a parameter adaptive control structure for linear multivariable systems this paper presents an adaptive control structure which can be used to assign all poles and zeros of a continuous time linear multivariable system represented by an m times m strictly proper transfer matrix t s provided t s has no right half plane zeros the controller parameters can be directly estimated from input output data the paper also serves to point out the type of a priori information necessary for multivariable adaptive controller design this information is a natural extension of that required in the scalar case

multidimensional integral inversion with applications in shape reconstruction in shape reconstruction the celebrated fourier slice theorem plays an essential role it allows one to reconstruct the shape of a quite general object from the knowledge of its radon transform s helgason the radon transform birkhauser boston boston 1980 in other words from the knowledge of projections of the object in case the object is a polygon g h golub p milanfar and j varah siam j sci comput 21 1999 pp 1222 1243 or when it defines a quadrature domain in the complex plane b gustafsson c he p milanfar and m putinar inverse problems 16 2000 pp 1053 1070 its shape can also be reconstructed from the knowledge of its moments essential tools in the solution of the latter inverse problem are quadrature rules and formal orthogonal polynomials in this paper we show how shape reconstruction from the knowledge of moments can also be realized in the case of general compact objects not only in two but also in higher dimensions to this end we use a less known homogeneous pade slice property again integral transforms in our case the multivariate stieltjes transform and univariate markov transform formal orthogonal polynomials in the form of pade denominators and multidimensional integration formulas or cubature rules play an essential role we emphasize that the new technique is applicable in all higher dimensions and illustrate it through the reconstruction of several two and three dimensional objects

vector bundles and f theory to understand in detail duality between heterotic string and f theory compactifications it is important to understand the construction of holomorphic g bundles over elliptic calabi yau manifolds for various groups g in this paper we develop techniques to describe these bundles and make several detailed comparisons between the heterotic string and f theory

a new set of necessary and sufficient conditions for a system to be prime in this note we first generalize the notion of the interactor wolovich and falb 1 and modify the input output structure algorithm of silverman 2 in order to obtain simple relations between the dimension of supremal output nulling invariant subspace v and the degree of the determinant of the interactor partial t and the integers obtained from the structure algorithm then we show that these relations can be used to derive a new set of necessary and sufficient conditions for a linear multivariable system to be prime morse 3

reconstructing polygons from moments with connections to array processing we establish a set of results showing that the vertices of any simply connected planar polygonal region can be reconstructed from a finite number of its complex moments these results find applications in a variety of apparently disparate areas such as computerized tomography and inverse potential theory where in the former it is of interest to estimate the shape of an object from a finite number of its projections whereas in the latter the objective is to extract the shape of a gravitating body from measurements of its exterior logarithmic potentials at a finite number of points we show that the problem of polygonal vertex reconstruction from moments can in fact be posed as an array processing problem and taking advantage of this relationship we derive and illustrate several new algorithms for the reconstruction of the vertices of simply connected polygons from moments

generalized output nulling subspaces riccati equation computation and applications four generalized output nulling subspaces ons are defined and it is shown that many subspaces important in the analysis of linear systems can be expressed as special cases of the ons on the other hand it is shown that the ons can be computed from the solutions to square root riccati equations applications to computation of subspaces contained in the state space and applications to system inversion are demonstrated the properties of the ons considered as time dependent subspace sequences are investigated

einstein hermitian connections on polystable principal bundles over a compact kahler manifold given a compact kahler manifold m and a connected reductive algebraic group g over inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i a prinlcipal g bundle over m admits an einstein hermitian connection if and only if the principal bundle is polystable if m is a projective manifold a higgs g bundle over m admits an einstein hermitian connection if and only if the higgs bundle is polystable

restriction theorems for principal bundles let e be a semistable or stable principal bundle over a smooth complex projective variety x and let d x be a complete intersection we study the semi stability of the restriction e d some of the results known for vector bundles such as grauert mulich flenner and mehta ramanathan theorems are generalized to principal bundles

