor and the width and depth of an encompassing container we first constrain these parameters with an interactive forward model and explicit geologic information then we generate an approximate probability distribution of polygons for a given set of parameter values from these we determine statistical distributions such as the variance between the observed and model fields the area the center of area and the occupancy probability the probability that a spatial point lies within the subsurface object we introduce replica exchange to mitigate trapping in local optima and to compute model probabilities and their uncertainties we apply our techniques to synthetic data sets and a natural data set collected across the rio grande gorge bridge i

a comparison of methods for approximating the vertical gradient of one dimensional magnetic field data the vertical gradient of a one dimensional magnetic field is known to be a useful aid in interpretation of magnetic data when the vertical gradient is required but has not been measured it is necessary to approximate the gradient using the available total field data an approximation is possible because a relationship between the total field and the vertical gradient can be established using fourier analysis after reviewing the theoretical basis of this relationship a number of methods for approximating the vertical gradient are derived these methods fall into two broad categories methods based on the discrete fourier transform and methods based on discrete convolution filters there are a number of choices necessary in designing such methods each of which will affect the accuracy of the computed values in differing and sometimes conflicting ways a comparison of the spatial and spectral accuracy of the methods derived here shows that it is possible to construct a filter which maintains a reason

rapid construction of equivalent sources using wavelets we have developed a fast algorithm for generating an equivalent source by using fast wavelet transforms based on orthonormal compactly supported wavelets we apply a 2d wavelet transform to each row and column of the coefficient matrix and subsequently threshold the transformed matrix to generate a sparse representation in the wavelet domain the algorithm then uses this sparse matrix to construct the the equivalent source directly in the wavelet domain performing an inverse wavelet transform then yields the equivalent source in the space domain using upward continuation of total field magnetic data between uneven surfaces as examples we have compared this approach with the direct solution using the dense matrix in the space domain we have shown that the wavelet approach can reduce the cpu time by as many as two orders of magnitude

relations between potential fields and some equivalent sources the concept of equivalent sources is described from first principles two types of sources that produce the same magnetic field are studied in detail thin sheets and uniaxially magnetized half spaces simple analytic solutions show that their magnetization variations are essentially given by the pseudogravity field and the magnetic field respectively while the former varies slowly to account for the slow variation in the vertically integrated magnetization the latter varies rapidly to account for the spatial variation in rock magnetization close to the observation points an extension of these simple distributions is the sandwich distribution using statistical arguments we construct sandwich distributions the depths and mean magnetizations of each layer are found from the decay of the azimuthally averaged power spectrum the equivalent layer magnetizations closely resemble the magnetic field anomaly when upward continued to a height equal to the mean depth of the layer

short distance asymptotics of ising correlations we prove that the short distance asymptotics for the even ising model scaling functions from below tc is given by the luther peschel formula generalizations to the odd scaling functions and holonomic fields are given

smooth fitting of geophysical data using continuous global surfaces continuous global surfaces cgs are a general framework for interpolation and smoothing of geophysical data the first of two smoothing techniques we consider in this paper is generalized cross validation gcv which is a bootstrap measure of the predictive error of a surface that requires no prior knowledge of noise levels the second smoothing technique is to define the cgs surface with fewer centers than data points and compute the fit by least squares lsqr the noise levels are implicitly estimated by the number and placement of the centers relative to the data points we show that both smoothing methods can be implemented using extensions to the existing fast framework for interpolation so that it is now possible to construct realistic smooth fits to the very large data sets typically collected in geophysics thin plate spline and kriging surfaces with gcv smoothing appear to produce realistic fits to noisy radiometric data the resulting surfaces are similar yet the thin plate spline required

smooth approximation of potential fields from noisy scattered data geophysical potential field data generally are observed at scattered sampling points and are contaminated by measurement and preprocessing errors analysis and further treatment require a representation of the underlying potential fields on a regular grid in the presence of noise an approximation of the data is more appropriate than an exact interpolation analysis of the smoothness of potential fields indicates an approximation by band limited functions the resulting least squares problem can be formulated as a linear system of equations in which the system matrix is of block toeplitz type this special structure allows a computationally attractive and robust solution via the fast fourier transform and the conjugate gradient algorithm on this basis we present a gridding method that incorporates additional knowledge about the physical properties of potential fields and the statistics of the data experimental results for synthetic and real world gravity data demonstrate good performance for highly sc

