inverse scattering for surface impedance from phase less far field data we present a numerical comparison of a regularized newton type method and a direct method for reconstructing the surface impedance function of a three dimensional acoustic scatterer with known shape from the full far field pattern for scattering of one incident time harmonic plane wave furthermore we propose a modification of the newton type algorithm to recover a real valued surface impedance from phase less far field data numerical reconstructions illustrate the feasibility of the methods

speed observation and position feedback stabilization of partially linearizable mechanical systems the problems of speed observation and position feedback stabilization of mechanical systems are addressed in this paper our interest is centered on systems that can be rendered linear in the velocities via a partial change of coordinates it is shown that the class is fully characterized by the solvability of a set of partial differential equations pdes and strictly contains the class studied in the existing literature on linearization for speed observation or control a reduced order globally exponentially stable observer constructed using the immersion and invariance methodology is proposed the design requires the solution of another set of pdes which are shown to be solvable in several practical examples it is also proven that the full order observer with dynamic scaling recently proposed by karagiannis and astolfi obviates the need to solve the latter pdes finally it is shown that the observer can be used in conjunction with an asymptotically stabilizing full state feedback interconnection and damping assignment passivity based controller preserving asymptotic stability

homotopy techniques for tensor decomposition and perfect identifiability let t be a general complex tensor of format n1 nd when the fraction i ni 1 i ni 1 is an integer and a natural inequality called balancedness is satisfied it is expected that t has finitely many minimal decomposition as a sum of decomposable tensors we show how homotopy techniques allow us to find all the decompositions of t starting from a given one in particular this gives a guess true with high probability about the total number of these decompositions this guess matches exactly with all cases previously known and predicts several unknown cases some surprising experiments yielded two new cases of generic identifiability formats 3 4 5 and 2 2 2 3 which have a unique decomposition as the sum of 6 and 4 decomposable tensors respectively we conjecture that these two cases together with the classically known matrix pencils are the only cases where generic identifiability holds i e the only identifiable cases building on the computational experiments we also use basic tools from algebraic geometry to prove these two new cases are indeed generically identifiable

on a class of special linear systems of mathbb p 3 in this paper we deal with linear systems of p 3 through fat points we consider the behavior of these systems under a cubic cremona transformation that allows us to produce a class of special systems which we conjecture to be the only ones

on a notion of speciality of linear systems in p n 2014 american mathematical society given a linear system in pn with assigned multiple general points we compute the cohomology groups of its strict transforms via the blow up of its linear base locus this leads us to give a new definition of expected dimension of a linear system which takes into account the contribution of the linear base locus and thus to introduce the notion of linear speciality we investigate such a notion giving sufficient conditions for a linear system to be linearly non special for an arbitrary number of points and necessary conditions for a small number of points

spherical blow ups of grassmannians and mori dream spaces abstract in this paper we classify weak fano varieties that can be obtained by blowing up general points in prime fano varieties we also classify spherical blow ups of grassmannians in general points and we compute their effective cone these blow ups are in particular mori dream spaces furthermore we compute the stable base locus decomposition of the blow up of a grassmannian in one point and we show how it is determined by linear systems of hyperplanes containing the osculating spaces of the grassmannian at the blown up point and by the rational normal curves in the grassmannian passing through the blown up point

on adaptive control of nonlinearly parameterized nonlinear systems towards a constructive procedure abstract a new framework to design immersion and invariance adaptive controllers for nonlinearly parameterized nonlinear systems was recently proposed by the authors the key step is the construction of a monotone mapping via a suitable selection of a controller tuning function which has to satisfy some integrability conditions this translates into the need to solve a partial differential equation pde in this paper this result is extended providing some answers to the questions of characterization of monotonizable systems and solvability of the pde first adding to the design a nonlinear dynamic scaling we obviate the need to solve the pde second for the case of factorizable nonlinearities the following results are established i it is shown that the monotonicity condition is satisfied if a linear matrix inequality is feasible ii directly verifiable involutivity conditions that ensure the solution of the pde are presented iii an explicit formula for the required tuning function is given provided the regressor matrix satisfies some rank conditions hence adding a dynamic scaling this yields a constructive solution to the problem

