viscous scalar conservation law with nonlinear flux feedback and global attractors abstract in this paper we study the forced viscous scalar conservation law on 0 1 with the nonlinear flux feedback at the boundary global existence and uniqueness are established for l bounded initial conditions and forcing functions under an appropriate growth condition on the flux function and nonlinear dissipation at the boundary we show the existence of an absorbing set that absorbs the whole space l 0 1 and the existence of a compact global attractor in the l topology

on maximum typical and generic ranks we show that for several notions of rank including tensor rank waring rank and generalized rank with respect to a projective variety the maximum value of rank is at most twice the generic rank we show that over the real numbers the maximum value of the real rank is at most twice the smallest typical rank which is equal to the complex generic rank

structural damage detection based on a micro genetic algorithm using incomplete and noisy modal test data this paper describes a procedure for detecting structural damage based on a micro genetic algorithm using incomplete and noisy modal test data as the number of sensors used to measure modal data is normally small when compared with the degrees of freedom of the finite element model of the structure the incomplete mode shape data are first expanded to match with all degrees of freedom of the finite element model under consideration the elemental energy quotient difference is then employed to locate the damage domain approximately finally a micro genetic algorithm is used to quantify the damage extent by minimizing the errors between the measured data and numerical results the process may be either of single level or implemented through two level search strategies the study has covered the use of frequencies only and the combined use of both frequencies and mode shapes the proposed method is applied to a single span simply supported beam and a three span continuous beam with multiple damage locations in the study the modal test data are simulated numerically using the finite element method the measurement errors of modal data are simulated by superimposing random noise with appropriate magnitudes the effectiveness of using frequencies and both frequencies and mode shapes as the data for quantification of damage extent are examined the effects of incomplete and noisy modal test data on the accuracy of damage detection are also discussed

multiple criterion method for determining structural damage a new multiple criterion updating method that minimizes the euclidean norm of the error vector obtained by adding the normalized eigenproblem equation and equation of motion with equal weighting functions is proposed the method is applied to detecting damage in structures and is tested on an unsymmetrical h shaped structure it is found that the multiple criterion updating method predicts the presence the position and the extent of damage the multiple criterion method is compared to the frequency response function method and the modal property based method by using the coordinate modal assurance criterion and the modal assurance criterion the multiple criterion method was found to give better results than the other two methods this is because it was better able to detect damage on the structure than the modal property method which failed to detect multiple damage cases and gave results that were less noisy i e less updating to undamaged elements than the frequency response method

induction for secant varieties of segre varieties this paper studies the dimension of secant varieties to segre varieties the problem is cast both in the setting of tensor algebra and in the setting of algebraic geometry an inductive procedure is built around the ideas of successive specializations of points and projections this reduces the calculation of the dimension of the secant variety in a high dimensional case to a sequence of calculations of partial secant varieties in low dimensional cases as applications of the technique we give a complete classification of defective p secant varieties to segre varieties for p 6 we generalize a theorem of catalisano geramita gimigliano on non defectivity of tensor powers of pn we determine the set of p for which unbalanced segre varieties have defective p secant varieties in addition we completely describe the dimensions of the secant varieties to the deficient segre varieties p1 x p1 x pn x pn and p2 x p3 x p3 in the final section we propose a series of conjectures about defective segre varieties

typical tensorial rank abstract upper bounds on the typical rank r n m l of tensors maximal border rank rank of almost all tensors of a given shape n m l are presented these improve previous results by a tkinson and lloyd for cubic shape tensors the typical rank is determined exactly r n n n n3 3n 2 n 3

optimal control of damped klein gordon equations with state constraints abstract in this paper we study the maximum principles for optimal control problems governed by the damped klein gordon equations with state constraints and we prove the existence of the optimal parameter and deduce the necessary conditions on the optimal parameter

structural damage detection by a new iterative regularization method and an improved sensitivity function abstract a new sensitivity based damage detection method is proposed to identify and estimate the location and severity of structural damage using incomplete noisy modal data for these purposes an improved sensitivity function of modal strain energy mse based on lagrange optimization problem is derived to adapt the initial sensitivity formulation of mse to damage detection problem with the aid of new mathematical approaches in the presence of incomplete noisy modal data the sensitivity matrix is sparse rectangular and ill conditioned which leads to an ill posed damage equation to overcome this issue a new regularization method named as regularized least squares minimal residual rlsmr is proposed to solve the ill posed damage equation this method relies on krylov subspace and exploits bidiagonalization and iterative algorithms to solve linear mathematical systems for the majority of krylov subspace methods conventional direct methods for the determination of an optimal regularization parameter may not be proper to cope with this limitation a hybrid technique is introduced that depends on the residual of rlsmr method the number of iterations and the bidiagonalization algorithm the accuracy and performance of the improved and proposed methods are numerically examined by a planner truss by incorporating incomplete noisy modal parameters and finite element modeling errors a comparative study on the initial and improved sensitivity functions is conduced to investigate damage detectability of these sensitivity formulations furthermore the accuracy and robustness of rlsmr method in detecting damage are compared with the well known tikhonov regularization method results show that the improved sensitivity of mse is an efficient tool for using in the damage detection problem due to a high sensitivity to damage and reliable damage detectability in comparison with the initial sensitivity function additionally it is observed that the rlsmr method with the aid of the hybrid technique successfully solves the ill posed damage equation and provides better damage detection results compared with the tikhonov regularization technique

