cancellation in additively twisted sums on gl n in a previous paper with schmid we considered the regularity of automorphic distributions for gl 2 r and its connections to other topics in number theory and analysis in this paper we turn to the higher rank setting establishing the nontrivial bound n t a n e 2 i n o e t 3 4 e uniformly in r for a n the coefficients of the l function of a cusp form on gl 3 z gl 3 r we also derive an equivalence theorem 7 1 between analogous cancellation statements for cusp forms on gl n r and the sizes of certain period integrals these in turn imply estimates for the second moment of cusp form l functions

adaptive estimation for a class of nonlinearly parameterized dynamical systems the technical note presents a new technique for the adaptive parameter estimation in nonlinear parameterized dynamical systems the technique proposes an uncertainty set update approach that guarantees forward invariance of the true value of the parameters in addition it is shown that in the presence of sufficiently exciting state trajectories the parameter estimates converge to the true values and the uncertainty set vanishes around the true value of the parameters the set based approach is also shown to identify when the parameter estimates are biased two simulation examples are presented that demonstrate the effectiveness of the technique

adaptive output feedback control of nonlinear systems using neural networks a direct adaptive output feedback control design procedure is developed for highly uncertain nonlinear systems that does not rely on state estimation the approach is also applicable to systems of unknown but bounded dimension in particular we consider single input single output nonlinear systems whose output has known but otherwise arbitrary relative degree this includes systems with both parameter uncertainty and unmodeled dynamics the result is achieved by extending the universal function approximation property of linearly parameterized neural networks to model unknown system dynamics from input output data the network weight adaptation rule is derived from lyapunov stability analysis and guarantees that the adapted weight errors and the tracking error are bounded numerical simulations of an output feedback controlled van der pol oscillator coupled with a linear oscillator is used to illustrate the practical potential of the theoretical results

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

technical communique further result on a dynamic recurrent neural network based adaptive observer for a class of nonlinear systems in kim et al 1997 a dynamic recurrent neural network based adaptive observer for a class of nonlinear systems automatica 33 8 1539 1543 authors present an excellent neural network nn observer for a class of nonlinear systems however the output error equation in their paper is strictly positive real spr which is restrictive assumption for nonlinear systems in this note by introducing a vector b 0 and lyapunov equation the observer design is obtained without requiring the spr condition thus our observer can be applied to a wider class of systems

estimates for rankin selberg l functions and quantum unique ergodicity abstract subconvex bounds in the weight aspect for rankin selberg l functions associated to two cusp forms are established these bounds are applied to prove the equidistribution of mass conjecture for cm forms

parameter estimation and compensation in systems with nonlinearly parameterized perturbations we consider a class of systems influenced by perturbations that are nonlinearly parameterized by unknown constant parameters and develop a method for estimating the unknown parameters the method applies to systems where the states are available for measurement and perturbations with the property that an exponentially stable estimate of the unknown parameters can be obtained if the whole perturbation is known the main contribution is to introduce a conceptually simple modular design that gives freedom to the designer in accomplishing the main task which is to construct an update law to asymptotically invert a nonlinear equation compensation for the perturbations in the system equations is considered for a class of systems with uniformly globally bounded solutions for which the origin is uniformly globally asymptotically stable when no perturbations are present we also consider the case when the parameters can only be estimated when the controlled state is bounded away from the origin and show that we may still be able to achieve convergence of the controlled state we illustrate the method through examples and apply it to the problem of downhole pressure estimation during oil well drilling

hyperelastic internal balance by multiplicative decomposition of the deformation gradient the multiplicative decomposition of the deformation gradient bf f hat bf f bf f is often used in finite deformation continuum mechanics as a basis for treating mechanical effects including plasticity biological growth material swelling and notions of material morphogenesis evolution rules for the particular effect from this list are then posed for f the tensor hat bf f is then invoked to describe a subsequent elastic accommodation and a hyperelastic framework is put in place for its determination using an elastic energy density function say w hat bf f as a constitutive specification here we explore the theory that emerges if both f and hat bf f are governed by hyperelastic criteria thus we consider energy densities w hat bf f bf f the decomposition of f is itself determined by energy minimization and the variation associated with the multiplicative decomposition gives a tensor relation that is interpreted as an internal balance requirement our initial development purposefully proceeds with minimal presumptions on the kinematic interpretation of the factors in the deformation gradient decomposition connections are then made to treatments that ascribe particular kinematic properties to the decomposition factors the theory of structured deformations is especially significant in this regard such theories have broad utility in describing certain substructural reconfigurations in solids to demonstrate in the context of the present variational treatment we consider a boundary value problem that involves an imposed twist if the twist is small then the minimizer is classically smooth at larger values of twist the energy minimizer exhibits a non smooth deformation that localizes slip at a singular surface

adaptive control of continuous time systems with convex concave parametrization this paper deals with adaptive control of a class of nonlinear dynamic systems with nonlinear parametrization in this class the state variables are assumed to be accessible and the nonlinearity in the parameters is assumed to be either convex or concave by introducing a tuning function and an adaptive law based on a min max strategy it is shown that such a class of dynamic systems can be adaptively controlled in a stable manner global boundedness of the overall adaptive system and tracking to within a desired precision are established with the new adaptive controller the proposed controller is applied to a precise positioning problem in the presence of nonlinearly parametrized friction dynamics it is shown that the controller leads to position errors and friction compensation that are orders of magnitude better than those based on estimation of linear parametrizations the fact that the new parameter estimation strategy used is distinct from the traditionally used gradient schemes permits the expansion of the scope of adaptive control which has been restricted hitherto in most cases to systems with linear parametrization

