a higher order triangular plate bending element revisited a new formulation of an eighteen degrees of freedom higher order triangular plate bending element using triangular area co ordinates is presented the displacement function w is taken as the complete fifth order polynomial in area co ordinates the normal slope along an edge of the triangle is constrained to vary cubically the twenty one constants are expressed explicity in terms of eighteen degrees of freedom the element stiffness matrix is expressed as a product of component matrices for which explicit expressions are developed and presented no numerical inversion or integration is necessary the formulation is expected to be useful specially for microcomputers

mathcal l _ 2 mathcal l _ infty output feedback controller design for fuzzy systems over switching parameters this paper focuses on the problem of mathcal l 2 mathcal l infty dynamic output feedback controller dofc design for nonlinear switched systems with nonlinear perturbations in the takagi sugeno fuzzy framework first the average dwell time approach is used to stabilize a nonlinear switched system exponentially under an arbitrary switching law then based on the technique of piecewise lyapunov functions a fuzzy rule dependent dofc is designed to ensure that the overall closed loop system is exponentially stable with a weighted mathcal l 2 mathcal l infty performance level left gamma alpha right the solvability condition for the desired dofc is derived using a linearization technique it is shown that the controller parameters can be obtained as solutions to a set of strict linear matrix inequalities that are numerically solvable with available standard software finally two simulation examples illustrate effectiveness of the developed technique including cognitive radio systems

schmitt trigger a solvable model of stochastic resonance an ideal schmitt trigger st is the simplest two state system available for realization of stochastic resonance sr an exact solution is found for the st driven by exponentially correlated gaussian noise plus a weak periodic signal the signal to noise ratio is shown to pass through a maximum at a specific value of the noise intensity a qualitative classification is given for a class of noise models which either exhibit sr or do not

a boundary element method for solving 2 d and 3 d static gradient elastic problems part i integral formulation abstract a boundary element formulation is developed for the static analysis of two and three dimensional solids and structures characterized by a linear elastic material behavior taking into account microstructural effects the simple gradient elastic theory of aifantis expressed in the framework of mindlin s general theory is used to model this material behaviour a variational statement is established to determine all possible classical and non classical due to gradient terms boundary conditions of the general boundary value problem the gradient elastic fundamental solution for both two and three dimensional cases is explicitly derived and used to construct the boundary integral representation of the solution with the aid of the reciprocal integral identity especially established for the gradient elasticity considered here it is found that for a well posed boundary value problem in addition to a boundary integral representation for the displacement a second boundary integral representation for its normal derivative is also necessary explicit expressions for interior displacements and stresses in integral form are also presented all the kernels in the integral equations are explicitly provided

finite elements for materials with strain gradient effects a finite element implementation is reported of the fleck hutchinson phenomenological strain gradient theory this theory fits within the toupin mindlin framework and deals with first order strain gradients and the associated work conjugate higher order stresses in conventional displacement based approaches the interpolation of displacement requires c1 continuity in order to ensure convergence of the finite element procedure for higher order theories mixed type finite elements are developed herein for the fleck hutchinson theory these elements use standard c0 continuous shape functions and can achieve the same convergence as c1 elements these c0 elements use displacements and displacement gradients as nodal degrees of freedom kinematic constraints between displacement gradients are enforced via the lagrange multiplier method the elements developed all pass a patch test the resulting finite element scheme is used to solve some representative linear elastic boundary value problems and the comparative accuracy of various types of element is evaluated copyright 1999 john wiley sons ltd

a reciprocity theorem in linear gradient elasticity and the corresponding saint venant principle in many practical applications of nanotechnology and in microelectromechanical devices typical structural components are in the form of beams plates shells and membranes when the scale of such components is very small the material microstructural lengths become important and strain gradient elasticity can provide useful material modelling in addition small scale beams and bars can be used as test specimens for measuring the lengths that enter the constitutive equations of gradient elasticity it is then useful to be able to apply approximate solutions for the extension shear and flexure of slender bodies such approach requires the existence of some form of the saint venant principle the present work presents a statement of the saint venant principle in the context of linear strain gradient elasticity a reciprocity theorem analogous to betti s theorem in classic elasticity is provided first together with necessary restrictions on the constitutive equations and the body forces it is shown that the order of magnitude of displacements are in accord with the sternberg s statement of the saint venant principle the cases of stretching shearing and bending of a beam were examined in detail using two dimensional finite elements the numerical examples confirmed the theoretical results 2005 elsevier ltd all rights reserved

mean square data based controller for nonlinear polynomial systems with multiplicative noise this paper presents the mean square optimal data based quadratic gaussian controller for stochastic nonlinear polynomial systems with a polynomial multiplicative noise a linear control input and a quadratic criterion over linear observations the mean square optimal closed form controller equations are obtained using the separation principle whose applicability to the considered problem is substantiated as an intermediate result the paper gives a closed form solution of the optimal regulator control problem for stochastic nonlinear polynomial systems with a polynomial multiplicative noise a linear control input and a quadratic criterion performance of the obtained mean square optimal data based controller is verified in the illustrative example against the conventional lqg controller that is optimal for linearized systems simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included

