a relativistic hypergeometric function we survey our work on a function generalizing 2f1 this function is a joint eigenfunction of four askey wilson type hyperbolic difference operators reducing to the askey wilson polynomials for certain discrete values of the variables it is defined by a contour integral generalizing the barnes representation of 2f1 it has various symmetries including a hidden d4 symmetry in the parameters by means of the associated hilbert space transform the difference operators can be promoted to self adjoint operators provided the parameters vary over a certain polytope in the parameter space for a dense subset of parameter shifts give rise to an explicit evaluation in terms of rational functions of exponentials hyperbolic functions and plane waves

general framework for dynamic substructuring history review and classification of techniques four decades after the development of the first dynamic substructuring techniques there is a necessity to classify the different methods in a general framework that outlines the relations between them in this paper a certain vision on substructuring methods is proposed by recalling important historical milestones that allow us to understand substructuring as a domain decomposition concept thereafter based on the dual and primal assembly of substructures a general framework for the classification of the methods is presented this framework allows us to indicate how the various classes of methods proposed along the years can be derived from a clear mathematical description of substructured problems current bottlenecks in experimental dynamic substructuring as well as solutions found in literature will also be briefly discussed

quantum 2 spheres and big q jacobi polynomials orthogonal bases for the algebras of functions of podles quantum 2 spheres are explicitly determined in terms of bigq jacobi polynomials this gives a group theoretic interpretation of the symmetric bigq jacobi polynomials and the symmetricq hahn polynomials

finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple lie algebra let g be a complex simple lie algebra we show that whent is not a root of 1 all finite dimensional representations of the quantum analogu t g are completely reducible and we classify the irreducible ones in terms of highest weights in particular they can be seen as deformations of the representations of the classical u g

quantization of poisson manifolds from the integrability of the modular function we discuss a framework for quantizing a poisson manifold via the quantization of its symplectic groupoid combining the tools of geometric quantization with the results of renault s theory of groupoid c algebras this setting allows very singular polarizations in particular we consider the case when the modular function is multiplicatively integrable i e when the space of leaves of the polarization inherits a groupoid structure if suitable regularity conditions are satisfied then one can define the quantum algebra as the convolution algebra of the subgroupoid of leaves satisfying the bohr sommerfeld conditions

some orthogonal very well poised functions recently ismail masson and suslov established a continuous orthogonality relation and some other properties of a bessel function on a q quadratic grid askey suggested that the bessel type orthogonality found in the above paper at the level really has a general character and can be extended up to the level very well poised fuctions are known as a nonterminating version of the classical askey wilson polynomials in this paper we prove askey s conjecture and discuss some properties of the orthogonal functions another type of the orthogonality relation for a very well poised function was recently found by askey rahman and suslov

relativistic lame functions the special case g 2 we study a class of eigenfunctions of an analytic difference operator generalizing the special lam operator paying particular attention to quantum mechanical aspects we show that in a suitable scaling limit the pertinent eigenfunctions lead to the eigenfunctions of the operator in a finite volume we establish various orthogonality and non orthogonality results by direct calculations generalize the one gap picture associated with the above lam operator and obtain duality properties for the hyperbolic trigonometric and rational specializations

structural damage assessment using a generalized minimum rank perturbation theory recently the authors proposed computationally attractive algorithms to determine the location and extent of structural damage for undamped structures assuming damage results in a localized change in stiffness properties the algorithms make use of a finite element model and a subset of measured eigenvalues and eigenvectors the developed theories approach the damage location and extent problem in a decoupled fashion first a theory is developed to determine the location of structural damage with location determined a damage extent theory is then developed the damage extent algorithm is a minimum rank perturbation which is consistent with the effects of many classes of structural damage on a finite element model in this work the concept of the minimum rank perturbation theory mrpt is adopted to determine the damage extent on the mass properties of an undamped structure in addition the mrpt is extended to the case of proportionall y damped structures for proportionally damped structures the mrpt is used to find the damage extent in any two of the three structural property matrices mass damping or stiffness finally illustrative case studies using both numerical and actual experimental data are presented he advent of the space shuttle has prompted considerable attention to the design and control of large space structures due to the large size and complexity of envisioned structures as well as the use of advanced materials to reduce structural weight it may become necessary to develop a structural health monitoring system to detect and locate structural damage as it occurs from experience gained in the machinery health monitoring field one would expect the vibration signature of the structure either frequency response functions and or modal parameters to provide useful information in determining the location and extent of structural damage assume that a refined finite element model fem of the structure has been developed before damage has occurred by refined we mean that the measured and analytical modal properties are in agreement next assume that at a later date some form of structural damage has occurred if significant the damage will result in a change in the structures modal parameters the question is can the discrepancy between the original fem modal properties and postdamage modal properties be used to ascertain structural damage most prior work in damage detection has used the general framework of fem refinement system identification in the development of damage assessment algorithms the motivation behind the development of fem refinement techniques is based on the need to validate engineering fems before their acceptance as the basis for final design analysis the standard problem has been to seek a refined fem that is as close to the original fem and whose modal properties are in agreement with those that are measured subject to various constraints such as symmetry and sparsity preservation a considerable amount of work in this area has been

