existence results for urysohn integral inclusions involving the henstock integral this paper presents two existence results for urysohn integral inclusions in banach spaces the set valued integral involved being the henstock integral in particular the existence of continuous solutions for integral inclusions of volterra and of hammerstein type is obtained our results extend the existence theorems given in literature in the single or set valued case under bochner or pettis integrability hypothesis the compactness of solutions set is also studied

on modifications of newton s second law and linear continuum elastodynamics in this paper we suggest a new perspective where newton s second law of motion is replaced by a more general law which is a better approximation for describing the motion of seemingly rigid macroscopic bodies we confirm a finding of willis that the density of a body at a given frequency of oscillation can be anisotropic the relation between the force and the acceleration is non local but causal in time conversely for every response function satisfying these properties and having the appropriate high frequency limit there is a model which realizes that response function in many circumstances the differences between newton s second law and the new law are small but there are circumstances such as in specially designed composite materials where the difference is enormous for bodies which are not seemingly rigid the continuum equations of elastodynamics govern behaviour and also need to be modified the modified versions of these equations presented here are a generalization of the equations proposed by willis to describe elastodynamics in composite materials it is argued that these new sets of equations may apply to all physical materials not just composites the willis equations govern the behaviour of the average displacement field whereas one set of new equations governs the behaviour of the averageweighted displacement field where the weighted displacement field may attach zero weight to hidden areas in the material where the displacement may be unobservable or not defined from knowledge of the average weighted displacement field one obtains an approximate formula for the ensemble averaged energy density two other sets of new equations govern the behaviour when the microstructure has microinertia i e where there are internal spinning masses below the chosen scale of continuum modelling in the first set the average displacement field is assumed to be observable while in the second set an average weighted displacement field is assumed to be observable

multi value microstructural descriptors for complex materials analysis of ground states we propose and analyze a multi scale and multi field description of complex materials in which we consider every material element as a system composed by q in mathbb n indistinct substructures we pay attention to the equilibrium configurations of such bodies we consider first rigid bodies with microstructure represented by means of q valued maps from the reference place to the manifold of microstructural shapes in that case just microenergetics appears then we enlarge the stage considering large strains and energies of ginzburg landau type with respect to the microstructural descriptor fields in both cases we provide conditions for semicontinuity of the relevant energies and the existence of ground states

invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity in this paper we present and analyze a variational model in nonlinear elasticity that allows for cavitation and fracture the main idea in unifying the theories of cavitation and fracture is to regard both cavities and cracks as phenomena of the creation of a new surface accordingly we define a functional that measures the area of the created surface this functional has relationships with the theory of cartesian currents we show that the boundedness of that functional implies sequential weak continuity of the determinant of the deformation gradient and that the weak limit of one to one almost everywhere deformations is also one to one almost everywhere we then use these results to obtain the existence of minimizers of variational models that incorporate elastic energy and this created surface energy taking into account orientation preserving and non interpenetration conditions

optimal disturbance reduction in linear multivariable systems this paper presents a computational solution to an important optimization problem arising in optimal sensitivity theory the approach is to treat the multivariable problem exactly as the scalar problem in that stability constraints are handled via interpolation the resulting computations are easily implemented using existing methods

semicontinuity problems in the calculus of variations soit f r 3 r une fonction deux fois continument differentiable et pour u w 1 1 a b f u a b a b f x u x u x dx si f r n r m r nm r satisfait 1 f est mesurable en x continue en cs et 2 0 f x s a x c s p p ou p 1 a est une fonction localement sommable non negative et c une constante non negative alors la fonctionnelle f u a b est sequentiellement faiblement semi continue inferieurement sur w 1 p r m si et seulement si f x s est quasi convexe pour chaque s et presque chaque x

regularity properties of deformations with finite energy the purpose of this paper is to point out some regularity properties of a class of functions which play an important role in nonlinear elasticity

sensitivity tradeoffs for multivariable plants this paper gives a characterization of the smallest upper bound on the norm of the sensitivity matrix over a frequency interval with the constraint that the norm remain bounded at all frequencies the matrix nevanlinna pick interpolation theory is applied to give a necessary and sufficient condition for the existence of a sensitivity matrix meeting the upper bound conditions on the j omega axis and the matrix nevnnlinna pick algorithm is used to compute the bounds a scalar example is also presented to demonstrate the tradeoffs between the bounds inside and outside a given operating frequency band