system identification method by using inverse solution of equations of motion in time domain and noisy condition abstract in direct system identification dsi method inverse solution of the equations of motion is applied to obtain physical parameters of a linear system structural mass damping and stiffness matrices with the small error in measurement caused by sensor drift or signal noise these physical parameters are identified with a significant drift in this paper a new simple post processing method is proposed for error reduction in dsi in the time domain in a manner that structural properties are identified without applying the optimization process in noisy condition baseline correction is applied through a nonic curve fitting approach the modified signals are partitioned into a number of sub signals and their mean is applied for system identification the number of sub signals is optimized so that the root mean square rms of off diagonal components of the mass matrix becomes near zero seeking more precision the residual force in every time step at all degrees of freedom dofs is minimized the validity of the proposed method is tested on a multistory structure subjected to a random force at the foundation level in terms of incomplete measurement and 5 noise identified parameters including mass stiffness and damping matrices have satisfying mean errors of 0 094 0 545 and 4 42 with the coefficient of variations of 0 35 1 38 and 6 98 respectively the sensitivity of the proposed method to the noise level is also investigated it is observed that the baseline slop of velocity and displacement signals are sharply increased when the noise level goes beyond 3

continuity and uniqueness of regularized output least squares optimal estimators the continuity and uniqueness properties of optimal estimators with respect to data are considered for different regularizations it is found that there is a weak stability for optimal estimators as set valued mappings under a weak regularization for stronger regularization results are obtained that give stability in stronger topologies and the finiteness of the set of optimal estimators finally we give conditions that imply uniqueness of optimal estimators and lipschitz continuity with respect to data

detecting structural damage using frequency response functions these techniques need a large number of sensors to locate damage and the structural response characteristics vary with small changes in boundary conditions and the environment in this condensed paper optimization of frequency response functions is investigated as a means to diagnose damage using a minimum number of sensors

waring loci and the strassen conjecture the waring locus of a form f is the collection of the degree one forms appearing in some minimal sum of powers decomposition of f in this paper we give a complete description of waring loci for several family of forms such as quadrics monomials binary forms and plane cubics we also introduce a waring loci version of strassen s conjecture which implies the original conjecture and we prove it in many cases

on global stabilization of burgers equation by boundary control abstract although often referred to as a one dimensional cartoon of navier stokes equation because it does not exhibit turbulence the burgers equation is a natural first step towards developing methods for control of flows recent references include burns and kang nonlinear dynamics 2 1991 235 262 choi et al j fluid mech 253 1993 509 543 ito and kang siam j control optim 32 1994 831 854 ito and yan j math anal appl 227 1998 271 299 byrnes et al j dynam control systems 4 1998 457 519 and van ly et al numer funct anal optim 18 1997 143 188 while these papers have achieved tremendous progress in local stabilization and global analysis of attractors the problem of global asymptotic stabilization has remained open this problem is non trivial because for large initial conditions the quadratic convective term which is negligible in a linear local analysis dominates the dynamics we derive nonlinear boundary control laws that achieve global asymptotic stability we consider both the viscous and the inviscid burgers equation using both neumann and dirichlet boundary control we also study the case where the viscosity parameter is uncertain as well as the case of stochastic burgers equation for some of the control laws that would require the measurement in the interior of the domain we develop the observer based versions

structural damage localization from modal strain energy change a method based on modal strain energy is presented for locating damage in a structure this method makes use of the change of modal strain energy in each structural element before and after the occurrence of damage some properties of this modal strain energy change are given to illustrate its sensitivity in locating the structural damage information required in the identification are the measured mode shapes and elemental stiffness matrix only without knowledge of the complete stiffness and mass matrices of the structure several damage cases in a simulated structure are studied in which the effect of random error in terms of measurement noise in the mode shapes and systematic error in terms of errors from incomplete measurements are considered this method is then applied to detect damage in a single bay two storey portal steel frame structure results illustrate that the msec is sensitive to damage and the proposed method is simple and robust in locating single or multiple damages in a structure