eigenstructure assignment approach for structural damage detection in this work a methodology for incorporating measured modal data into an existing refined finite element model is examined with the objective of detecting and locating structural damage the algorithm is based on the partial inverse problem in that only partial spectral information is required the technique utilizes a symmetric eigenstructure assignment algorithm to perform the partial spectral assignment algorithms to enhance mode shape assignability and to preserve sparsity in the damaged fem are developed the sparsity preservation is of particular importance when considering damage detection in trusslike structures several examples are presented to highlight the key points made within the paper

elliptic hypergeometry of supersymmetric dualities ii orthogonal groups knots and vortices we consider seiberg electric magnetic dualities for 4d mathcal n 1 sym theories with so n gauge group for all such known theories we construct superconformal indices scis in terms of elliptic hypergeometric integrals equalities of these indices for dual theories lead both to proven earlier special function identities and new conjectural relations for integrals in particular we describe a number of new elliptic beta integrals associated with the s confining theories with the spinor matter fields reductions of some dualities from sp 2n to so 2n or so 2n 1 gauge groups are described interrelation of scis and the witten anomaly is briefly discussed possible applications of the elliptic hypergeometric integrals to a two parameter deformation of 2d conformal field theory and related matrix models are indicated connections of the reduced scis with the state integrals of knot theory generalized agt duality for 3 3 d theories and a 2d vortex partition function are described

elliptic hypergeometric series on root systems abstract we derive a number of summation and transformation formulas for elliptic hypergeometric series on the root systems a n c n and d n in the special cases of classical and q series our approach leads to new elementary proofs of the corresponding identities

relativistic lame functions revisited a basis for the eigenfunctions of the relativistic elliptic two particle calogero moser hamiltonian is known for a dense set in the natural parameter space we study the question whether an interpolating basis exists employing an asymptotic power series ansatz for the hyperbolic specialization we determine all of the coefficients explicitly which gives rise to formal interpolating eigenfunctions for the elliptic case we also need a power series ansatz for the eigenvalues we obtain the first few coefficients explicitly thus obtaining evidence for the existence of interpolating formal eigenfunctions and eigenvalues

a semidefinite program for distillable entanglement we show that the maximum fidelity obtained by a positive partial transpose p p t distillation protocol is given by the solution to a certain semidefinite program this gives a number of new lower and upper bounds on p p t distillable entanglement and thus new upper bounds on 2 locally distillable entanglement in the presence of symmetry the semidefinite program simplifies considerably becoming a linear program in the case of isotropic and werner states using these techniques we determine the p p t distillable entanglement of asymmetric werner states and maximally correlated states we conclude with a discussion of possible applications of semidefinite programming to quantum codes and 1 local distillation

grassmannian legendre functions the grassmannian analogues of the legendre polonomials are obtained from the corresponding grassmannian hermite multinomials the generating function recurrence relations and differential equation are given in contrast to the hermitian case there is no berezin weight function that orthogonalizes these functions generalizations to the tchebyscheff and gegenbauer cases are also possible

properties of generalized univariate hypergeometric functions based on spiridonov s analysis of elliptic generalizations of the gauss hypergeometric function we develop a common framework for 7 parameter families of generalized elliptic hyperbolic and trigonometric univariate hypergeometric functions in each case we derive the symmetries of the generalized hypergeometric function under the weyl group of type e 7 elliptic hyperbolic and of type e 6 trigonometric using the appropriate versions of the nassrallah rahman beta integral and we derive contiguous relations using fundamental addition formulas for theta and sine functions the top level degenerations of the hyperbolic and trigonometric hypergeometric functions are identified with ruijsenaars relativistic hypergeometric function and the askey wilson function respectively we show that the degeneration process yields various new and known identities for hyperbolic and trigonometric special functions we also describe an intimate connection between the hyperbolic and trigonometric theory which yields an expression of the hyperbolic hypergeometric function as an explicit bilinear sum in trigonometric hypergeometric functions