linear integral transformations and hierarchies of integrable nonlinear evolution equations abstract integrable hierarchies of nonlinear evolution equations are investigated on the basis of linear integral equations these are riemann hilbert type of integral transformations which leave invariant an infinite sequence of ordinary differential matrix equations of increasing order in an indefinite parameter k the potential matrices in these equations obey a set of nonlinear recursion relations leading to a heirarchy of nonlinear partial differential equations in decreasing order the same equations give rise to a reciprocal hierarchy associated with heisenberg ferromagnet type of equations central in the treatment is an embedding of the hierarchy into an infinite matrix structure which is constructed on the basis of the integral equations in terms of this infinite matrix structure the equations governing the hierarchies become quite simple furthermore it leads in a straightforward way to various generalizations such as to other types of linear spectral problems multicomponent system and lattice equations generalizations to equations associated with noncommuting flows follow as a direct consequence of the treatment finally some results on conserved densities and the hamiltonian structure are briefly discussed

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

from multiplicative unitaries to quantum groups ii abstract it is shown that all important features of a c algebraic quantum group a defined by a modular multiplicative w depend only on the pair a rather than the multiplicative unitary operator w the proof is based on thorough study of representations of quantum groups as an application we present a construction and study properties of the universal dual of a quantum group defined by a modular multiplicative unitary without assuming existence of haar weights

using an equivalent source with positivity for low latitude reduction to the pole without striation we present a reformulation of reduction to the pole rtp of magnetic data at low latitudes and the equator using equivalent sources the proposed method addresses both the theoretical difficulty of low latitude instability and the practical issue of computational cost we prove that a positive equivalent source exists when the magnetic data are produced by normal induced magnetization and we show that the positivity is sufficient to overcome the low latitude instability in the space domain we further apply a regularization term directly to the recovered rtp field to improve the solution the use of equivalent source also naturally enables the processing of data acquired on uneven surface the result is a practical algorithm that is effective at the equatorial region and can process large scale data sets with uneven observation heights

hopf images in locally compact quantum groups abstract this manuscript is devoted to the study of the concept of a generating subset a k a hopf image of a morphism in the setting of locally compact quantum groups the aim of this paper is to provide an accurate description of the hopf image of a given morphism we extend and unify the previously existing approaches for compact and discrete quantum groups and present some results that can shed light on some local perspective in the theory of quantum groups in particular we provide a characterization of fullness of hopf image in the language of partial actions as well as in representation theoretic terms in the spirit of representation c categories extending some known results to the broader setting of non compact quantum groups

interpolation of potential field data by equivalent layer and minimum curvature a comparative analysis interpolation using only the observations at discrete points is an ill posed problem because it admits infinite solutions usually to reduce ambiguity a priori information about the sample function is introduced current interpolation methods in mineral exploration introduce only the constraints of continuity and smoothness of the interpolating function in interpolating potential field anomalies the constraint that the sampled function is harmonic may be introduced by the equivalent layer method elm we compare the performance of the elm and the minimum curvature method mcm in interpolating potential field anomalies by applying these methods to synthetic magnetic data simulating an aeromagnetic survey in the case the anomaly flanks and peak are undersampled the elm performs better than the mcm in recovering the anomaly gradients and peak in the case of elongated linear anomalies the elm recovers the exact linear pattern but the mcm introduces spurious oscillations in the linear pattern also

nonlinear inversion of gravity data using the schmidt lichtenstein approach the nonlinear inversion of the gravity from a single density interface can be performed through a power series expansion the method is based on the schmidt lichtenstein approach for solving nonlinear integral equations after expanding the nonlinear integral operator for the gravity effect as an operator power series the inverse operator series is found by applying a technique formally equivalent to the classical inversion scheme of a scalar power series unlike the forward power series expansion however the convergence of the inverse series is restricted to a low frequency domain characterized by a cutoff frequency that is dependent upon the amplitude of the gravity anomaly the magnitude of the density contrast and the mean depth of the interface to ensure the stability of the inversion scheme a suitable low pass filtering has to be performed by taking advantage of the noniterative nature of the inversion scheme and the fast fourier transform the method is efficiently applied to invert a profi

