the singular set of solutions to non differentiable elliptic systems we estimate the hausdorff dimension of the singular set of solutions to elliptic systems of the type if the vector fields a and b are holder continuous with respect to the variable x with exponent then the hausdorff dimension of the singular set of any weak solution is at most n 2

adaptive predefined performance control for mimo systems with unknown direction via generalized fuzzy hyperbolic model an adaptive predefined performance control problem is investigated for a class of multiple input multiple output systems with unknown control direction and unknown backlash like hysteresis nonlinearities by using generalized fuzzy hyperbolic model gfhm compared with the existing methods the main features are as follows the prediction error is introduced to construct the adaptive laws which means that the approximate accuracy of the gfhm is solved the nussbaum type gain is utilized to deal with the unknown control direction which avoids the requirement of direction a priori and by transforming the tracking errors into new error variables the prescribed steady state and transient performance can be ensured it is shown that the proposed control approach can guarantee that all the signals of the resulting closed loop systems are bounded and the output tracks a desired trajectory while the tracking errors are confined all times within the prescribed bounds finally two simulation results and some comparisons are provided to verify the effectiveness of the proposed approach since the proposed control strategy is only implemented in a healthy case how to extend the strategy to a faulty case will be a further topic

modeling identification and control of a class of nonlinear systems in this paper we propose a new fuzzy hyperbolic model for a class of complex systems which is difficult to model the fuzzy hyperbolic model is a nonlinear model in nature and can be easily derived from a set of fuzzy rules it can also be seen as a feedforward neural network model and so we can identify the model parameters by bp algorithm we prove that the stable controller can be designed based on linear system theory two methods of designing the controller for the fuzzy hyperbolic model are proposed the results of simulation support the effectiveness of the model and the control scheme

on rank one convex functions that are homogeneous of degree one we show that positively 1 homogeneous rank one convex functions are convex at 0 and at matrices of rank one the result is a special case of an abstract convexity result that we establish for positively 1 homogeneous directionally convex functions defined on an open convex cone in a finite dimensional vector space from these results we derive a number of consequences including various generalizations of the ornstein l1 non inequalities most of the results were announced in c r acad sci paris ser i 349 407 409 2011

adaptive fuzzy control of mimo nonlinear systems this paper presents a novel fuzzy basis function approach for adaptive control of multi input and multi output mimo systems in the method the nonlinear plant is first linearised and the fuzzy basis function vector is introduced to adaptively learn the upper bound of the system uncertainty vector while its output is used as the parameter of the compensator in the sense that both the robustness and the asymptotic error convergence can be obtained for the closed loop nonlinear control system

step fluctuations for a faceted crystal a statistical mechanics model for a faceted crystal is the 3d ising model at zero temperature it is assumed that in one octant all sites are occupied by atoms the remaining ones being empty allowed atom configurations are such that they can be obtained from the filled octant through successive removals of atoms with breaking of precisely three bonds if v denotes the number of atoms removed then the grand canonical boltzmann weight is q v 0 q 1 as shown by cerf and kenyon in the limit q 1 a deterministic shape is attained which has the three facets 100 010 001 and a rounded piece interpolating between them we analyse the step statistics as q 1 in the rounded piece it is given by a determinantal process based on the discrete sine kernel exactly at the facet edge the steps have more space to meander their statistics is again determinantal but this time based on the airy kernel in particular the border step is well approximated by the airy process which has been obtained previously in the context of growth models our results are based on the asymptotic analysis for space time inhomogeneous transfer matrices

a regularity theorem for minimizers of quasiconvex integrals we prove c1 partial regularity for minimizers of functionals with quasiconvex integrand f x u du depending on vector valued functions u the integrand is required to be twice continuously differentiable in du and no assumption on the growth of the derivatives of f is made a polynomial growth is required only on f itself