global solutions to the equations of a ginzburg landau theory for structural phase transitions in shape memory alloys abstract global existence of smooth solutions is proved for the system of partial differential equations governing the dynamics of martensic phase transitions in shape memory alloys the free energy is assumed in ginzburg landau form and nonconvex in the order parameter

rankin selberg l functions in the level aspect keywords moments rankin selberg convolution level aspect convexity breaking reference tan article 2002 003doi 10 1215 s0012 7094 02 11416 1 record created on 2008 11 14 modified on 2017 05 12

nonconvex model of material growth mathematical theory the model of volumetric material growth is introduced in the framework of finite elasticity the new results obtained for the model are presented with complete proofs the state variables include the deformations temperature and the growth factor matrix function the existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown the mathematical results can be applied to a wide class of growth models in mechanics and biology

bounds for gl 3 gl 2 l functions and gl 3 l functions in this paper we will give the subconvexity bounds for self dual gl 3 l functions in the t aspect as well as subconvexity bounds for self dual gl 3 gl 2 l functions in the gl 2 spectral aspect

simultaneous identification and stabilization of nonlinearly parameterized discrete time systems by nonlinear least squares algorithm this paper addresses the challenging problem of designing an adaptive feedback strategy for simultaneous identification and stabilization for a class of nonlinearly parameterized uncertain systems in discrete time the nonlinear least squares nls algorithm is applied to estimate the unknown parameters and it turns out to be the standard least squares ls algorithm whenever the model is linearly parameterized based on this algorithm both the strong consistency of the estimator and the global stability of the system are achieved with the output feedback design for the scalar parameter case

material growth in thermoelastic continua theory algorithmics and simulation a theoretical formulation of stress induced volumetric material growth in thermoelastic continua is developed material growth is regulated by a three surface activation criterion and corresponding flow rules a simple model is proposed based on this formulation and its algorithmic implementation including a method for solving the underlying differential algebraic equations for growth is examined in the context of an implicit finite element method selected numerical simulations are presented that showcase the predictive capacity of the model for both soft and hard biomaterials

adaptive control of a class of nonlinearly parameterized plants a stable adaptive control method is developed for a class of first order nonlinearly parameterized plants the method is based on modified adaptive algorithms that yield a stable system in which the output errors are guaranteed to converge to zero the stability analysis is carried out using suitably constructed lyapunov functions

adaptive control with nonconvex parameterization deals with the problem of nonconvex parameterization in adaptive control for a class of nonlinear dynamic systems new algorithms for stable adaptive control are introduced sufficient conditions for achieving control objectives of adaptive control with new algorithms are investigated simulation examples are presented for illustration

parameter convergence in nonlinearly parameterized systems a large class of problems in parameter estimation concerns nonlinearly parametrized systems over the past few years a stability framework for estimation and control of such systems has been established we address the issue of parameter convergence in such systems in this paper systems with both convex concave and general parameterizations are considered in the former case sufficient conditions are derived under which parameter estimates converge to their true values using a min max algorithm in the latter case to achieve parameter convergence a hierarchical min max algorithm is proposed where the lower level consists of a min max algorithm and the higher level component updates the bounds on the parameter region within which the unknown parameter is known to lie using this hierarchical algorithm a necessary and sufficient condition is established for global parameter convergence in systems with a general nonlinear parameterization in both cases the conditions needed are shown to be stronger than linear persistent excitation conditions that guarantee parameter convergence in linearly parametrized systems explanations and examples of these conditions and simulation results are included to illustrate the nature of these conditions a general definition of nonlinear persistent excitation that leads to parameter convergence is proposed at the end of this paper

sparse equidistribution problems period bounds and subconvexity we introduce a geometric method to bound periods of automorphic forms the key features of this method are the use of equidistribution results in place of mean value theorems and the systematic use of mixing and the spectral gap applications are given to equidistribution of sparse subsets of horocycles and to equidistribution of cm points to subconvexity of the triple product period in the level aspect over number fields which implies subconvexity for certain standard and rankin selberg l functions and to bounding fourier coefficients of automorphic forms

state estimation for discrete time dynamical networks with time varying delays and stochastic disturbances under the round robin protocol this paper is concerned with the state estimation problem for a class of nonlinear dynamical networks with time varying delays subject to the round robin protocol the communication between the state estimator and the nodes of the dynamical networks is implemented through a shared constrained network in which only one node is allowed to send data at each time instant the round robin protocol is utilized to orchestrate the transmission order of nodes by using a switch based approach the dynamics of the estimation error is modeled by a periodic parameter switching system with time varying delays the purpose of the problem addressed is to design an estimator such that the estimation error is exponentially ultimately bounded with a certain asymptotic upper bound in mean square subject to the process noise and exogenous disturbance furthermore such a bound is subsequently minimized by the designed estimator parameters a novel lyapunov like functional is employed to deal with the dynamics analysis issue of the estimation error sufficient conditions are established to guarantee the ultimate boundedness of the estimation error in mean square by applying the stochastic analysis approach then the desired estimator gains are characterized by solving a convex problem finally a numerical example is given to illustrate the effectiveness of the estimator design scheme

on the mechanics of solids with a growing mass a general constitutive theory of the stress modulated growth of biomaterials is presented with a particular accent given to pseudo elastic soft living tissues the governing equations of the mechanics of solids with a growing mass are revisited within the framework of finite deformation continuum thermodynamics the multiplicative decomposition of the deformation gradient into its elastic and growth parts is employed to study the growth of isotropic transversely isotropic and orthotropic biomaterials an explicit representation of the growth part of the deformation gradient is given in each case which leads to an effective incremental formulation in the analysis of the stress modulated growth process the rectangular components of the instantaneous elastic moduli tensor are derived corresponding to selected forms of the elastic strain energy function physically appealing structures of the stress dependent evolution equations for the growth induced stretch ratios are proposed