unbounded elements affiliated with c algebras and non compact quantum groups the affiliation relation that allows to include unbounded elements operators into thec algebra framework is introduced investigated and applied to the quantum group theory the quantum deformation of the two fold covering of the group of motions of euclidean plane is constructed a remarkable radius quantization is discovered it is also shown that the quantumsu 1 1 group does not exist on thec algebra level for real value of the deformation parameter

reproducing kernel hilbert space method for optimal interpolation of potential field data the rkhs based optimal image interpolation method presented by chen and de figueiredo 1993 is applied to scattered potential field measurements the rkhs which admits only interpolants consistent with laplace s equation is defined and its kernel derived the algorithm is compared to bicubic spline interpolation and is found to yield vastly superior results

asymptotics of a class of solutions to the cylindrical toda equations the small t asymptotics of a class of solutions to the 2d cylindrical toda equations is computed the solutions qk t have the representation qk t log det i k k log det i k k 1 where kk are integral operators this class includes the n periodic cylindrical toda equations for n 2 our results reduce to the previously computed asymptotics of the 2d radial sinh gordon equation and for n 3 and with an additional symmetry constraint they reduce to earlier results for the radial bullough dodd equation both of these special cases are examples of painleviii and have arisen in various applications the asymptotics of qk t are derived by computing the small t asymptotics det i k k b k t n a k

an adaptive iterative method for downward continuation of potential field data from a horizontal plane we have developed an improved adaptive iterative method based on the nonstationary iterative tikhonov regularization method for performing a downward continuation of the potential field data from a horizontal plane our method uses the tikhonov regularization result as initial value and has an incremental geometric choice of the regularization parameter we compared our method with previous methods tikhonov regularization landweber iteration and integral iteration method the downwardcontinuation performance of these methods in spatial and wavenumber domains were compared with the aspects of their iterative schemes filter functions and downwardcontinuation operators applications to synthetic gravity and real aeromagnetic data showed that our iterative method yields a better downward continuation of the data than other methods our method shows fast computation times and a stable convergence in addition the l curve criterion for choosing the regularization parameter is expressed here in the wavenumber domain and used to speed up computations and to adapt the wavenumber domain iterative method

on exact solutions to the cylindrical poisson boltzmann equation with applications to polyelectrolytes using exact results from the theory of completely integrable systems of the painleve toda type we examine the consequences for the theory of polyelectrolytes in the nonlinear poisson boltzmann approximation

application of cauchy type integrals in developing effective methods for depth to basement inversion of gravity and gravity gradiometry data one of the most important applications of gravity surveys in regional geophysical studies is determining the depth to basement conventional methods of solving this problem are based on the spectrum and or euler deconvolution analysis of the gravity field and on parameterization of the earth s subsurface into prismatic cells we have developed a new method of solving this problem based on 3d cauchy type integral representation of the potential fields traditionally potential fields have been calculated using volume integrals over the domains occupied by anomalous masses subdivided into prismatic cells this discretization can be computationally expensive especially in a 3d case the technique of cauchy type integrals made it possible to represent the gravity field and its gradients as surface integrals in this approach only the density contrast surface between sediment and basement needed to be discretized for the calculation of gravity field this was especially significant in the modeling and inversion of gravity data for determining the depth to the basement another important result was developing a novel method of inversion of gravity data to recover the depth to basement based on the 3d cauchy type integral representation our numerical studies determined that the new method is much faster than conventional volume discretization method to compute the gravity response our synthetic model studies also showed that the developed inversion algorithm based on cauchy type integral is capable of recovering the geometry and depth of the sedimentary basin effectively with a complex density profile in the vertical direction

fredholm determinants and the mkdv sinh gordon hierarchies for a particular class of integral operatorsk we show that the quantity phi log det i k log det i k satisfies both the integrated mkdv hierarchy and the sinh gordon hierarchy this proves a conjecture of zamolodchikov