updating finite element dynamic models using an element by element sensitivity methodology a sensitivity based methodology for improving the finite element model of a given structure using test modal data and a few sensors is presented the proposed method searches for both the location and sources of the mass and stiffness errors and does not interfere with the theory behind the finite element model while correcting these errors the updating algorithm is derived from the unconstrained minimization of the squared 2 norms of the modal dynamic residuals via an iterative two step staggered procedure at each iteration the measured mode shapes are first expanded assuming that the model is error free then the model parameters are corrected assuming that the expanded mode shapes are exact the numerical algorithm is implemented in an element by element fashion and is capable of zooming on the detected error locations several simulation examples which demonstrate the potential of the proposed methodology are discussed i introduction e ven though the field of finite element analysis of structural dynamic problems has witnessed tremendous progress in the last two decades greater confidence is still placed in experimental data therefore the finite element model of a given structure is often updated to reflect the results of a particular experiment usually the computed eigenmodes are compared with the measured frequencies and mode shapes if both sets are not in agreement the finite element model is refined via a two step updating procedure which 1 locates the errors and 2 corrects them clearly the first step is the most challenging of the two once the location of the errors is known it is relatively easy to correct them especially if the error sources can be identified however locating and identifying these errors can be a difficult task for the following reasons in general only a few experimental modes are available and these may be contaminated with random and systematic measuring errors moreover only a subset of the degrees of freedom dof in the finite element model can be monitored and as for practical and economical reasons only a few sensors can be utilized

spherical functions on homogeneous superspaces homogeneous superspaces arising from the general linear supergroup are studied within a hopf algebraic framework spherical functions on homogeneous superspaces are introduced and the structures of the superalgebras of the spherical functions on classes of homogeneous superspaces are described explicitly

real time updating of structural mechanics models using kalman filtering modified constitutive relation error and proper generalized decomposition the paper aims at proposing a new strategy for real time identification or updating of structural mechanics models defined as dynamical systems the main idea is to introduce the modified constitutive relation error concept which is a practical tool that enables to efficiently solve identification problems with highly corrupted data into the kalman filtering which is a classical framework for data assimilation furthermore a pgd based model reduction method is performed in order to optimize capabilities of the online updating strategy performances of the proposed approach in terms of robustness gain and computational cost reduction are illustrated on several unsteady thermal applications

unitary representations of uq 2 ℝ the modular double and the multiparticle q deformed toda chain the paper deals with the analytic theory of the quantum q deformed toda chains the technique used combines the methods of representation theory and the quantum inverse scattering method the key phenomenon which is under scrutiny is the role of the modular duality concept first discovered by l faddeev in the representation theory of noncompact semisimple quantum groups explicit formulae for the whittaker vectors are presented in terms of the double sine functions and the wave functions of the n particle q deformed open toda chain are given as a multiple integral of the mellin barnes type for the periodic chain the two dual baxter equations are derived

a generalized hypergeometric function satisfying four analytic difference equations of askey wilson type the hypergeometric function 2 f 1 can be written in terms of a contour integral involving gamma functions we generalize this barnes representation by using a certain generalized gamma function as a building block in this way we obtain a new 2 f 1 generalization with various symmetry features we determine the analyticity properties of the r function in all of its eight arguments and show that it is a joint eigenfunction of four distinct askey wilson type difference operators two acting on v and two on the askey wilson polynomials can be obtained by a suitable discretization of v or

some mathematical constants the theory of multiple gamma functions was studied in about 1900 and has been revived in the study of determinants of laplacians in the middle or so of 1980s there are some classes of mathematical constants involved naturally in the gamma and multiple gamma functions here we introduce those known mathematical constants associated with the gamma and multiple gamma functions and will show how they are involved if possible

a generalized hypergeometric function ii asymptotics and d 4 symmetry in previous work we introduced and studied a function r a a bf c v hat v that generalizes the hypergeometric function in this paper we focus on a similarity transformed function mathcal e a a gamma v hat v with parameters 4 related to the couplings c 4 by a shift depending on a a we show that the function is invariant under all maps w with w in the weyl group of type d 4 choosing a a positive and bf gamma hat v real we obtain detailed information on the re v asymptotics of the function in particular we explicitly determine the leading asymptotics in terms of plane waves and the c function that implements the similarity r

detecting quantum entanglement we review the criteria for separability and quantum entanglement both in a bipartite as well as a multipartite setting we discuss bell inequalities entanglement witnesses entropic inequalities bound entanglement and several features of multipartite entanglement we indicate how these criteria bear on the experimental detection of quantum entanglement

a quantum duality principle for coisotropic subgroups and poisson quotients we develop a quantum duality principle for coisotropic subgroups of a formal poisson group and its dual namely starting from a quantum coisotropic subgroup for a quantization of a given poisson group we provide functorial recipes to produce quantizations of the dual coisotropic subgroup in the dual formal poisson group by the natural link between subgroups and homogeneous spaces we argue a quantum duality principle for poisson homogeneous spaces which are poisson quotients i e have at least one zero dimensional symplectic leaf as an application we provide an explicit quantization of the homogeneous sln space of stokes matrices with the poisson structure given by dubrovin and ugaglia