a new iterative model updating method using incomplete frequency response function data abstract a new iterative model updating method is proposed for reduced model using incomplete frequency response function frf data it uses a modified difference vector between the analytical and experimental frf data to construct a linear sensitivity updating equation system to improve the convergence performance of the proposed algorithm a concept of pseudo master degree of freedom dof is put forward and the finite element fe model is reduced to the measured and user selected pseudo dofs the frfs at pseudo master dofs are estimated using the impedance matrix of iteratively modified analytical model and the measured frfs at master dofs they are only used to improve the sensitivity matrix and difference calculation between the analytical and experimental frf data without introducing additional difference equation at the end a 25 truss structure is used to evaluate the performance of the proposed method

an experimentally validated damage detection theory in smart structures abstract a method for the non destructive detection and location of damage using parameterized partial differential equations and galerkin approximation techniques is presented damages in a structure cause changes in the physical coefficients of mass density elastic modulus and damping coefficients this paper examines the use of beam like structure with piezoceramic sensors and actuators to perform identification of those physical parameters and hence to detect the damage the method casts the inverse problem as an optimization problem the iterative method is based on enhanced least square error minimization experimental results are presented from tests on cantilevered aluminum beams damaged at different locations and with damage of different dimensions it is demonstrated that the method can sense the presence of damage and locate and characterize the damage to a satisfactory precision

an integral equation for changes in the structural dynamics characteristics of damaged structures this paper presents a relationship between the structural dynamic characteristics of damaged and intact structures such a relationship is derived in the form of an integral equation and is used to develop a method of flaw identification the resulting flaw identification procedure uses the experimental data and relates the flaw to the observed structural dynamic response the algorithm enables one to detect the damage locations and the corresponding damage magnitude simultaneously numerical simulations and experiments are conducted to validate the theory

using transfer function parameter changes for damage detection of structures a novel approach is presented for damage detection of large flexible structures by using the parameter change of the transfer function first an interval modeling technique which represents the system uncertainty under the environmental change via the intervals of transfer function parameters is used to distinguish the structural damage from the environmental change in this paper a coherence approach is developed for locating the damage position when the structural damage is observed only a few sensors are required in using the proposed coherence approach for damage detection this has the advantage of using the proposed algorithm for practical applications also this approach has the flexibility of using the multi input and multi output system a nine bay truss example is used to demonstrate and verify the approach developed nomenclature a b denominator and numerator parameters of transfer function c coherence of the tested system to damage g interval model g transfer function k number of modes m number of outputs n number of tests for environmental change p parameter vector of transfer function r magnitude ratio of the tested system to damage r jr magnitude ratio bounds w weight of parameter change wa w weights of intervals for interval model x y unit vectors of cartesian coordinate system ap parameter change vector superscripts

optimal controls of 3 dimensional navier stokes equations with state constraints this work is concerned with the maximum principles for optimal control problems governed by 3 dimensional navier stokes equations some types of state constraints time variables are considered

on the validity of the direct sum conjecture the direct sum conjecture states that the multiplicative complexity of disjoint sets of bilinear computations is the sum of their separate multiplicative complexities this conjecture is known to hold for only a few specialized cases in this paper we establish its validity for large classes of computations one such class can be defined as follows let s 1 be a set of r m times n bilinear forms and let s 2 be a different set of s p times q bilinear forms then if 2 in r m n s p q we show that the direct sum conjecture holds over any field the proof involves some nontrivial facts from linear algebra and relies on the theory of invariant polynomials this result also settles the multiplicative complexity of pairs of bilinear forms over any field with large enough cardinality it is also shown that the direct sum conjecture is true for the case when r mn 2

structural model updating using frequency response function and quasi linear sensitivity equation a method is presented for structural mass and stiffness estimation including damping effects and using vibration data it uses the frequency response function frf and natural frequencies data for finite element model updating the frf data are compiled using the measured displacement velocity or acceleration of the damaged structure a least square algorithm method with appropriate normalization is used for solving the over determined system of equations with noise polluted data sensitivity equation normalization and proper selection of measured frequency points improved the accuracy and convergence in finite element model updating using simulated measurements shows that this method can detect locate and quantify the severity of damage within structures

on the ideals of secant varieties to certain rational varieties abstract if x p n is a reduced and irreducible projective variety it is interesting to find the equations describing the higher secant varieties of x in this paper we find those equations in the following cases x p n 1 p n t p n is the segre embedding of the product and n is large with respect to the n i theorem 2 4 the x are some unbalanced segre veronese embeddings x is a del pezzo surface