string orthogonal polynomials string equations and 2 toda symmetries 1 the 2 toda lattice and its generic symmetries 2 a larger class of symmetries for special initial conditions 3 borel decomposition of moment matrices tau functions and string orthogonal polynomials 4 from string orthogonal polynomials to the 2 toda lattice and the string equation 5 virasoro constraints on two matrix integrals comment 45 pages latex

on the connection problem for painleve i we study the dependence of the tau function of the painleve i equation on the generalized monodromy of the associated linear problem in particular we compute the connection constants relating the tau function asymptotics on five canonical rays at infinity the result is expressed in terms of the dilogarithms of cluster type coordinates in the space of the stokes data

construction of solutions of the sine gordon equation by means of fredholm determinants abstract a new straightforward and rigorous approach to the theory of the sine gordon equation is presented it provides a simple and unified view of the three known methods for solution namely hirota s method of generating n soliton solutions the inverse scattering transform and backlund transformations in addition new types of solutions corresponding to multiple poles in the scattering data can be easily obtained the principal tool used is the theory of fredholm determinants generalisations to other soliton equations seem to be possible

asymptotics of a τ function arising in the two dimensional ising model the short distance assymptotics of the function associated to the 2 point function of the two dimensional ising model is computed as a function of the integration constant defined from the long distance behavior of the function the result is expressible in terms of the barnes double gamma function equivalently the barnesg function

monodromy dependence and connection formulae for isomonodromic tau functions we discuss an extension of the jimbo miwa ueno differential 1 form to a form closed on the full space of extended monodromy data of systems of linear ordinary differential equations with rational coefficients this extension is based on the results of m bertola generalizing a previous construction by b malgrange we show how this 1 form can be used to solve a long standing problem of evaluation of the connection formulae for the isomonodromic tau functions which would include an explicit computation of the relevant constant factors we explain how this scheme works for fuchsian systems and in particular calculate the connection constant for the generic painleve vi tau function the result proves the conjectural formula for this constant proposed by iorgov lisovyy and tykhyy we also apply the method to non fuchsian systems and evaluate constant factors in the asymptotics of the painleve ii tau function

on integrals of the tronquee solutions and the associated hamiltonians for the painleve ii equation abstract we consider a family of tronquee solutions of the painleve ii equation q s 2 q s 3 s q s 2 1 2 1 2 which is characterized by the stokes multipliers s 1 e 2 i s 2 s 3 e 2 i with being a free parameter these solutions include the well known generalized hastings mcleod solution as a special case if 0 we derive asymptotics of integrals of the tronquee solutions and the associated hamiltonians over the real axis for 1 2 and 0 with the constant terms evaluated explicitly our results agree with those already known in the literature if the parameters and are chosen to be special values some applications of our results in random matrix theory are also discussed

a cohomological description of property t for quantum groups abstract we prove a delorme guichardet type theorem for discrete quantum groups expressing property t of the quantum group in question in terms of its first cohomology groups as an application we show that the first l 2 betti number of a discrete property t quantum group vanishes

closed quantum subgroups of locally compact quantum groups abstract we investigate the fundamental concept of a closed quantum subgroup of a locally compact quantum group two definitions one due to s vaes and one due to s l woronowicz are analyzed and relations between them discussed among many reformulations we prove that the former definition can be phrased in terms of quasi equivalence of representations of quantum groups while the latter can be related to an old definition of podle from the theory of compact quantum groups the cases of classical groups duals of classical groups compact and discrete quantum groups are singled out and equivalence of the two definitions is proved in the relevant context a deep relationship with the quantum group generalization of the herz restriction theorem from classical harmonic analysis is also established in particular in the course of our analysis we give a new proof of the herz restriction theorem