the possible dimensions of the higher secant varieties let x c p be an irreducible closed subvariety of projective space the kth higher secant variety of x denoted x is the closure of the union of all linear spaces spanned by k points of x let a ix dim x dim x l it is known that the sequence ty x is nonincreasing and that there may be at most one 1 in such a sequence we prove that these two conditions are also sufficient conditions for an arbitrary sequence a of nonnegative integers to be the fl x s for an irreducible variety x to this end we exhibit the ideals of the higher secant varities of rational normal scrolls as determinantal ideals this allows us to compute their dimensions showing that there is in fact always a rational normal scroll x such that ak x a for any sequence a satisfying the two conditions above adlandsvik al a2 and flenner and vogel f v much of this work has centered on the behavior of the differences ak x dimx dimx 1 of the dimensions of consecutive higher secant varieties it is well known that this sequence is nonincreasing and that there is at most one 1 in the sequence palatini claimed moreover that once ak x 1 were counterexamples a2 we answer here the question of what sequences actually appear as the ai x s of some variety x some of the guiding examples of varieties with degenerate higher secant varieties come from rational normal scrolls explicit equations for the scrolls themselves have been known for some time cf acgh we give a determi nantal presentation of the ideals of their higher secant varieties generalizing a result for rational normal scrolls in w this presentation enables us to compute the dimensions of all the higher secant varieties of a rational normal scroll and gives examples of varieties x with a prescribed nonincreasing ak x with at most one 1

the inverse scattering problem for time harmonic acoustic waves the inverse scattering problem we are considering in this paper is to determine the shape of a sound soft bounded connected obstacle from a knowledge of the time harmonic incident wave with frequency in the resonance region and the far field pattern of the scattered wave after some introductory remarks we begin by describing the method of integral equations and the null field method for solving the direct scattering problem this enables us to define an operator t mapping the boundary of the scattering obstacle and the incident field onto the far field pattern the inverse scattering problem is to invert this operator in order to do this we first must examine the range of t i e to characterize the class of far field patterns and to establish the existence of t on the range of t i e to show the uniqueness of the solution to the inverse scattering problem this analysis shows that for a given measured far field pattern in general no solution exists to the inverse scattering problem and if a solution does exist it does not depend continuously on the measured data i e the problem is improperly posed this motivates us to consider a linearized model and to examine various methods for studying linearized improperly posed problems based on the ideas of a priori assumptions and compactness arguments we then consider a simple model problem that focuses on the nonlinear character of the inverse scattering problem and motivated by our study of the linearized model reformulate the inverse scattering problem as a problem in constrained optimization we conclude by considering the numerical solution of this nonlinear optimization problem approach your problems from the right end and begin with the answers then one day perhaps you will find the final question from the hermit clad in crane feathers in the chinese maze murders by r van gulik

an inverse scattering problem from an impedance obstacle in this paper we consider an inverse scattering problem from an obstacle with impedance boundary condition our aim is to recover the unknown scatterer from the far field pattern iteratively assuming the impedance function our method while remaining in the framework of newton s method based on a system of two nonlinear integral equations which is equivalent to the original inverse problem avoids the need of calculating a direct problem at each iteration because of the ill posedness of this problem regularization method for example tikhonov regularization is incorporated in our solution scheme several numerical examples with only one incident wave are given at the end of the paper to show the feasibility of our method

reconstruction of the shape and surface impedance from acoustic scattering data for an arbitrary cylinder the inverse scattering for an obstacle d subset r 2 with mixed boundary condition can be considered as a prototype for radar detection of complex obstacles with coated and noncoated parts of the boundary we construct some indicator functions for this inverse problem using the far field pattern directly without the necessity of transforming the far field to the near field based on careful singularity analysis these indicator functions enable us to reconstruct the shape of the obstacle and distinguish the coated from the noncoated part of the boundary moreover an explicit representation formula for the surface impedance in the coated part of the boundary is also given our reconstruction scheme reveals that the coated part of the obstacle is less visible than the noncoated one which corresponds to the physical fact that the coated boundary absorbs some part of the scattered wave numerics are presented for the reconstruction formulas which show that both the boundary shape and the surface impedan

on stability for a translated obstacle with impedance boundary condition abstract this paper considers an inverse problem of determining the location of a known obstacle and its boundary impedance from one or two incident waves we firstly derive a concrete formula of the far field pattern due to a translation of the obstacle and perturbation of its boundary impedance based on this formula we establish lipschitz stability for the recovery of translation of an obstacle with one incident wave in the special case of obstacle being a ball lipschitz stability for the recovery of both location and its boundary coefficient can be obtained using two incident waves

on linear systems of p 3 through multiple points abstract we prove a conjecture about the dimension of linear systems of surfaces of degree d in p 3 through at most eight multiple points in general position

observers are unnecessary for output feedback control of lagrangian systems we address and solve some long standing yet well documented open problems on output feedback tracking control of euler lagrange systems with arbitrarily high relative degree this includes underactuated systems our main contribution is to establish a theoretical foundation for the use of so called dirty derivatives a common ad hoc replacement of unavailable state measurements such as generalized velocities whence obviating the the use of observers for the purpose of position feedback tracking control reminiscent of passivity based control for robot manipulators our control law is globally lipschitz and the controller dynamics is linear for relative degree two fully actuated lagrangian systems without dissipative forces friction and with bounded inertia matrix we establish uniform global asymptotic stability in closed loop furthermore we show that our control approach applies to lagrangian systems augmented by a chain of integrators relative degree m 2 systems the design method which is based on a recursive procedure in the spirit of backstepping control is intuitive as it exploits structural properties such as passivity and inherent input output stability as a corollary we solve an output feedback global tracking control problem for flexible joint robots but also for systems coupled with output feedback linearizable actuator dynamics in addition we discuss remaining open problems of fairly general interest in the realm of analysis and design of robust nonlinear systems