a new computational method for transient dynamics including the low and the medium frequency ranges this paper deals with a new computational method for transient dynamic analysis which enables one to cover both the low and medium frequency ranges this is a frequency approach in which the low frequency part is obtained through a classical technique while the medium frequency part is handled through the variational theory of complex rays vtcr initially introduced for vibrations preliminary examples are shown

reduced bases for model updating in structural dynamics based on constitutive relation error abstract this paper deals with the application of a model reduction method to the updating of models of industrial structures with many degrees of freedom the updating method is based on the concept of constitutive relation error this is an iterative method in which each iteration consists of a first step in which the most important errors in the model are localized and a second step in which these errors are corrected the reduction method follows a classical approach in which we introduce a truncated modal basis to which the static responses associated with different excitations are added the efficiency of the method is illustrated on one example of a finite element model containing 10 000 degrees of freedom in the first part we update the mass and stiffness properties of the model based on eigenmodes and eigenfrequencies in the second part the damping properties are updated based on the frequency response functions of the structure

entanglement detection and lower bound of the convex roof extension of the negativity we present a set of inequalities based on mean values of quantum mechanical observables similar to nonlinear entanglement witnesses for bipartite quantum systems these inequalities give rise to sufficient and necessary conditions for separability of all bipartite pure states and even some mixed states in terms of these mean values of quantum mechanical observables a measurable lower bound of the convex roof extension of the negativity is derived

comparison of deterministic and probabilistic approaches to identify the dynamic moving load and damages of a reinforced concrete beam two classical civil engineering inverse problems are considered the first deals with the determination of dynamic moving loads applied to a reinforced concrete beam the second one corresponds to the monitoring and the damage assessment the concrete damage due to overloading is modeled by a loss of the concrete young modulus whereas the steel bar damage due to corrosion effects is modeled by a reduction of the steel bar cross section to identify the loading and damage parameters deterministic and probabilistic model updating techniques are applied and compared in the deterministic approach a gradient descent technique based on the adjoint framework is used to minimize the data misfit functional with a tikhonov regularization term then a regularization by a means of bayes s rule is considered in a probabilistic approach the estimation is of the minimum variance type achieved with the help of the transformed ensemble kalman filter

modified constitutive relation error an identification framework dealing with the reliability of information abstract this paper proposes an identification strategy based on the principles of the modified constitutive relation error m cre the basic idea is to construct mechanical fields and material parameters that are a trade off between all the available information but with no further hypothesis the paper focuses on the identification of elastic properties from dic digital image correlation data in statics and the dealing of various kinds of boundary conditions unknown or known is especially discussed we study our methodology on numerical examples in both homogeneous and heterogeneous isotropic elasticity but a target application is the orthotopic behavior of aeronautic composites

a comparison of the entanglement measures negativity and concurrence in this paper we investigate two different entanglement measures in the case of mixed states of two qubits we prove that the negativity of a state can never exceed its concurrence and is always larger than 1 c 2 c2 1 c where c is the concurrence of the state furthermore we derive an explicit expression for the states for which the upper or lower bound is satisfied finally we show that similar results hold if the relative entropy of entanglement and the entanglement of formation are compared

selecting a ritz basis for the reanalysis of the frequency response functions of modified structures abstract the exact reanalysis of a structure is time consuming and when repeated reanalyses are needed it is often preferable to use an approximate ritz technique this approximate method consists in expressing the new frequency response function as a linear combination of vectors in a truncated modal basis one notices that even though the convergence to the exact frequency response function is monotonic it is generally irregular when the number of vectors introduced in the modal sub basis increases a solution to this consists of choosing the additional eigenvectors of the basis in such a way so as to give a best representation of the new frequency response function this choice is not an easy task particularly when the parametric modifications are very local and of large amplitudes this article describes an original approximate reanalysis technique for accurately evaluating frequency response of a modified structure it introduces new concepts for evaluating the static contribution of neglected eigenvectors resulting in a set of additional vectors completing the original ritz basis this method will be appreciated by designers working on the optimization of a prototype it can also be used during the iterations of a model updating procedure based on measured frequency response functions

pairings and actions for dynamical quantum groups abstract dynamical quantum groups constructed from a frst construction using a solution of the quantum dynamical yang baxter equation are equipped with a natural pairing the interplay of the pairing with structures corepresentations and dynamical representations is studied and natural left and right actions are introduced explicit details for the elliptic u 2 dynamical quantum group are given and the pairing is calculated explicitly in terms of elliptic hypergeometric functions dynamical analogues of spherical and singular vectors for corepresentations are introduced