worst case identification of continuous time systems via interpolation we consider a worst case robust control oriented identification problem recently studied by several authors this problem is one of h identification in the continuous time setting we give a more general formulation of this problem the available a priori information in this paper consists of a lower bound on the relative stability of the plant a frequency dependent upper bound on a certain gain associated with the plant and an upper bound on the noise level the available experimental information consists of a finite number of noisy plant point frequency response samples the objective is to identify from the given a priori and experimental information an uncertain model that includes a stable nominal plant model and a bound on the modeling error measured in h norm our main contributions include both a new identification algorithm and several new explicit lower and upper bounds on the identification error the proposed algorithm belongs to the class of interpolatory algorithms which are known to possess a desirable optimality property under a certain criterion the error bounds presented improve upon the previously available ones in the aspects of both providing a more accurate estimate of the identification error as well as establishing a faster convergence rate for the proposed algorithm

erratum and addendum to cartesian currents weak diffeomorphisms and existence theorems in nonlinear elasticity this archive volume 106 1989 97 159 our proof of theorem 1 of 3 p 107 is not correct since the claim iii of proposition 1 is false moreover it is not clear whether the space cart 2 r x in definition 1 is dosed because of this to minimize functionals in cart 2 r n becomes unreasonable our idea was to consider the smallest closed set with respect to weak convergence in cg containing the graphs of regular mappings according to that the definition of cart 2 r n has to be changed into the following

differential and integral equations with henstock kurzweil integrable functions abstract in this paper we apply fixed point theorems for increasing mappings in ordered normed spaces to prove existence and comparison results for solutions of discontinuous functional differential and integral equations containing henstock kurzweil integrable functions

worst case system identification in h sub spl infin validation of a priori information essentially optimal algorithms and error bounds resolves several important open issues pertaining to a worst case control oriented system identification problem known as identification in h sub spl infin first a method is presented for developing confidence that certain a priori information available for identification is not invalid this method requires the solution of a certain nondifferentiable convex program second an essentially optimal identification algorithm is constructed this algorithm is worst case strongly optimal to within a factor of two finally new upper and lower bounds on the optimal identification error are derived and used to estimate the identification error associated with the given algorithm interestingly the development of each of these results draws heavily upon the classical nevanlinna pick interpolation theory as such the authors results establish a clear link between the areas of system identification and optimal interpolation theory both the formulation and techniques in this paper are applicable to problems where the frequency data available for identification may essentially be arbitrarily distributed

growth of solutions for measure differential equations and dynamic equations on time scales abstract in this paper we investigate the asymptotic behavior for measure differential equations and dynamic equations on time scales via generalized ordinary differential equations generalized odes for short at first we establish new results that guarantee the existence of unbounded solutions for generalized odes and after that using the known correspondence between generalized odes and measure differential equations also between measure differential equations and dynamic equations on time scales we obtain similar results for these equations finally we present an application to illustrate our main results

measure functional differential equations and functional dynamic equations on time scales abstract we study measure functional differential equations and clarify their relation to generalized ordinary differential equations we show that functional dynamic equations on time scales represent a special case of measure functional differential equations for both types of equations we obtain results on the existence and uniqueness of solutions continuous dependence and periodic averaging

quasiconvexity and uniqueness of equilibrium solutions in nonlinear elasticity in this paper we prove the uniqueness of the solution to certain simple displacement boundary value problems in the nonlinear theory of homogeneous hyperelasticity for a body occupying a star shaped reference configuration rn whose boundary is subjected to an affine deformation i e there exists a constant n n matrix f and a constant n vector b such that x fx b for all x we consider all smooth equilibrium configurations satisfying this boundary condition clearly the homogeneous deformation x fx b for all x in bar omega is one such solution our aim is to prove under suitable hypotheses that it is the only such solution

cartesian currents weak diffeomorphisms and existence theorems in nonlinear elasticity in this paper we introduce some new classes of functions among these a class of weak diffeomorphisms in these classes we prove by direct methods the existence of minimizers for several kinds of variational integrals in particular we prove the existence of one to one orientation preserving maps that minimize suitable energies associated with hyperelastic materials the minimizers are also proved to satisfy equilibrium equations finally radial deformations are discussed in connection with cavitation

the hamiltonian structure of nonlinear elasticity the material and convective representations of solids rods and plates it is our belief that a thorough understanding of the mathematical underpinnings of elasticity is crucial to its analytical and numerical implementation for example in the analysis of rotating structures the coupling of the equations for geometrically inexact models obtained by linearization or other approximations with those for rotating rigid bodies can easily lead to misleading artificial softening effects that can significantly alter numerical results see simo and vuquoc 1986c especially equations 3 and 5 in this paper we consider fully nonlinear geometrically exact models for rods plates and shells which take into account shear and torsion as well as the usual bending effects in traditional rod and plate models these models can be obtained either from the three dimensional theory by a systematic use of projection methods see e g antman 1972 and naghdi 1972 or by a direct approach within the context of cosserat continuum remarkably the two approaches lead to essentially the same form of the governing field equations in the present context we have chosen as a model problem a particular rod model which may be regarded as an extension of the classical kirchhoff love model see love 1944 to include shear deformations as in

