exact boundary controllability of a microbeam model abstract in this paper we study the exact controllability property of a microbeam model by means of a single boundary control we use the multiplier method together with the controllability observability duality to obtain a time t 0 such that the corresponding linear equation is exactly controllable provided that the control time is greater than t 0 our exact controllability result improves the one obtained in vatankhah et al 2014 20 which uses six boundary controls instead of a single one

iterative regularization for elliptic inverse problems elliptic inverse problems can be formulated using coefficient dependent energy least squares functionals resulting in a smooth convex objective functional a variational inequality emerges as a necessary and sufficient optimality condition the principle of iterative regularization when coupled with the auxiliary problem principle results in a strongly convergent scheme for the solution of elliptic inverse problems

exact boundary controllability of vibrating non classical euler bernoulli micro scale beams abstract this study investigates the exact controllability problem for a vibrating non classical euler bernoulli micro beam whose governing partial differential equation pde of motion is derived based on the non classical continuum mechanics in this paper it is proved that via boundary controls it is possible to obtain exact controllability which consists of driving the vibrating system to rest in finite time this control objective is achieved based on the pde model of the system which causes that spillover instabilities do not occur

admissibility and exact observability of observation operators for micro beam model time and frequency domain approaches this study focuses on the exact observability of a non classical euler bernoulli micro beam equation this non classical model was derived based on the strain gradient elasticity theory which is intended to explain the phenomenon of size effect at the micron scale spectral properties of the corresponding state operator are studied an asymptotic expression for eigenvalues is calculated and eigenfunctions are analyzed in order to check the necessary conditions for the exact observability of the system by examining the eigenfunctions it is shown that among non collocated boundary outputs only measurement of the non classical moment at the root of the beam yields an admissible observation operator and also defines an exactly observable system an alternative proof based on the multiplier method which is commonly employed in the literature on the observability and controllability of infinite dimensional dynamical systems is presented to provide a comparison between the time and frequency domain approaches

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

exact controllability for the schrodinger equation the exact controllability of schrodinger equation in bounded domains with dirichlet boundary condition is studied both the boundary controllability and the internal controllability problems are considered concerning the boundary controllability the paper proves the exact controllability in h 1 omega with l 2 boundary control on the other hand the exact controllability in l 2 omega is proved with l 2 controls supported in a neighborhood of the boundary both results hold for an arbitrarily small time the method of proof combines both the hum hilbert uniqueness method and multiplier techniques

indentification of some source densities of the distribution type abstract in this paper we investigate the solvability of an ill posed two dimensional fredholm integral equation of the first kind which allows the solutions of distribution type the problem is first transformed into a well posed differential integral equation using output least squares approach with a regularization of bounded variations a globally convergent iterative method is proposed and some numerical results are presented the methodology discussed may be applied for the identification of the boundary shape of the defects of a dielectric material or the interface between different materials

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

a unified approach to the construction of minimax designs summary we present a unified approach for constructing large sample optimal designs when the optimality criterion is of the minimax type the assumed model is a general linear regression model with a known efficiency function defined on a closed and bounded space an equivalence theorem is formulated and computer algorithms for generating minimax optimal designs are proposed it is shown that this methodology is simple and rather general it can be used to construct for example minimax variance optimal designs minimax with respect to the single parameters designs and e optimal designs an application of this procedure to find an optimal design for minimizing the maximum predictive variance over a compact region in a heteroscedastic design problem is included

optimal designs for dose response models with restricted design spaces in dose response studies the dose range is often restricted due to concerns over drug toxicity and or efficacy we present restricted and unrestricted interval locally optimal designs with respect to a very general class of optimality criteria for estimating the underlying dose response curve the underlying curve belongs to a diversified set of link functions suitable for the dose response studies and having a common canonical form these include the fundamental binary response models the logit and the probit as well as the skewed versions of these models the results are illustrated through the re design of a dose ranging trial conducted at the merck research laboratories zeng and zhu 1997 this work is a generalization of the results of dai and zhu 2002 in terms of the design interval the underlying dose response curve and the optimality criterion

approximate inverse method for stable analytic continuation in a strip domain numerical analytic continuation is in general an ill posed problem and some special regularization methods are needed in this paper we apply the approximate inverse method to deal with the problem in a strip domain w z x iy c x r 0 y

exact controllability of the schrodinger equation in this paper we study the controllability of the linear schrodinger equation on bounded domains in r n first we state and prove a simple functional analytic characterization of the exact controllability of abstract schrodinger type equations which does not use the hilbert uniqueness method in a second part we discuss generalizations of results of machtyngier siam j control optim 32 1994 24 on the exact internal and boundary controllability of schrodinger equation by allowing lower order terms in the schrodinger equation this may be a first step to prove results on the exact controllability of semilinear nonlinear schrodinger equations which is a big problem

e optimal designs for linear and nonlinear models with two parameters summary a method for constructing e optimal designs for a broad class of two parameter models is presented the procedure is based on the two dimensional geometry of the induced design space and of the first elfving set and guarantees to find e optimal designs which have exactly two points of support for e optimal designs based on three support points the procedure is less clear cut efficient designs based on essentially two points can be constructed using the geometry of the first elfving set but globally e optimal designs must at least in general be found by other strategies such as those based on symmetry considerations the geometry of the second elfving set systematic searches or numerical methods the methodology is illustrated by means of selected examples involving generalised linear models

optimal designs for a class of nonlinear regression models for a broad class of nonlinear regression models we investigate the local e and c optimal design problem it is demonstrated that in many cases the optimal designs with respect to these optimality criteria are supported at the chebyshev points which are the local extrema of the equi oscillating best approximation of the function f 0 0 by a normalized linear combination of the regression functions in the corresponding linearized model the class of models includes rational logistic and exponential models and for the rational regression models the e and c optimal design problem is solved explicitly in many cases

boundary controllability of the korteweg de vries equation on a bounded domain this paper studies boundary controllability of the korteweg de vries equation posed on a finite interval in which because of the third order character of the equation three boundary conditions are required to secure the well posedness of the system we consider the cases where one two or all three of those boundary data are employed as boundary control inputs the system is first linearized around the origin and the corresponding linear system is proved to be exactly boundary controllable if using two or three boundary control inputs in the case where only one control input is allowed to be used the linearized system is known to be only null controllable if the single control input acts on the left end of the spatial domain by contrast if the single control input acts on the right end of the spatial domain the linearized system is shown to be exactly controllable if and only if the length of the spatial domain does not belong to a set of critical values moreover the nonlinear system is shown

energy decay of a microbeam model with a locally distributed nonlinear feedback control abstract in this paper we address the problem of internal stabilization of the deflection of a microbeam which is modeled by a sixth order hyperbolic equation employing multiplier techniques and an integral inequality we prove that a locally distributed nonlinear feedback control forces the energy associated to the deflection to decay exponentially or polynomially to zero as a consequence of this the deflection goes to the rest position as the time goes to infinity

energy decay for the modified kawahara equation posed in a bounded domain abstract studied here is the eventual dissipation of solutions to initial boundary value problems for the modified kawahara equation with and without a localized damping term included it is shown that solutions of undamped problems posed on a bounded interval may not decay if the length of the interval is critical in contrast the energy associated to the locally damped problems is shown to be exponentially decreased independently of the interval length