on waringʼs problem for systems of skew symmetric forms abstract this paper is devoted to a problem of finding the smallest positive integer s m n k such that m 1 generic skew symmetric k 1 forms in n 1 variables as linear combinations of the same s m n k decomposable skew symmetric k 1 forms this problem is analogous to a well known problem called waring s problem for symmetric forms and can be very naturally translated into a classical problem in algebraic geometry in this paper we will go through some basics of algebraic geometry describe how objects in algebraic geometry can be associated to systems of skew symmetric forms and discuss algebro geometric approaches to establish the existence of triples m n k where s m n k is more than expected

grassmann secants identifiability and linear systems of tensors abstract for any irreducible non degenerate variety x p r we give a criterion for the k s identifiability of x if k s 1 r then the k s identifiability holds for x if and only if the s identifiability holds for the segre product seg p k x moreover if the s th secant variety of x is not defective and it does not fill the ambient space then we can produce a family of pairs k s for which the k s identifiability holds for x

a review of some recent results on the output least squares formulation of parameter estimation problems abstract in this paper recent advances in the analysis of the output least squares formulation of parameter estimation problems for distributed parameter systems are summarized we address problems of identifiability discuss the notion of output least squares stability involving tikhonov regularization in a nonlinear environment give results on the approximation of these infinite dimensional problems by finite dimensional ones and review numerical techniques

boundary and distributed control of the viscous burgers equation in this paper the dynamics of the forced burgers equation ut vuxx uux f x subject to both neumann boundary conditions and periodic boundary conditions using boundary and distributed control is analyzed for the boundary control problem we show that the controlled unforced burgers equation i e the closed loop system is exponentially stable when the viscosity v is known and globally asymptotically stable when v is unknown as for the distributed control problem we apply karhunen loeve decomposition on the dynamics of the forced burgers equation to generate a low dimensional dynamical system whose dynamics is similar to that of burgers equation then a feedback linearization control is used on the reduced system to exponentially stabilize the dynamics of the equation numerical simulations for the boundary and distributed controls are presented to support the analytical results

on tensors of border rank l in cm n l notice this is the author s version of a work that was accepted for publication in linear algebra and its applications changes resulting from the publishing process such as peer review editing corrections structural formatting and other quality control mechanisms may not be reflected in this document changes may have been made to this work since it was submitted for publication a definitive version was subsequently published in linear algebra and its applications june 23 2011 doi 10 1016 j laa 2011 05 013 the original publication is available at www elsevier com

the carroll and chang conjecture of equal indscal components when candecomp parafac gives perfect fit abstract the candecomp parafac algorithm approximates a set of matrices x 1 x i by products of the form ac i b with c i diagonal i 1 i carroll and chang have conjectured that when the matrices are symmetric the resulting a and b will be column wise proportional for cases of perfect fit ten berge et al have shown that the conjecture holds true in a variety of cases but may fail when there is no unique solution in such cases obtaining proportionality by changing part of the solution seems possible the present paper extends and further clarifies their results in particular where ten berge et al solved all i 2 2 cases now all i 3 3 cases and also the i 4 4 cases for i 2 8 and 9 are clarified in a number of cases a and b necessarily have column wise proportionality when candecomp parafac is run to convergence in other cases proportionality can be obtained by using specific methods no cases were found that seem to resist proportionality

a dissipative pseudospectral method for the two dimensional navier stokes equations a pseudospectral method for solving the two dimensional navier stokes equations with periodic boundary conditions is developed the numerical method preserves the zero dissipation property of the nonlinear convective term using weak variational forms the convergence properties of the authors scheme are analyzed

tensor decompositions and applications this survey provides an overview of higher order tensor decompositions their applications and available software a tensor is a multidimensional or n way array decompositions of higher order tensors i e n way arrays with n geq 3 have applications in psycho metrics chemometrics signal processing numerical linear algebra computer vision numerical analysis data mining neuroscience graph analysis and elsewhere two particular tensor decompositions can be considered to be higher order extensions of the matrix singular value decomposition candecomp parafac cp decomposes a tensor as a sum of rank one tensors and the tucker decomposition is a higher order form of principal component analysis there are many other tensor decompositions including indscal parafac2 candelinc dedicom and paratuck2 as well as nonnegative variants of all of the above the n way toolbox tensor toolbox and multilinear engine are examples of software packages for working with tensors