two globally convergent adaptive speed observers for mechanical systems a globally exponentially stable speed observer for mechanical systems was recently reported in the literature under the assumptions of known or no coulomb friction and no disturbances in this note we propose and adaptive version of this observer which is robust vis a vis constant disturbances moreover we propose a new globally convergent speed observer that besides rejecting the disturbances estimates some unknown friction coefficients for a class of mechanical systems that contains several practical examples

brief paper a globally exponentially convergent immersion and invariance speed observer for mechanical systems with non holonomic constraints the problem of velocity estimation for general n degrees of freedom mechanical systems is of great practical and theoretical interest for unconstrained systems many partial solutions have been reported in the literature however even in this case the basic question of whether it is possible to design a globally convergent speed observer remains open in this paper an affirmative answer to the question is given for general mechanical systems with knon holonomic constraints by proving the existence of a 3n 2k 1 dimensional globally exponentially convergent speed observer an observer for unconstrained mechanical systems is obtained as a particular case of this general result instrumental for the construction of the speed observer is the use of the immersion and invariance technique in which the observer design problem is recast as a problem of rendering attractive and invariant a manifold defined in the extended state space of the plant and the observer

the determination of the surface impedance of an obstacle from measurements of the far field pattern we consider the problem of determining the surface impedance of an obstacle from measurements of the far field pattern of a scattered time harmonic acoustic wave it is shown that this problem can be stabilized by assuming that the impedance is holder continuous with an a priori bound given on the impedance and its holder coefficient a constructive method for determining the impedance is given through the use of the backus gilbert method for solving improperly posed moment problems

inverse scattering problem from an impedance obstacle via two steps method in this paper we deal with the inverse scattering problem for an impedance obstacle the aim is to recover both the impedance function and the scatterer simultaneously based on boundary integral equations our method splits the inverse problem into a well posed direct problem followed by a smaller ill posed problem which has advantages both in understanding the inverse problem and in the numerical reconstructions

the inverse electromagnetic scattering problem for a perfectly conducting cylinder the problem of determining the shape of the cross section of a simply connected perfectly conducting infinite cylinder from a knowledge of the far field pattern for all angles of observation and small values of the wavenumber is considered the method proposed relies heavily on conformal mapping techniques in particular it is shown that if the transfinite diameter is known each fourier coefficient of the far field pattern of the electric field determines a laurent coefficient of the conformal mapping taking the exterior of the unit disk onto the exterior of the unknown cross section the transfinite diameter is determined by changing the polarization of the incoming wave and measuring the far field pattern of the resulting magnetic field of particular interest is the case when only a finite number of the fourier coefficients of the far field pattern are known in this situation error estimates are obtained by using results on coefficient estimates for univalent functions

postulation of general quintuple fat point schemes in p 3 we study the postulation of a general union y of double triple quartuple and quintuple points of p 3 in characteristic 0 we prove that y has good postulation in degree d 11 the proof is based on the combination of the horace differential lemma with a computer assisted proof we also classify the exceptions in degree 9 and 10

on generic identifiability of symmetric tensors of subgeneric rank we prove that the general symmetric tensor in sdcn 1 of rank r is identifiable provided that r is smaller than the generic rank that is its waring decomposition as a sum of r powers of linear forms is unique only three exceptional cases arise all of which were known in the literature our original contribution regards the case of cubics d 3 while for d 4 we rely on known results on weak defectivity by ballico ciliberto chiantini and mella

a globally exponentially stable tracking controller for mechanical systems using position feedback a solution to the problem of global exponential tracking of mechanical systems without velocity measurements is given in the technical note the proposed controller is obtained combining a redesign of the recently reported exponentially stable immersion and invariance velocity observer and a new state feedback passivity based controller which assigns to the closed loop a port hamiltonian structure with a desired energy function the result is applicable to a large class of mechanical systems including those with unbounded inertia matrix and possible presence of friction forces unlike previous results that rely on the presence exact knowledge and pervasiveness of these forces our design treats them as disturbances which are suitably compensated