fine properties of functions with bounded deformation the paper is concerned with the fine properties of functions in the space of functions with bounded deformation we analyse the set of lebesgue points and the set where these functions have one sided approximate limits moreover following the analogy with we decompose the symmetric distributional derivative into an absolutely continuous part a jump part and a cantor part the main result of the paper is a structure theorem for functions showing that these parts of the derivative can be recovered from the corresponding ones of the one dimensional sections moreover we prove that functions are approximately differentiable in almost every point of their domain

interior gradient regularity for bv minimizers of singular variational problems we consider a class of vectorial integrals with linear growth where as a key feature some degenerate singular behavior is allowed for generalized minimizers of these integrals in bv we establish interior gradient regularity and as a consequence uniqueness up to constants in particular these results apply for 1 p 2 to the singular model integrals z 1 jrw x j p 1 p dx

regularity results for stationary electro rheological fluids we prove regularity results for weak solutions to systems modelling electro rheological fluids in the stationary case as proposed in 27 31 a particular case of the system we consider is

the singular set of ω minima we consider minima open image in new window of convex variational integrals in the vectorial case n n 2 and we provide estimates for the hausdorff dimension of their singular sets

higher integrability for minimizers of integral functionals with p q growth abstract we prove higher integrability for minimizers u r n of integral functionals f du a x u dx where f satisfies a non standard growth condition of p q type z p f z l 1 z q p

partial regularity for bv minimizers we establish an varepsilon regularity result for the derivative of a map of bounded variation that minimizes a strongly quasiconvex variational integral of linear growth and as a consequence the partial regularity of such bv minimizers this result extends the regularity theory for minimizers of quasiconvex integrals on sobolev spaces to the context of maps of bounded variation previous partial regularity results for bv minimizers in the linear growth set up were confined to the convex situation

a new approach to counterexamples to l 1 estimates korn s inequality geometric rigidity and regularity for gradients of separately convex functions the derivation of counterexamples to l1 estimates can be reduced to a geometric decomposition procedure along rank one lines in matrix space we illustrate this concept in two concrete applications firstly we recover a celebrated and rather complex counterexample by ornstein proving the failure of korn s inequality and of the corresponding geometrically nonlinear rigidity result in l1 secondly we construct a function f 2 which is separately convex but whose gradient is not in bvloc in the sense that the mixed derivative 2f x1 x2 is not a bounded measure

korn type inequalities in orlicz spaces abstract we exhibit balance conditions between a young function a and a young function b for a korn type inequality to hold between the l b norm of the gradient of vector valued functions and the l a norm of its symmetric part in particular we extend a standard form of the korn inequality in l p with 1 p and an orlicz version involving a young function a satisfying both the 2 and the 2 condition

the singular set of minima of integral functionals in this paper we provide upper bounds for the hausdorff dimension of the singular set of minima of general variational integrals open image in new window where f is suitably convex with respect to dv and holder continuous with respect to x v in particular we prove that the hausdorff dimension of the singular set is always strictly less than n where open image in new window

regularity and existence of solutions of elliptic equations with p q growth conditions for some positive constants m a4 and for exponents q 2 p 2 2 under 1 2 1 3 and some other assumptions by assuming also that the quotient q p is sufficiently close to one in dependence on n precisely if q p c n n 2 then we prove that every weak solution to 1 1 of class 4 4 0 is locally lipschitz continuous in q moreover there are positive constants 8 c and 0 2 1 such that

exact solutions for kpz type growth processes random matrices and equilibrium shapes of crystals abstract three models from statistical physics can be analyzed by employing space time determinantal processes 1 crystal facets in particular the statistical properties of the facet edge and equivalently tilings of the plane 2 one dimensional growth processes in the kardar parisi zhang universality class and directed last passage percolation 3 random matrices multi matrix models and dyson s brownian motion we explain the method and survey results of physical interest