stratified exponential families graphical models and model selection we describe a hierarchy of exponential families which is useful for distinguishing types of graphical models undirected graphical models with no hidden variables are linear exponential families lefs directed acyclic graphical dag models and chain graphs with no hidden variables including dag models with several families of local distributions are curved exponential families cefs graphical models with hidden variables are what we term stratified exponential families sefs a sef is a finite union of cefs of various dimensions satisfying some regularity conditions we also show that this hierarchy of exponential families is noncollapsing with respect to graphical models by providing a graphical model which is a cef but not a lef and a graphical model that is a sef but not a cef finally we show how to compute the dimension of a stratified exponential family these results are discussed in the context of model selection of graphical models

parameter estimation regularity and the penalty method for a class of two point boundary value problems we study a penalization technique for a class of parameter estimation problems associated with elliptic equations moreover a regularization phenomenon of the minimizers is discussed for various parameters in the equation and for different observation operators finally it is shown that under weak assumptions the norm constraints are active

resolution of regularized output least squares estimation procedures the regularized output least squares estimation technique is considered as an example of an estimation procedure in order to evaluate sensitivity of mappings that arise in the context of identical twin test problems for such test problems one specifies a reasonable test parameter to generate data from which the test parameter is to be recovered by means of an estimation procedure the properties of the mapping taking the test coefficient to the optimal estimator are studied conditions are determined under which the mapping is well defined as a function of the set of admissible parameters into itself resolution properties are related to the properties of the derivative of this mapping examples are considered using this information to formulate what is meant to be an optimal observer and to determine the optimal location of observers

a link between quantum entanglement secant varieties and sphericity in this paper we shed light on the relations between three concepts studied in representation theory algebraic geometry and quantum information theory first spherical actions of reductive groups on projective spaces second secant varieties of homogeneous projective varieties and the related notions of rank and border rank third quantum entanglement our main result concerns the relation between the problem of the state reconstruction from its reduced one particle density matrices and the minimal number of separable summands in its decomposition more precisely we show that sphericity implies that states of a given rank cannot be approximated by states of a lower rank we call states for which such an approximation is possible exceptional states for three important from a quantum entanglement perspective cases of distinguishable fermionic and bosonic particles we also show that non sphericity implies the existence of exceptional states remarkably the exceptional states belong to non bipartite entanglement classes in particular we show that the w type states and their appropriate modifications are exceptional states stemming from the second secant variety for three cases above we point out that the existence of the exceptional states is a physical obstruction for deciding the local unitary equivalence of states by means of the one particle reduced density matrices finally for a number of systems of distinguishable particles with a known orbit structure we list all exceptional states and discuss their possible importance in entanglement theory

non uniqueness of critical points in variational data assimilation abstract in this paper we apply the 4d var data assimilation scheme to the initialization problem for a family of quasilinear evolution equations the resulting variational problem is non convex so it need not have a unique minimizer we comment on the implications of non uniqueness for numerical applications then prove uniqueness results in the following situations 1 the observational times are sufficiently small 2 the prior covariance is sufficiently small we also give an example of a data set where the cost functional has a critical point of arbitrarily large morse index thus demonstrating that the geometry can be highly nonconvex even for a relatively mild nonlinearity

identification of joint properties of a structure using frf data abstract the connections between structural components i e joints are extremely difficult to model accurately by using a pure analytical approach alternatively joint properties can be extracted from experimental data a method for identifying extracting joint properties from the measured frequency response function frf data is presented in this paper one of the major difficulties in accurate identification of joint properties is that the identification results can be significantly affected by various errors in the measured data even if errors in the measured data are at an insignificantly low level say 5 in frfs their effects on the identification can be severe enough so that in some cases the predicted joint properties can be completely irrelevant to the true properties of joints apart from the accuracy of the data used for the identification the accuracy of the identification also significantly depends upon the mathematical formulae used for the identification even with the same experimental data the accuracies of the identification by different methods can be significantly different therefore developing methods that are insensitive to measurement errors is of utmost importance for the identification of joint properties from experimental data in this paper techniques for improving the accuracy of joint identification are discussed it is demonstrated that by using all available information effectively the accuracy of the identification can be much improved both numerical and experimental examples are presented

backstepping boundary control of burgers equation with actuator dynamics in this paper we propose a backstepping boundary control law for burgers equation with actuator dynamics while the control law without actuator dynamics depends only on the signals u 0 t and u 1 t the backstepping control also depends on ux 0 t ux 1 t uxx 0 t and uxx 1 t making the regularity of the control inputs the key technical issue of the paper with elaborate lyapunov analysis we prove that all these signals are suciently regular and the closed loop system including the boundary dynamics is globally h 3 stable and well posed c 2000 elsevier science b v all rights reserved