a note on n axially symmetric harmonic maps from b 3 to s 2 minimizing the relaxed energy for any n 2 we provide an explicit example of an n axially symmetric map u h1 b2 s2 c0 b 2 b 1 where br p r3 p r with degu b2 0 strictly minimizing in b1 the relaxed dirichlet energy of bethuel brezis and coron f u b2 12 b2 u 2dxdydz 4 u b2 and having u b2 0 u b1 const here u b2 is in a generalized sense the lenght of a minimal connection joining the topological singularities of u by strictly minimizing in b1 we intend that f u b2 f v b2 for every v h1 b2 s2 with v b2 b1 u b2 b1 and v u this result which we shall also rephrase in terms of cartesian currents following giaquinta modica and soucek stands in sharp contrast with a results of hardt lin and poon for the case n 1 and partially answers a long standing question of giaquinta modica and soucek in particular it is a first example of a minimizer of the relaxed energy having non trivial minimal connection we explain how this relates to the regularity of minimizers of f

the modeling of deformable bodies with frictionless self contacts we propose a mathematical model for m dimensional deformable bodies moving in mathbb r n that allows for frictionless contacts or self contacts while forbidding transversal self intersection to this end a topological constraint is imposed to the set of admissible deformations we restrict our analysis to the static case although the dynamic case is briefly addressed at the end of the article in this case no transversal self intersection can occur as long as 2m n so our modeling is mainly designed to handle the case 2m geqq n for nonlinear hyperelastic bodies we prove the existence of at least one minimizer of the energy on the set of admissible deformations under suitable assumptions on the stored energy function moreover for certain choices of m and n under regularity assumptions on the minimizers the solutions of the minimization problem satisfy euler lagrange equations

covariance in plasticity covariance is imposed to the second law of thermodynamics and consequences are shown for elastic perfectly plastic bodies in this setting pointwise balances of standard and configurational action

injectivity and self contact in nonlinear elasticity let be a bounded open connected subset of 3 with a sufficiently smooth boundary the additional condition det dx vol is imposed on the admissible deformations of a hyperelastic body whose reference configuration is we show that the associated minimization problem provides a mathematical model for matter to come into frictionless contact with itself but not interpenetrate we also extend j ball s theorems on existence to this case by establishing the existence of a minimizer of the energy in the space w1 p 3 p 3 that is injective almost everywhere

a new result on impulsive differential equations involving non absolutely convergent integrals in this paper we obtain as an application of a darbo type theorem global solutions for differential equations with impulse effects under the assumption that the function on the right hand side is integrable in the henstock sense we thus generalize several previously given results in literature for ordinary or impulsive equations

existence of minimizers for a finite strain micromorphic elastic solid we investigate geometrically exact generalized continua of micromorphic type in the sense of eringen the two field problem for the macrodeformation and the affine microdeformation p gl 3 r in the quasistatic conservative load case is investigated in a variational form depending on material constants two existence theorems in sobolev spaces are given for the resulting nonlinear boundary value problems these results comprise existence results for the micro incompressible case p sl 3 r and the cosserat micropolar case p so 3 r in order to treat external loads a new condition called bounded external work has to be included which overcomes the conditional coercivity of the formulation the possible lack of coercivity is related to fracture of the micromorphic solid the mathematical analysis uses an extended korn first inequality the methods of choice are the direct methods of the calculus of variations

uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity introduction 97 constitutive assumptions 99 0 the stored energy function and weak equilibrium solutions 101 1 properties of radial equilibrium solutions 105 2 uniqueness of solutions to boundary value problems for shells 111 3 uniqueness of cavitating solutions 117 4 existence of radial equilibria 121 5 asymptotic behaviour of equilibria for shells 128 6 concluding remarks 132 7 appendix 133 references 135

cauchy born rule and the stability of crystalline solids static problems we study the connection between atomistic and continuum models for the elastic deformation of crystalline solids at zero temperature we prove under certain sharp stability conditions that the correct nonlinear elasticity model is given by the classical cauchy born rule in the sense that elastically deformed states of the atomistic model are closely approximated by solutions of the continuum model with stored energy functionals obtained from the cauchy born rule the analysis is carried out for both simple and complex lattices and for this purpose we develop the necessary tools for performing asymptotic analysis on such lattices our results are sharp and they also suggest criteria for the onset of instabilities of crystalline solids