ranks of tensors secant varieties of segre varieties and fat points abstract a classical unsolved problem of projective geometry is that of finding the dimensions of all the higher secant varieties of the segre embeddings of an arbitrary product of projective spaces an important subsidiary problem is that of finding the smallest integer t for which the secant variety of projective t spaces fills the ambient projective space in this paper we give a new approach to these problems the crux of our method is the translation of a well known lemma of terracini into a question concerning the hilbert function of fat points in a multiprojective space our approach gives much new information on the classical problem even in the case of three factors a case also studied in the area of algebraic complexity theory

an inverse acoustic scattering problem for an obstacle with an impedance boundary condition abstract the scattering of a plane time harmonic acoustic wave in two dimensional euclidean space by a bounded obstacle d with an impedance boundary condition imposed on its surface is considered a constructive method is given for determining approximations to both the shape of d and the surface impedance from low frequency measurements of the asymptotic behavior of the scattered waves corresponding to three different incident waves this is done using integral equation methods and conformal mapping techniques to arrive at a generalized moment problem for the determination of the unknown shape a fredholm integral equation of the first kind for the determination of the surface impedance is examined by restricting the surface impedance a priori to lie in a certain compact set and by considering a related constrained optimization problem it is shown that the problem of determining the surface impedance is well posed

robust energy shaping control of mechanical systems the problem of robustness improvement vis a vis external disturbances of energy shaping controllers for mechanical systems is addressed in this paper first it is shown that if the inertia matrix is constant constant disturbances both matched and unmatched can be rejected simply adding a suitable integral action interestingly not at the passive output for systems with non constant inertia matrix additional damping and gyroscopic forces terms must be added to reject matched disturbances and moreover enforce the property of integral input to state stability with respect to matched disturbances the stronger property of input to state stability this time with respect to matched and unmatched disturbances is ensured with further addition of nonlinear damping finally it is shown that including a partial change of coordinates the controller can be significantly simplified preserving input to state stability with respect to matched disturbances

linear systems on the blow up of p1 n abstract in this note we study linear systems on the blow up of p 1 n at r points in very general position we prove that the fibers of the projections p 1 n p 1 s 1 s n 1 can give contribution to the speciality of the linear system this allows us to give a new definition of expected dimension of a linear system in p 1 n which we call fiber dimension finally we state a conjecture about linear systems on p 1 3

high precision identification of an object optimality conditions based concept of imaging a class of inverse problems for the identification of an unknown geometric object from given measurements is considered a concept for object imaging based on optimality conditions and level sets is introduced which provides high resolution properties of the identification problem and stability to discretization and noise errors as a specific case the identification of the center of a test object of arbitrary shape and unknown boundary conditions from d boundary measurements in d spatial dimensions in the context of the helmholtz equation is described in detail for analysis and numerical realization methods from topology optimization generalized singular perturbations endowed with variational techniques and a petrov galerkin enrichment within generalized fem are used

collisions of fat points and applications to interpolation theory abstract we address the problem to determine the flat limit of the collision of fat points in p n we give a description of the limit scheme in many cases in particular in low dimension and multiplicities the problem turns out to be closely related with interpolation theory and as an application we exploit collisions to prove new cases of laface ugaglia conjecture

birational aspects of the geometry of varieties of sums of powers abstract varieties of sums of powers describe the additive decompositions of a homogeneous polynomial into powers of linear forms the study of these varieties dates back to sylvester and hilbert but only few of them for special degrees and number of variables are concretely identified in this paper we aim to understand a general birational behavior of vsp to do this we birationally embed these varieties into grassmannians and prove the rational connectedness of many vsp in arbitrary degrees and number of variables

weakly defective varieties a projective variety x is k weakly defective when its intersection with a general k 1 tangent hyperplane has no isolated singularities at the k 1 points of tangency if x is k defective i e if the k secant variety of x has dimension smaller than expected then x is also k weakly defective the converse does not hold in general a classification of weakly defective varieties seems to be a basic step in the study of defective varieties of higher dimension we start this classification here describing all weakly defective irreducible surfaces our method also provides a new proof of the classical terracini s classification of k defective surfaces

secant varieties of segre veronese embeddings of p 1 r we use a double degeneration technique to calculate the dimension of the secant variety of any segre veronese embedding of mathbb p 1 r

a separation principle for underactuated lossless lagrangian systems we study under actuated lagrangian systems without dissipative forces augmented by a chain of integrators for such systems we solve the open problem of global tracking control via position measurements only strictly speaking we establish uniform global asymptotic stability for the closed loop system as a corollary we obtain an original statement for flexible joint robots which closes a long standing open problem of output feedback nonlinear control

the determination of the surface impedance of a partially coated obstacle from far field data a variational method is given for determining the essential supremum of the surface impedance of a partiallycoated perfect conductor from a knowledge of the far field pattern of the time harmonic electric field at fixed frequency it is assumed that the shape of the scatterer has been determined e g bysolving the far field equation and using the linear sampling method numerical examples are given for the scalar case with constant surface impedance