a numerical study of the eigenparameters of a damaged cantilever abstract when a structure is subjected to damage its dynamic response changes characterized by shifts in the eigenvalues and modifications of the eigenvectors considerable effort has been put into investigating the relationship between the damage location the damage size and the corresponding changes in the eigenparameters in most cases emphasis has been on using the shift in eigenvalues as a means of determining the damage location and the information derived from the change in eigenvectors has largely remained obscure in this paper a systematic study is presented of the relationship between damage location damage size and the changes in the eigenvalues and eigenvectors of a cantilever when subjected to damage a finite element model of a uniform cross sectioned cantilever was chosen to provide data for analysis the changes in the eigenvalues and eigenvectors are shown to follow a definite trend in relation to the location and extent of damage

dynamics and control of the 2 d navier stokes equations abstract this paper deals with the dynamics and control of the two dimensional 2 d navier stokes n s equations with a spatially periodic and temporally steady forcing term first we construct a dynamical system of nine nonlinear differential equations by fourier expansion and truncation of the 2 d n s equations then we study the dynamics of the obtained reduced order system by analyzing the system s attractors for different values of the reynolds number r e by applying the symmetry of the equations on one of the system s attractors a symmetric limit trajectory that is part of the dynamics is obtained moreover a lyapunov based control strategy to control the dynamics of the system for a given r e is designed finally numerical simulations are undertaken to validate the theoretical developments

the symptom observation matrix for monitoring and diagnostics abstract monitoring of complex technical systems in operation service is a task concerning safety reliability and risk management additionally the monitoring and diagnosis of such systems is also recommended for the reduction of costs and to increase the life of systems under consideration the fundamental quantities for monitoring and diagnosis are symptoms contained in measured data of a time variant system symptoms are observable and sensitive with respect to faults or damage questions such as how to find symptoms how they should be evaluated for information condensation in order to detect and if possible to localize faults or damage are discussed and additionally the choice of the measuring matrix and the test forces are treated in the context of the state space formulation of time variant models for the purpose of information condensation and the evaluation of symptoms the symptom observation matrix is introduced and manipulated by the singular value decomposition the properties of the observation matrix with its singular values and singular vectors show their applicability for monitoring and diagnosis

geometry and the complexity of matrix multiplication it has been known for some time that algebraic geometry and representation theory are useful for proving lower bounds on the complexity of the matrix multiplication operator in this talk i will explain how geometry can be used to prove both upper and lower bounds after a discussion of the problem and its history i will present very recent work with m michalek on border rank algorithms faculty host eric allender

numerical methods for nonlinear inverse problems inverse problems of distributed parameter systems with applications to optimal control and identification are considered numerical methods and their numerical analysis for solving this kind of inverse problems are presented main emphasis being on the estimates of the rate of convergence for various schemes finally based on the given error estimates a two grid method and related algorithms are introduced which can be used to solve nonlinear inverse problems effectively

identifiability of parameters in latent structure models with many observed variables while hidden class models of various types arise in many statistical applications it is often difficult to establish the identifiability of their parameters focusing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones we demonstrate a general approach for establishing identifiability utilizing algebraic arguments a theorem of j kruskal for a simple latent class model with finite state space lies at the core of our results though we apply it to a diverse set of models these include mixtures of both finite and nonparametric product distributions hidden markov models and random graph mixture models and lead to a number of new results and improvements to old ones in the parametric setting this approach indicates that for such models the classical definition of identifiability is typically too strong instead generic identifiability holds which implies that the set of nonidentifiable parameters has measure zero so that parameter inference is still meaningful in particular this sheds light on the properties of finite mixtures of bernoulli products which have been used for decades despite being known to have nonidentifiable parameters in the nonparametric setting we again obtain identifiability only when certain restrictions are placed on the distributions that are mixed but we explicitly describe the conditions

optimal control of fluid equations with buoyancy we consider the optimal control of a set of fluid equations made up of the momentum equations coupled with an equation modeling thermal effects control is exerted by means of heat sources within the fluid with the goal of controlling the temperature or velocity distribution of the fluid existence as well as the regularity properties of optimal controls are analyzed stability with respect to observations is discussed finally compactness of the solution set and uniqueness properties are determined

on comon s conjecture over arbitrary fields abstract comon s conjecture asserts that for a symmetric tensor the rank is equal to the symmetric rank for the field of real numbers r or the field of complex numbers c zhang et al proved the conjecture for the case that the rank of a symmetric tensor does not exceed the order in this paper we show that over arbitrary fields this conjecture is true when the rank of a tensor is less than its order moreover we construct a counterexample in which the rank of a symmetric tensor whose rank equals its order