polynomial equivalent layer we have developed a new cost effective method for processing large potential field data sets via the equivalent layer technique in this approach the equivalent layer is divided into a regular grid of equivalent source windows inside each window the physical property distribution is described by a bivariate polynomial hence the physical property distribution within the equivalent layer is assumed to be a piecewise polynomial function defined on a set of equivalent source windows we perform any linear transformation of a large set of data as follows first we estimate the polynomial coefficients of all equivalentsource windows by using a linear regularized inversion second we transform the estimated polynomial coefficients of all windows into the physical property distribution within the whole equivalent layer finally we premultiply this distribution by the matrix of green s functions associated with the desired transformation to obtain the transformed data the regularized inversion deals with a linear system of equations with dimensions based on the total number of polynomial coefficients within all equivalent source windows this contrasts with the classical approach of directly estimating the physical property distribution within the equivalent layer which leads to a system based on the number of data because the number of data is much larger than the number of polynomial coefficients the proposed polynomial representation of the physical property distribution within an equivalent layer drastically reduces the number of parameters to be estimated by comparing the total number of floating point operations required to estimate an equivalent layer via our method with the classical approach both formulated with cholesky s decomposition we can verify that the computation time required for building the linear system and for solving the linear inverse problem can be reduced by as many as three and four orders of magnitude respectively applications to synthetic and real data show that our method performs the standard linear transformations of potential field data accurately

continuation of potential fields between arbitrary surfaces an equivalent source algorithm is described for continuing either one or two dimensional potential fields between arbitrary surfaces in the two dimensional case the dipole surface is approximated as a set of plane faces with constant moments over each face in the one dimensional case the plane faces of the dipole surface reduce to straight line segments application of the algorithm to model and field examples of aeromagnetic data shows the method to be effective and accurate even when the terrain has strong topographic relief and is composed of highly magnetic volcanic rocks

toda soliton limits on general backgrounds abstract starting from an arbitrary background solution of the toda lattice we study limits of n soliton solutions on this given background as n tends to infinity this yields a new class of solutions of the toda lattice simultaneously we solve an inverse spectral problem for one dimensional jacobi operators we explicitly construct jacobi operators whose spectrum contains a given countable bounded set of eigenvalues and whose absolutely continuous spectrum coincides with that of a given background operator

toeplitz determinants with merging singularities we study asymptotic behavior for determinants of n n toeplitz matrices corresponding to symbols with two fisher hartwig singularities at the distance 2t 0 from each other on the unit circle we obtain large n asymptotics which are uniform for 0 t t0 where t0 is fixed they describe the transition as t 0 between the asymptotic regimes of 2 singularities and 1 singularity the asymptotics involve a particular solution to the painlev e v equation we obtain small and large argument expansions of this solution as applications of our results we prove a conjecture of dyson on the largest occupation number in the ground state of a one dimensional bose gas and a conjecture of fyodorov and keating on the second moment of powers of the characteristic polynomials of random matrices

quantum groups with projection on von neumann algebra level abstract we introduce an axiomatization of the notion of a semidirect product of locally compact quantum groups and study their properties our approach is slightly different from the one introduced in the thesis of s roy 16 and unlike the investigations of roy we work within the von neumann algebraic picture this allows the use of powerful techniques related to crossed products by actions of locally compact quantum groups in particular we show existence of a braided comultiplication on the algebra spanned by slices of braided multiplicative unitary

isomonodromy aspects of the tt equations of cecotti and vafa ii riemann hilbert problem in guest et al arxiv 1209 2045 part i we computed the stokes data for the smooth solutions of the tt toda equations whose existence we had previously established by p d e methods here we formulate the existence problem as a riemann hilbert problem based on this stokes data and solve it under certain conditions theorem 5 4 in the process we compute the connection matrix for all smooth solutions thus completing the computation of the monodromy data theorem 5 5 we also give connection formulae relating the asymptotics at zero and infinity of all smooth solutions theorem 4 1 clarifying the region of validity of the formulae established earlier by tracy and widom finally we resolve some conjectures of cecotti and vafa concerning the positivity of s st where s is the stokes matrix and the unimodularity of the eigenvalues of the monodromy matrix theorem 5 6 in particular we show that unitarity implies regularity for the tt toda equations