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

hyperbolic beta integrals abstract hyperbolic beta integrals are analogues of euler s beta integral in which the role of euler s gamma function is taken over by ruijsenaars hyperbolic gamma function they may be viewed as q q bibasic analogues of the beta integral in which the two bases q and q are interrelated by modular inversion and they entail q analogues of the beta integral for q 1 the integrals under consideration are the hyperbolic analogues of the ramanujan integral the askey wilson integral and the nassrallah rahman integral we show that the hyperbolic nassrallah rahman integral is a formal limit case of spiridonov s elliptic nassrallah rahman integral

constitutive error based material parameter estimation procedure for hyperelastic material abstract we have explored hyperelastic material parameter identification problem via minimizing trace of the error in constitutive relation function from partial and corrupted displacement measurements under quasi static loading the inverse problem is posed as an optimization problem where the cost function measures the error in constitutive relation due to a constitutively incompatible pair of stress and strain field incompatibility of stress and strain arises due to dissimilar constraints is imposed in generating these fields an alternating approach is adopted to solve the optimization problem a simple yet effective penalty based approach is adopted to generate strain field that weakly satisfy available measurements while the regularization due to illposedness is achieved through the penalization parameter this also allows us to consider partial and corrupted data map in our reconstruction strategy after generating incompatible fields desired reconstruction is obtained via minimizing the constitutive disparity in the process we obtain explicit parameter update formula finally we show the applicability and computational capabilities of the proposed method via limited number of numerical experiments

direct method to construct integrals for nth order autonomous ordinary difference equations a direct method to construct integrals for an nth order autonomous ordinary difference equation oe wnnf wn wnn1 is presented as an illustration we first consider third order autonomous oe wn3

first order analytic difference equations and integrable quantum systems we present a new solution method for a class of first order analytic difference equations the method yields explicit minimal solutions that are essentially unique special difference equations give rise to minimal solutions that may be viewed as generalized gamma functions of hyperbolic trigonometric and elliptic type euler s gamma function being of rational type we study these generalized gamma functions in considerable detail the scattering and weight functions u and w functions associated to various integrable quantum systems can be expressed in terms of our generalized gamma functions we obtain detailed information on these u and w functions exploiting the difference equations they satisfy

updating structural dynamic models with emphasis on the damping properties the control of complex structural models is a e eld of growing interest the problem studied herein concerns damping updating using experimental frequency response functions although there are several methods improving structural dynamic models only a few of them deal specie cally with damping improvements the method introduced is built on mechanical bases using an error measure on the constitutive relations the tuning strategy uses an iterative process each iteration consisting of two steps the e rst one is the localization of the erroneous regions the second step is the correction of the parameters belonging to these regions examples illustrate the sensitivity of the error to the damping defects and its effectiveness for updating damped structures

krull s theory for the double gamma function abstract the barnes g function g x 1 2 satisfies the functional equation log g x 1 log g x log x we complement w krull s work in bemerkungen zur differenzengleichung g x 1 g x x math nachrichten 1 1948 365 376 with additional results that yield a different characterization of the function g new expansions and sharp bounds for g on x 0 in terms of gamma and digamma functions a new expansion for the gamma function and summation formulae with polygamma functions

quantum deformations of certain simple modules over enveloping algebras soit f un corps soit f 0 un sous corps de f soit u l algebre enveloppante universelle sur f 0 de l algebre de lie de kac moody correspondant a la matrice a d entiers on montre qu un module integrable de poids le plus eleve v de u admet une deformation quantique

complete integrability of relativistic calogero moser systems and elliptic function identities poincare invariant generalizations of the galilei invariant calogero moser a particle systems are studied a quantization of the classical integrals s1 sn is presented such that the operators si9 sn mutually commute as a corollary it follows that si9 9sn poisson commute these results hinge on functional equations satisfied by the weierstrass and 0 functions a generalized cauchy identity involving the function leads to an n x n matrix l whose symmetric functions are proportional to sl5 9sn

quantum zonal spherical functions and macdonald polynomials abstract a unified theory of quantum symmetric pairs is applied to q special functions previous work characterized certain left coideal subalgebras in the quantized enveloping algebra and established an appropriate framework for quantum zonal spherical functions here a distinguished family of such functions invariant under the weyl group associated to the restricted roots is shown to be a family of macdonald polynomials as conjectured by koornwinder and macdonald our results place earlier work for lie algebras of classical type in a general context and extend to the exceptional cases

the associated askey wilson polynomials we derive some contiguous relations for very well poised 8 7 series and use them to construct two linearly independent solutions of the three term recurrence relation of the associated askey wilson polynomials we then use these solutions to find explicit representations of two families of associated askey wilson polynomials we identify the corresponding continued fractions as quotients of two very well poised 807 series and find the weight functions