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

a dissipative feedback control synthesis for systems arising in fluid dynamics a dissipative feedback control synthesis is constructed to regulate the systems arising in fluid dynamics the feedback law is obtained by utilizing nonlinear dynamic programming techniques the control law is designed for driving the system to a prescribed equilibrium state and enhancing the energy dissipation effects of the dynamical system two dimensional navier stokes equations and burgers equation are used for numerical experiments to illustrate the effects of the feedback synthesis and the theoretical results

a study of uniqueness for the initialization problem for burgers equation the initialization problem for burgers equation with viscosity is formulated as an optimal control problem the existence of a solution of this problem is established directly and the optimality system is obtained from this system we deduce regularity properties of the optimal initial conditions these regularity properties imply the compactness of the set u0 of optimal initial conditions by introducing sufficiency conditions for optimality we deduce conditions under which there are in fact finitely many elements in the set u0 finally we determine conditions that imply the optimality system has a unique solution it then follows that there is only one element in u0

ranks of tensors and a generalization of secant varieties abstract we introduce subspace rank as a tool for studying ranks of tensors and x rank more generally we derive a new upper bound for the rank of a tensor and determine the ranks of partially symmetric tensors in c 2 c b c b we review the literature from a geometric perspective

data assimilation for the navier stokes α equations abstract the well posedness of the data assimilation problem for the navier stokes equations on a bounded three dimensional domain is investigated the data assimilation procedures under consideration are the adjoint method of variational data assimilation 4d var and the method of continuous data assimilation concerning the adjoint method the existence of optimal initial conditions with respect to an observation dependent cost functional is proven the optimizers are characterized by a first order necessary condition involving the adjoint linearized navier stokes equations and conditions for the uniqueness of the initial conditions are given well posedness of the continuous data assimilation problem is proven and convergence rates in terms of observational resolution are provided

structural damage detection using measured frf data abstract the underlying principle behind structural damage detection techniques is that vibration signature e g modal properties or frequency response function frf data is a sensitive indicator of structural physical integrity and thus can be used to detect damage since indirectly measured modal data contain accumulative errors incurred in modal parameter extraction and provide much less information than frf data it is more reasonable and reliable to use directly measured frf data for structural damage detection in this paper a new damage detection algorithm is formulated to utilize an original analytical model and frf data measured prior and posterior to damage for structural damage detection based on nonlinear perturbation equations of frf data an algorithm has been derived which can be used to determine a damage vector indicating both location and magnitude of damage from perturbation equations of frf data an additional development with respect to the proposed technique is an effective technique introduced for weighting perturbation equations of frf data at selected locations and frequencies so as to reduce influence of measurement errors on accuracy of damage detection to the minimum for extension of the proposed algorithm to cases of incomplete measurement in terms of coordinates an iterative version of the proposed algorithm has been introduced the validity and applicability of the proposed damage detection algorithm have been demonstrated through numerical and experimental studies on a practical plane 3 bay frame structure respectively

rank and optimal computation of generic tensors abstract the typical rank maximal border rank of tensors of a given size and the set of optimal bilinear computations of typical tensors of a given rank are investigated for the size n n 3 with n odd the complement of the set of tensors of maximal border rank is a hypersurface its equation is given

descent gradient methods for nonsmooth minimization problems in ill posed problems descent gradient methods are the most frequently used algorithms for computing regularizers of inverse problems they are either directly applied to the discrepancy term which measures the difference between operator evaluation and data or to a regularized version incorporating suitable penalty terms in its basic form gradient descent methods converge slowly we aim at extending different optimization schemes which have been recently introduced for accelerating these approaches by addressing more general penalty terms in particular we use a general setting in infinite hilbert spaces and examine accelerated algorithms for regularization methods using total variation or sparsity constraints to illustrate the efficiency of these algorithms we apply them to a parameter identification problem in an elliptic partial differential equation using total variation regularization

a frequency domain method of structural damage identification formulated from the dynamic stiffness equation of motion this paper introduces a frequency domain method of structural damage identification it is formulated in a general form from the dynamic stiffness equation of motion for a structure and then applied to a beam structure only the dynamic stiffness matrix for the intact state appears in the final form of the damage identification algorithm as the structure model the appealing features of the present damage identification method are 1 it requires only the frequency response functions experimentally measured from the damaged structure as the input data and 2 it can locate and quantify many local damages at the same time the feasibility of the present damage identification method is tested through some numerically simulated damage identification analyses and then experimental verification is conducted for a cantilevered beam with damage caused by introducing three slots