the equivalent data concept applied to the interpolation of potential field data the equivalent layer calculation becomes more efficient by first converting the observed potential data set to a much smaller equivalent data set thus saving considerable cpu time this makes the equivalent source method of data interpolation very competitive with other traditional gridding techniques that ignore the fact that potential anomalies are harmonic functions the equivalent data set is obtained by using a least squares iterative algorithm at each iteration that solves an underdetermined system fitting all observations selected from previous iterations and the observation with the greatest residual in the preceding iteration the residuals are obtained by computing a set of predicted observations using the estimated parameters at the current iteration and subtracting them from the observations the use of cholesky s decomposition to implement the algorithm leads to an efficient solution update everytime a new datum is processed in addition when applied to interpolation problems using equiva

on the analysis of incomplete spectra in random matrix theory through an extension of the jimbo miwa ueno differential abstract several distribution functions in the classical unitarily invariant matrix ensembles are prime examples of isomonodromic tau functions as introduced by jimbo miwa and ueno jmu in the early 1980s 45 recent advances in the theory of tau functions 41 based on earlier works of b malgrange and m bertola have allowed to extend the original jimbo miwa ueno differential form to a 1 form closed on the full space of extended monodromy data of the underlying lax pairs this in turn has yielded a novel approach for the asymptotic evaluation of isomonodromic tau functions including the exact computation of all relevant constant factors we use this method to efficiently compute the tail asymptotics of soft edge hard edge and bulk scaled distribution and gap functions in the complex wishart ensemble provided each eigenvalue particle has been removed independently with probability 1 0 1

discrete linear transformations of potential field data we present a new approach to perform any linear transformation of gridded potential field data using the equivalent layer principle it is particularly efficient for processing areas with a large amount of data an n n data window is inverted using an m m equivalent layer with m greater than n so that the equivalent sources extend beyond the data window only the transformed field at the center of the data window is computed by premultiplying the equivalent source matrix by the row of the green s matrix associated with the desired transformation corresponding to the center of the data window since the inversion and the multiplication by the green s matrix are independent of the data they are performed beforehand and just once for given values of n m and the depth of the equivalent layer as a result a grid operator for the desired transformation is obtained which is applied to the data by a procedure similar to discrete convolution the application of this procedure in reducing synthetic anoma

emergence of a singularity for toeplitz determinants and painleve v we obtain asymptotic expansions for toeplitz determinants corresponding to a family of symbols depending on a parameter t for t positive the symbols are regular so that the determinants obey szeg s strong limit theorem if t 0 the symbol possesses a fisher hartwig singularity letting t 0 we analyze the emergence of a fisher hartwig singularity and a transition between the two different types of asymptotic behavior for toeplitz determinants this transition is described by a special painleve v transcendent a particular case of our result complements the classical description of wu mccoy tracy and barouch of the behavior of a 2 spin correlation function for a large distance between spins in the two dimensional ising model as the phase transition occurs

a short note on the scaling function constant problem in the two dimensional ising model we provide a simple derivation of the constant factor in the short distance asymptotics of the tau function associated with the 2 point function of the two dimensional ising model this factor was first computed by tracy commun math phys 142 297 311 1991 via an exponential series expansion of the correlation function further simplifications in the analysis are due to tracy and widom commun math phys 190 697 721 1998 using fredholm determinant representations of the correlation function and wiener hopf approximation results for the underlying resolvent operator our method relies on an action integral representation of the tau function and asymptotic results for the underlying painleve iii transcendent from mccoy et al j math phys 18 1058 1092 1977

examples of non compact quantum group actions abstract we present two examples of actions of non regular locally compact quantum groups on their homogeneous spaces the homogeneous spaces are defined in a way specific to these examples but the definitions we use have the advantage of being expressed in purely c algebraic language we also discuss continuity of the obtained actions finally we describe in detail a general construction of quantum homogeneous spaces obtained as quotients by compact quantum subgroups

some classes of solutions to the toda lattice hierarchy we apply an analogue of the zakharov shabat dressing method to obtain infinite matrix solutions to the toda lattice hierarchy using an operator transformation we convert some of these into solutions in terms of integral operators and fredholm determinants others are converted into a class of operator solutions to the l periodic toda hierarchy