invariants and orthogonal q polynomials associated with cq osp 1 2 abstract the spaces of invariants and the zonal spherical functions associated with quantum super 2 spheres defined by c q osp 1 2 are discussed connection between the zonal spherical functions and orthogonal q polynomials from the askey wilson scheme is investigated

a generalized hypergeometric function iii associated hilbert space transform for generic parameters a a c 0 2 4 we associate a hilbert space transform to the relativistic hypergeometric function r a a bf c v hat v studied in previous papers restricting the couplings c to a certain polytope we show that the renormalized r function kernel gives rise to an isometry from the even subspace of l 2 mathbb r hat w hat v d hat v to the even subspace of l2 w v dv where hat w hat v and w v are positive and even weight functions we prove that the orthogonal complement of the range of this isometry is spanned by n pairwise orthogonal functions the latter are in essence askey wilson polynomials arising from the r function by choosing hat v i kappa n with kappa 0 ldots kappa n 1 distinct negative numbers the two commuting analytic difference operators acting on the variable v for which r is a joint eigenfunction give rise to two commuting self adjoint hamiltonians on the even subspace of l2 w v dv we explicitly determine the relation of the time dependent scattering theory for these dynamics to their joint spectral transform

gisin s theorem for arbitrary dimensional multipartite states we present a set of bell inequalities which are sufficient and necessary for separability of general pure multipartite quantum states in arbitrary dimensions the relations between bell inequalities and distillability are also studied we show that any quantum states that violate one of these bell inequalities are distillable

building a suited reduced modal basis for updating 3d acoustic models with the constitutive law error method abstract we have recently reported the possibility of developing an updating technique for acoustic finite element models based on the constitutive law error proposed by p ladeveze and co workers in structural dynamics like with every updating technique we are confronted with and interested in reducing the computational time the main idea of this paper consists in building a reduced modal basis made of two contributions static modes complete a truncated modal basis corresponding to the frequency range of computation the static modes are associated to the system excitation for instance a normal velocity boundary condition but also to the system damping and to the reference measurements updating acoustic models using the reduced modal basis shows a significant cpu time saving with respect to the full non reduced system with an acceptable accuracy

an energy error based method for the resolution of the cauchy problem in 3d linear elasticity a new method is described for the problem of expanding known displacement fields at the boundary of a solid together with the surface tractions on it towards the solid interior up to the inaccessible part of the boundary the solid is supposedly linearly elastic with known elastic moduli but not necessarily homogeneous nor isotropic the problem is the cauchy problem for the lame operator a new form of this cauchy problem suited for applications associated with surface tangential fields measurements is also stated and studied the method is based on the splitting of the elastic fields into two separate solutions of wellposed problems the gap between these fields is subsequently minimised with respect to the unknown boundary data in order to produce the desired expanded elastic fields the gap used here is an energy error associated with the elastic energy of the system various 3d applications are given including non linear boundary conditions on the unreachable boundary

a variational approach for parameter estimation based on balanced proper orthogonal decomposition abstract the adjoint method has been used significantly for parameter estimation this requires a significant programming effort to build adjoint model code and is computationally expensive as cost of one adjoint simulation often exceeds several original model runs the work proposed here is variational data assimilation based on balanced proper orthogonal decomposition bpod to identify uncertain parameters in numerical models and avoids the implementation of the adjoint with respect to model input parameters an ensemble of model simulations forward and backward is used to determine the model subspace while considering both inputs and outputs of the system by projecting the original model onto this subspace an approximate linear reduced model is obtained the adjoint of the tangent linear model is replaced by the adjoint of linear reduced model and the minimization problem is then solved in the reduced space at very low computational cost the performance of the method are illustrated with a number of data assimilation experiments in a 2d advection diffusion model the results demonstrate that the bpod based estimation approach successfully estimates the diffusion coefficient for both advection and diffusion dominated problems the paper also proposes an efficient method for computing the observable subspace when the number of observations is large is also proposed

new elliptic solutions of the yang baxter equation we consider finite dimensional reductions of an integral operator with the elliptic hypergeometric kernel describing the most general known solution of the yang baxter equation with a rank 1 symmetry algebra the reduced r operators reproduce at their bottom the standard baxter s r matrix for the 8 vertex model and sklyanin s l operator the general formula has a remarkably compact form and yields new elliptic solutions of the yang baxter equation based on the finite dimensional representations of the elliptic modular double the same result is also derived using the fusion formalism