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

damage detection in elastic structures using vibratory residual forces and weighted sensitivity a methodology is presented for detecting structural damage in elastic structures by nondestructiv e means measured modal test data along with a correlated analytical structural model are used to locate potentially damaged regions using residual modal force vectors and to conduct a weighted sensitivity analysis to assess the extent of mass and or stiffness variations where damage is characterized as a stiffness reduction the current approach is unique among other approaches in that it accounts for 1 variations in system mass system stiffness and mass center locations 2 perturbations of both the natural frequencies and modal vectors and 3 statistical confidence factors for the structural parameters and potential experimental instrumentation error moreover this procedure can be used with either full or reduced models a wide variety of numerical examples are presented that show that the current method provides a precise indication of both the location and the extent of structural damage lexible space structures launch vehicles and satellites are susceptible to structural damage over their operating lives from impact operating loads and fatigue undetected and uncorrected damage can lead to structural deterioration of their members and consequently jeopardize the flight safety of the structure thus numerous damage inspection methods and monitoring procedures have been developed examples include x ray ultrasonic testing magnetic resonance coin tap dye penetration and visual inspection these methods can be time consuming and are local assessments often requir ing the exposure of structural elements to the inspector and equipment for detecting damage as a monitoring system for detecting damage of spacecraft in orbit i e space station freedom none of these methods are appropriate an alterna tive approach which formed the basis for our current study is to recognize the fact that modal vibration test data struc tural natural frequencies and mode shapes characterize the state of the structure 1 therefore postflight and in flight e g monitoring data can be used to distinguish whether changes damage have occurred to the structure by comparing these data with a set of baseline data modal testing as a means of inspection has several advantages direct exposure of struc tural elements is not required and at the same time more of the complete structure can be inspected in one modal test by having appropriately placed sensors the consequences of this are a reduction in schedule and cost the use of vibration test data to locate structural damage has been attempted to evaluate the integrity of offshore oil and gas platforms 2 3 composite laminates 4 continuum struc tures 5 8 and recently large space structures 9 11 the early ana lytical and experimental approaches2 3 had limited success as a result of inadequate instrumentation and addressing only fre quency shifts associated with stiffness changes while ignoring changes in the modal vectors the continuum based meth ods5 8 provide valuable insight into the magnitude of fre quency shifts but their usefulness is severely limited to simple structures bars beams plates with unrealistic boundary con

stability enhancement by boundary control in 2 d channel flow in this paper we stabilize the parabolic equilibrium profile in a two dimensional 2 d channel flow using actuators and sensors only at the wall the control of channel flow was previously considered by speyer and coworkers and bewley and coworkers who derived feedback laws based on linear optimal control and implemented by wall normal actuation with an objective to achieve global lyapunov stabilization we arrive at a feedback law using tangential actuation using teamed pairs of synthetic jets or rotating disks and only local measurements of wall shear stress allowing to embed the feedback in microelectromechanical systems mems hardware without need for wiring this feedback is shown to guarantee global stability in at least h sup 2 norm which by sobolev s embedding theorem implies continuity in space and time of both the flow field and the control as well as their convergence to the desired steady state the theoretical results are limited to low values of reynolds number however we present simulations that demonstrate the effectiveness of the proposed feedback for values five order of magnitude higher

generic and typical ranks of multi way arrays abstract the concept of tensor rank was introduced in the 20s in the 70s when methods of component analysis on arrays with more than two indices became popular tensor rank became a much studied topic the generic rank may be seen as an upper bound to the number of factors that are needed to construct a random tensor we explain in this paper how to obtain numerically in the complex field the generic rank of tensors of arbitrary dimensions based on terracini s lemma and compare it with the algebraic results already known in the real or complex fields in particular we examine the cases of symmetric tensors tensors with symmetric matrix slices complex tensors enjoying hermitian symmetries or merely tensors with free entries

optimal tracking of parameter drift in a chaotic system experiment and theory we present a method of optimal tracking for chaotic dynamical systems with a slowly drifting parameter the net drift in the parameter is assumed to be small this makes detecting and tracking the drift more difficult the method relies on the existence of underlying deterministic behavior in the dynamical system yet neither requires a system model nor develops one we begin by describing an experimental study where a heuristic optimality criterion gave good tracking performance the tracking method there was based on maximizing smoothness and overall variation in the drift observer which was found by solving an igenvalue problem we then develop a theory based on simplifying assumptions about the chaotic dynamics to explain the success of the tracking method for chaotic systems for signals from deterministic systems that are sufficiently complex in a sense that we make precise typical drift observers provide poor tracking performance and require the drift to be particularly slow in contrast our theory shows that the optimality criterion seeks out a special drift observer that both provides better tracking performance and allows the drift to be appreciably faster for periodic or quasiperiodic systems no chaos good tracking is easily achievable and the present method is irrelevant for stochastic systems no determinism the optimal tracking method does not asymptotically improve tracking performance exhaustive numerical simulations of a simple drifting chaotic map first without and then with stochastic forcing show agreement with theoretical predictions of tracking performance and validate the theory