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

new integral estimates for deformations in terms of their nonlinear strains if u is a bi lipschitzian deformation of a bounded lipschitz domain in ln n 2 we show that the lp norm p 1 p n of a certain nonlinear strain function e u associated with u dominates the distance in lq q np n p if p n from u to a suitably chosen rigid motion of n this work extends that of f john who proved corresponding estimates for p 1 under the hypothesis that u has uniformly small strain we also obtain a bound for the oscillation of du in l2 these estimates are apparently the first to apply with no a priori pointwise hypotheses upon the strain of u in 3 the integral int limits omega e u 2d 3 is dominated by typical hyperelastic energy functionals proposed in the literature for modeling the behavior of rubber thus the case n 3 p 2 gives the first general bound for the deformations of such materials in terms of the associated nonlinear elastic work

dynamical scaling implications of ferrari prahofer and spohn s remarkable spatial scaling results for facet edge fluctuations spurred by theoretical predictions from ferrari et al phys rev e 69 035102 r 2004 we rederived and extended their result heuristically with experimental colleagues we used stm line scans to corroborate their prediction that the fluctuations of the step bounding a facet exhibit scaling properties distinct from those of isolated steps or steps on vicinal surfaces the correlation functions was shown to go as t 0 15 3 decidedly different from the t 0 26 2 behavior for fluctuations of isolated steps

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

fluctuations of an atomic ledge bordering a crystalline facet when a high symmetry facet joins the rounded part of a crystal the step line density vanishes as square root of r with r denoting the distance from the facet edge this means that the ledge bordering the facet has a lot of space to meander as caused by thermal activation we investigate the statistical properties of the border ledge fluctuations in the scaling regime they turn out to be non gaussian and related to the edge statistics of gaussian unitary ensemble multimatrix models

a novel approach to reliable output feedback control of fuzzy affine systems with time delays and sensor faults this paper proposes a novel system augmentation approach to the delay dependent reliable piecewise affine mathscr h infty static output feedback control for nonlinear systems with time varying delay and sensor faults in the piecewise markovian lyapunov functional based framework the nonlinear plant is described by a continuous time takagi sugeno fuzzy affine model with parametric uncertainties and the sensor faults are characterized by a markov process specifically by applying a state input augmentation technique the original closed loop system is first reformulated into a descriptor fuzzy affine system based on a new piecewise markovian lyapunov krasovskii functional combined with a wirtinger based integral inequality improved reciprocally convex inequality and s procedure a novel bounded real lemma is then derived for the underlying closed loop system furthermore by taking advantage of the redundancy of descriptor system formulation together with a linearization procedure the piecewise affine controller synthesis is carried out it is shown that the desired piecewise affine controller gains can be attained by solving a linear matrix inequality based optimization problem finally simulation examples are performed to confirm the effectiveness and less conservatism of the presented approach

the regularity of minima for the dirichlet problem on bd we establish that the dirichlet problem for linear growth functionals on text bd the functions of bounded deformation gives rise to the same unconditional sobolev and partial text c 1 alpha regularity theory as presently available for the full gradient dirichlet problem on text bv functions of bounded deformation play an important role in for example plasticity however by ornstein s non inequality contain text bv as a proper subspace thus techniques to establish regularity by full gradient methods for variational problems on bv do not apply here in particular applying to all generalised minima that is minima of a suitably relaxed problem despite their non uniqueness and reaching the ellipticity ranges known from the text bv case this paper extends previous sobolev regularity results by gmeineder and kristensen in j calc var 58 56 2019 in an optimal way

quasiconvexity and partial regularity in the calculus of variations we prove partial regularity of minimizers of certain functionals in the calculus of variations under the principal assumption that the integrands be uniformly strictly quasiconvex this is of interest since quasiconvexity is known in many circumstances to be necessary and sufficient for the weak sequential lower semicontinuity of these functionals on appropriate sobolev spaces examples covered by the regularity theory include functionals with integrands which are convex in the determinants of various submatrices of the gradient matrix