new solutions of the star triangle relation with discrete and continuous spin variables a new solution to the star triangle relation is given for an ising type model of interacting spins containing integer and real valued components boltzmann weights of the model are given in terms of the lens elliptic gamma function and are based on yamazaki s recently obtained solution of the star star relation the star triangle relation given here implies seiberg duality for the 4 d index of the su 2 quiver gauge theory and the corresponding two component spin case of the star star relation of yamazaki a proof of the star triangle relation is given resulting in a new elliptic hypergeometric summation integration identity the star triangle relation in this paper contains the master solution of bazhanov and sergeev as a special case two other limiting cases are considered one of which gives a new star triangle relation in terms of ratios of infinite q products while the other case gives a new way of deriving a star triangle relation that was previously obtained by the author

constitutive error based parameter estimation technique for plate structures using free vibration signatures abstract in this paper a variant of constitutive equation error based material parameter estimation procedure for linear elastic plates is developed from partially measured free vibration sig natures it has been reported in many research articles that the mode shape curvatures are much more sensitive compared to mode shape themselves to localize inhomogeneity complying with this idea an identification procedure is framed as an optimization problem where the proposed cost function measures the error in constitutive relation due to incompatible curvature strain and moment stress fields unlike standard constitutive equation error based procedure wherein a solution of a couple system is unavoidable in each iteration we generate these incompatible fields via two linear solves a simple yet effective penalty based approach is followed to incorporate measured data the penalization parameter not only helps in incorporating corrupted measurement data weakly but also acts as a regularizer against the ill posedness of the inverse problem explicit linear update formulas are then developed for anisotropic linear elastic material numerical examples are provided to show the applicability of the proposed technique finally an experimental validation is also provided

ruijsenaars hypergeometric function and the modular double of u q sl 2 c abstract simultaneous eigenfunctions of two askey wilson second order difference operators are constructed as formal matrix coefficients of the principal series representation of the modular double of the quantized universal enveloping algebra u q sl 2 c these eigenfunctions are shown to be equal to ruijsenaars hypergeometric function under a proper parameter correspondence

boundary quantum knizhnik zamolodchikov equations and bethe vectors solutions to boundary quantum knizhnik zamolodchikov equations are constructed as bilateral sums involving off shell bethe vectors in case the reflection matrix is diagonal and only the 2 dimensional representation of mathcal u q widehat mathfrak sl 2 is involved we also consider their rational and classical degenerations

inversions of integral operators and elliptic beta integrals on root systems we prove a novel type of inversion formula for elliptic hypergeometric integrals associated to a pair of root systems using the a c inversion formula to invert one of the known c type elliptic beta integrals we obtain a new elliptic beta integral for the root system of type a validity of this integral is established by a different method as well

quantum flag manifolds quantum symmetric spaces and their associated universal k matrices abstract let u be a connected simply connected compact lie group with complexification g let u and g be the associated lie algebras let be the dynkin diagram of g with underlying set i and let u q u be the associated quantized universal enveloping algebra of u for some 0 q distinct from 1 let o q u be the coquasitriangular quantized function hopf algebra of u whose drinfeld double o q g r we view as the quantized function algebra of g considered as a real algebraic group we show how the datum of an involution of and a invariant function i r can be used to deform o q g r into a algebra o q id g r by a modification of the drinfeld double construction we then show how by a generalized theory of universal k matrices a specific subalgebra of o q id g r admits homomorphisms into both u q u and o q u the images being coideal subalgebras of respectively u q u and o q u we illustrate the theory by showing that two main classes of examples arise by such coideals namely quantum flag manifolds and quantum symmetric spaces except possibly for certain exceptional cases in the former case this connects to work of the first author and neshveyev while for the latter case we heavily rely on recent results of balagovic and kolb

a perspective on adaptive modeling and meshing am m the purpose of this study is to develop an integrated approach to adaptive modeling in conjunction with adaptive meshing this involves consideration of the modeling error from various sources and the discretization error in the numerical scheme adapting the model to control error due to geometry boundary data constitutive relations and model parameters can be integrated with adaptive mesh control to improve numerical reliability other factors such as stabilization by artificial dissipation and regularization are considered a class of hybrid algorithms are developed to combine these approaches

on the growth of logarithmic differences difference quotients and logarithmic derivatives of meromorphic functions a crucial ingredient in the recent discovery by ablowitz halburd herbst and korhonen 2000 2007 that a connection exists between discrete painleve equations and finite order nevanlinna theory is an estimate of the integrated average of log f z 1 f z on z r we obtained essentially the same estimate in our previous paper 2008 independent of halburd et al 2006 we continue our study in this paper by establishing complete asymptotic relations amongst the logarithmic differences difference quotients and logarithmic derivatives for finite order meromorphic functions in addition to the potential applications of our new estimates in integrable systems they are also of independent interest in particular our findings show that there are marked differences between the growth of meromorphic functions with nevanlinna order less than and greater than one we have established a difference analogue of the classical wiman valiron type estimates for meromorphic functions with order less than one which allow us to prove that all entire solutions of linear difference equations with polynomial coefficients of order less than one must have positive rational order of growth we have also established that any entire solution to a first order algebraic difference equation with polynomial coefficients must have a positive order of growth which is a difference analogue of a classical result of polya