parameter and structure identification of linear multivariable systems abstract in this paper a parameter and structure identification scheme which can be used for both continuous and discrete time systems is presented this scheme has an on line nature and it incorporates standard techniques such as state variable filters and adaptation laws developed through stability analysis the canonical form being used is based on the output injection which is constructed to assign all the poles of the system to an arbitrary chosen real number it is therefore named the canonical form

conjugacy classes in affine kac moody groups and principal g bundles over elliptic curves abstract for a simple complex lie group g the connected components of the moduli space of semistable g bundles over an elliptic curve are weighted projective spaces or quotients of weighted projective spaces by a finite group action in this note we will provide a new proof of this result using the invariant theory of affine kac moody groups in particular the action of the twisted coxeter element on the root system of g

moduli spaces for principal bundles in arbitrary characteristic in this article we solve the problem of constructing moduli spaces of semistable principal bundles and singular versions of them over smooth projective varieties over algebraically closed ground fields of positive characteristic

a stable numerical method for inverting shape from moments we derive a stable technique based upon matrix pencils for the reconstruction of or approximation by polygonal shapes from moments we point out that this problem can be considered the dual of 2 d numerical quadrature over polygonal domains an analysis of the sensitivity of the problem is presented along with some numerical examples illustrating the relevant points finally an application to the problem of gravimetry is explored where the shape of a gravitationally anomalous region is to be recovered from measurements of its exterior gravitational field

degree of dieudonne determinant defines the order of nonlinear system abstractthe paper proves that the order of the minimal state space realisation of a set of irreducible implicit input output i o difference equations is equal to the degree of the dieudonne dete

on the stack of semistable g bundles over an elliptic curve in a recent paper ben zvi and nadler proved that the induction map from b bundles of degree 0 to semistable g bundles of degree 0 over an elliptic curve is a small map with galois group isomorphic to the weyl group of g we generalize their result to all connected components of text bun g for an arbitrary reductive group g we prove that for every degree i e topological type there exists a unique parabolic subgroup such that any semistable g bundle of this degree has a reduction to it and moreover the induction map is small with galois group the relative weyl group of the levi this provides new examples of simple automorphic sheaves which are constituents of eisenstein sheaves for the trivial local system

moduli space of principal sheaves over projective varieties let g be a connected reductive group the late ramanathan gave a notion of semi stable principal g bundle on a riemann surface and constructed a projective moduli space of such objects we generalize ramanathan fs notion and construction to higher dimension allowing also objects which we call semistable principal g sheaves in order to obtain a projective moduli space a principal g sheaf on a projective variety x is a triple p e o where e is a torsion free sheaf on x p is a principal g bundle on the open set u where e is locally free and o is an isomorphism between e u and the vector bundle associated to p by the adjoint representation we say it is semi stable if all filtrations e of e as sheaf of killing orthogonal algebras i e filtrations with e ui e i 1 and ei ej e e e i j have pei rke pe rkei 0 where pei is the hilbert polynomial of ei after fixing the chern classes of e and of the line bundles associated to the principal bundle p and characters of g we obtain a projective moduli space of semistable principal g sheaves we prove that in case dimx 1 our notion of semi stability is equivalent to ramanathan fs notion

fourier gauss fraunhofer porod and the shape from moments problem we show how the fourier transform of a shape in any number of dimensions can be simplified using gauss s law and evaluated explicitly for polygons in two dimensions polyhedra in three dimensions etc we also show how this combination of fourier and gauss can be related to numerous classical problems in physics and mathematics examples include fraunhofer diffraction patterns porod s law the shape from moments problem and davis s extension of the motzkin schoenberg formula to polygons in the complex plane

a direct computational method for determining the maximal a b invariant subspace contained in ker c a useful method for calculation of the maximal a b invariant subspace contained in ker c is presented the method demands reduction of certain matrices into echelon form and application of rank test for low dimensional real matrices the approach presented allows unification of the approach of bhattacharyya vardulakis and wonham