a unified procedure for construction of theories of deformable media ii generalized continua in contrast to classical theories discussed in the accompanying paper part i the present paper deals exclusively with generalized continua a term that refers to a body embedded in a euclidean three dimensional space with each of its material points endowed with additional kinematic structure such generalized continua are conveniently identified here by cosserat or directed continua in which the additional structure is represented by independent director fields and the material domain of the body manifold is classified according to the four categories a a three dimensional volume b a two dimensional surface c a one dimensional space curve and d a point in the derivation of a thermomechanical theory for each of these categories we use the same unified procedure as in part i but now the various energies that enter the balance of energy must be modified to include additional kinetic ingredients new theories of this kind have increasingly provided over the last three decades effective means of formulating and studying new behaviour of materials in both fluid and solid mechanics that were not previously possible by the classical theories our attention is first focused in the development of the theory for the first category and this is discussed in two stages first for a cosserat continuum with a single director and then for n directors our derived results include for the first time a derivation from the balance of energy of balances of director momenta and balances of entropies in the presence of more than one independent temperature field the treatments of categories b to d are somewhat shorter since their developments are formally similar to that of category a

closure properties for integral problems driven by regulated functions via convergence results abstract in this paper we give necessary and sufficient conditions for the convergence of kurzweil stieltjes integrals with respect to regulated functions using the notion of asymptotical equiintegrability one thus generalizes several well known convergence theorems as applications we provide existence and closure results for integral problems driven by regulated functions both in single and set valued cases in the particular setting of bounded variation functions driving the equations we get features of the solution set of measure integrals problems

a selection principle for mappings of bounded variation e helly s selection principle states that an infinite bounded family of real functions on the closed interval which is bounded in variation contains a pointwise convergent sequence whose limit is a function of bounded variation we extend this theorem to metric space valued mappings of bounded variation then we apply the extended helly selection principle to obtain the existence of regular selections of non convex set valued mappings any set valued mapping from an interval of the real line into nonempty compact subsets of a metric space which is of bounded variation with respect to the hausdorff metric admits a selection of bounded variation also we show that a compact valued set valued mapping which is lipschitzian absolutely continuous or of bounded riesz variation admits a selection which is lipschitzian absolutely continuous or of bounded riesz variation respectively

feasibility of h design specifications an interpolation method given a set of h design specifications the issue is to check whether there exists a controller whose order is free which satisfies these specifications the classical solution which is based on youla parametrization and convex closed loop design is not really satisfactory since it should use an infinite dimensional basis of filters which cannot be done in practice let j the minimal value of the design objective over such an infinite dimensional basis of filters a nevanlinna pick interpolation method is proposed here to compute lower and upper bounds of j by solving the design problem on a finite set of frequencies finite time convergence of the algorithm is proved

asymmetric variations of multifunctions with application to functional inclusions abstract under certain initial conditions we prove the existence of set valued selectors of univariate compact valued multifunctions of bounded jordan variation when the notion of variation is defined taking into account only the pompeiu asymmetric excess between compact sets from the target metric space for this we study subtle properties of the directional variations we show by examples that all assumptions in the main existence result are essential as an application we establish the existence of set valued solutions x t of bounded variation to the functional inclusion of the form x t f t x t satisfying the initial condition x t 0 x 0

measure driven differential inclusions measure driven differential inclusions arise when we attempt to derive necessary conditions of optimality for optimal impulsive control problems with nonsmooth data we introduce the concept of a robust solution to a measure driven inclusion which extends to a multifunction setting interpretations of solutions to measure driven differential equations provided by dal maso and rampazzo and others closure properties of sets of robust solutions are established and notions of relaxation investigated implications for optimality conditions for impulsive control problems are pursued in a companion paper

a corpuscular approach to continuum mechanics basic considerations the macroscopic behaviour of a material derives ultimately from its microstructure which at the molecular level and below is of a fundamentally discrete nature as much is often known of the microstructure molecular interactions and thermal motions associated with specific materials it is of interest to ascertain whether and to what extent such information can usefully be incorporated into continuum models the first step in this direction is to treat discrete fundamental entities for example molecules ions or atoms as particles point masses and relate continuum theories to corpuscular considerations this is of course an important feature of the kinetic theory of gases lattice dynamics and statistical mechanics the first two theories take account of particle interactions and thermal motions as these pertain to general motions of moderately rarefied gases and vibrations in ordered solids respectively but such considerations play no explicit part in standard formulations of statistical mechanics many discussions which bear upon the relations between discrete descriptions of materials and continuum mechanics have been given motivated in the main by considerations of microstructure such as the contributions of ericksen 1960 1961 dahler scriven 1963 eringen suhubi 1964 green rivlin 1964 krumhansl 1965 eringen kroner krumhansl kunin mindlin and rivlin in kroner 1968 rivlin 1968 1976 alblas 1976 and capriz podio guidugli 1976 1977 this work is intended to complement the aforementioned by emphasising the roles played in general by corpuscular interactions and thermal motions in the formulation of continuum theories