improvement of a large analytical model using test data a method has been developed which uses measured normal modes and natural frequencies to improve an analytical mass and stiffness matrix model of a structure the method directly identifies without iteration a set of minimum changes in the analytical matrices which force the eigensolutions to agree with the test measurements an application is presented in which the analytical model had 508 degrees of freedom and 19 modes were measured at 101 locations on the structure the resulting changes in the model are judged to be small compared to expectations of error in the analysis thus the improved model is accepted as a reasonable model of the structure with improved dynamic response characteristics in addition it is shown that the procedure may be a useful tool in identifying apparent measured modes which are not true normal modes of the structure nomenclature analytical matrix matrix of changes identity matrix full improved stiffness and mass matrices n x n full analytical k m matrices n x n partitions of ka ma corresponding to test coordinates partitions of ka ma corresponding to coupling elements partitions of ka ma corresponding to unmea sured coordinates number of measured modes number of degrees of freedom in the model measures of changes eqs 15 17 matrix norm sum of the squares of all the elements rectangular modal matrix normalized n x m th mode th column of measured and unmeasured partitions of diagonal matrix of measured natural frequencies m xm natural frequency of th mode 12 17 sum of the squares of all elements of matrix

q special functions with q 1 and their application to discrete integrable systems solutions for certain discrete integrable systems are constructed by using integral solutions for hypergeometric q difference systems with q 1 we apply a solution for lauricella s d type hypergeometric q difference system with q 1 to construct a solution for the discrete kp hierarchy furthermore an integral solution of a q difference analogue of bessel s equation is newly introduced and applied to construct a solution for a q difference analogue of the cylindrical toda equation with q 1

modified constitutive relation error identification strategy for transient dynamics with corrupted data the elastic case abstract in this paper we present an identification strategy for transient dynamic tests with corrupted data and its first development for the identification of elastic properties this method is based on the modified constitutive relation error principle which was initially introduced for model updating in vibration analysis the governing principle of the method consists in splitting the equations of the problem into two groups a reliable group and an uncertain group and defining mechanical fields which verify the equations of the reliable group exactly and those of the uncertain group only approximately then these fields are used to estimate the quality of the model to be identified we tested our method on various examples and found it to be very robust with respect to high levels of perturbations furthermore we show that this good performance is due to the fact that the method takes into account all the experimental data in a single calculation and introduces a distance between the measurements and the calculation we also propose an alternative strategy dedicated to cases where there is no a priori knowledge of the perturbations

unextendible product bases and bound entanglement an unextendible product basis upb for a multipartite quantum system is an incomplete orthogonal product basis whose complementary subspace contains no product state we give examples of upbs and show that the uniform mixed state over the subspace complementary to any upb is a bound entangled state we exhibit a tripartite 2 3 2 3 2 upb whose complementary mixed state has tripartite entanglement but no bipartite entanglement i e all three corresponding 2 3 4 bipartite mixed states are unentangled we show that members of a upb are not perfectly distinguishable by local positive operator valued measurements and classical communication s0031 9007 99 09360 6

right coideal subalgebras in u _q so_ 2n 1 we offer a complete classification of right coideal subalgebras which contain all group like elements for the multiparameter version of the quantum group uq sln 1 provided that the main parameter q is not a root of 1 as a consequence we determine that for each subgroup of the group g of all group like elements the quantum borel subalgebra uq sln 1 contains n 1 different homogeneous right coideal subalgebras u such that u g if q has a finite multiplicative order t 2 the classification remains valid for homogeneous right coideal subalgebras of the multiparameter version of the lusztig quantum group uq sln 1 in the paper we consider the quantifications of kac moody algebras as character hopf algebras v k kharchenko a combinatorial approach to the quantifications of lie algebras pacific j math 203 1 2002 191 233

an addition type formula for the elliptic digamma function abstract eisenstein derived addition formulas for the weierstrass zeta function from the addition formula for the cotangent function and the fact that the weierstrass zeta function can be represented as an infinite sum of the cotangent functions in this paper we apply this idea of eisenstein s to the addition type formula for the double cotangent function established by the author we show that the elliptic digamma function defined by the logarithmic derivative of the elliptic gamma function satisfies an addition type formula this formula includes the addition formula for the weierstrass zeta function evaluation formulas for the double eisenstein series introduced by tsumura and the double shuffle relations for the double eisenstein series proved by gangl kaneko zagier