boundary element formulation for plane problems in couple stress elasticity summary couple stresses are introduced to account for the microstructure of a material within the framework of continuum mechanics linear isotropic versions of such materials possess a characteristic material length l that becomes increasingly important as problem dimensions shrink to that level e g as the radius a of a critical hole reduces to a size comparable to l consequently this size dependent elastic theory is essential to understand the behavior at micro and nano scales and to bridge the atomistic and classical continuum theories here we develop an integral representation for two dimensional boundary value problems in the newly established fully determinate theory of isotropic couple stress elastic media the resulting boundary only formulation involves displacements rotations force tractions and moment tractions as primary variables details on the corresponding numerical implementation within a boundary element method are then provided with emphasis on kernel singularities and numerical quadrature afterwards the new formulation is applied to several computational examples to validate the approach and to explore the consequences of size dependent couple stress elasticity copyright 2011 john wiley sons ltd

robust stochastic resonance signal detection and adaptation in impulsive noise stochastic resonance sr occurs when noise improves a system performance measure such as a spectral signal to noise ratio or a cross correlation measure all sr studies have assumed that the forcing noise has finite variance most have further assumed that the noise is gaussian we show that sr still occurs for the more general case of impulsive or infinite variance noise the sr effect fades as the noise grows more impulsive we study this fading effect on the family of symmetric ensuremath alpha stable bell curves that includes the gaussian bell curve as a special case these bell curves have thicker tails as the parameter ensuremath alpha falls from 2 the gaussian case to 1 the cauchy case to even lower values thicker tails create more frequent and more violent noise impulses the main feedback and feedforward models in the sr literature show this fading sr effect for periodic forcing signals when we plot either the signal to noise ratio or a signal correlation measure against the dispersion of the ensuremath alpha stable noise linear regression shows that an exponential law ensuremath gamma mathrm opt ensuremath alpha ca ensuremath alpha describes this relation between the impulsive index ensuremath alpha and the sr optimal noise dispersion ensuremath gamma mathrm opt the results show that sr is robust against noise outliers so sr may be more widespread in nature than previously believed such robustness also favors the use of sr in engineering systems we further show that an adaptive system can learn the optimal noise dispersion for two standard sr models the quartic bistable model and the fitzhugh nagumo neuron model for the signal to noise ratio performance measure this also favors practical applications of sr and suggests that evolution may have tuned the noise sensitive parameters of biological systems

stochastic resonance in neuron models periodically stimulated sensory neurons typically exhibit a kind of statistical phase locking to the stimulus they tend to fire at a preferred phase of the stimulus cycle but not at every cycle hence the histogram of interspike intervals isih i e of times between successive firings is multimodal for these neurons with peaks centered at integer multiples of the driving period a particular kind of residence time histogram for a large class of noisy bistable systems has recently been shown to exhibit the major features of the neural data in the present paper we show that an excitable cell model the fitzhugh nagumo equations also reproduces these features when driven by additive periodic and stochastic forces this model exhibits its own brand of stochastic resonance as the peaks of the isih successively go through a maximum when the noise intensity is increased further the presence of a noise induced limit cycle introduces a third time scale in the problem this limit cycle is found to modify qualitatively the phase locking picture e g by suppressing certain peaks in the isih finally the role of noise and possibly of stochastic resonance sr in the neural encoding of sensory information is discussed

memoryless approach to the lq and lqg problems with variable input delay this note studies the lq and lqg problems for linear time invariant systems with a single time varying input delay and instantaneous memoryless state feedback we extend the memoryless state feedback solution proposed in 1 in two directions we prove that in the deterministic case a memoryless state feedback can be in general optimal only up to a certain delay for which we provide a sufficient and sometimes strict bound moreover we show that this memoryless control is optimal also in the case of time varying delays and that the quadratic cost functional has the same value as in the case without delay for time varying delays the control law requires that the relationship between time points in which the input is generated and applied is known and invertible even if the delay function needs not to be differentiable or even continuous finally we prove that the cost functional is bounded also in the stochastic case for the same delay interval as in the deterministic case but with a larger cost than the delay less lqg solution

the modified cramer rao bound in vector parameter estimation in this paper we extend the scalar modified cramer rao bound mcrb to the estimation of a vector of nonrandom parameters in the presence of nuisance parameters the resulting bound is denoted with the acronym mcrvb where v stands for vector as with the scalar bound the mcrvb is generally looser than the conventional crvb but the two bounds are shown to coincide in some situations of practical interest the mcrvb is applied to the joint estimation of carrier frequency phase and symbol epoch of a linearly modulated waveform corrupted by correlated impulsive noise encompassing white gaussian noise as a particular case wherein data symbols and noise power are regarded as nuisance parameters in this situation calculation of the conventional crvb is infeasible while application of the mcrvb leads to simple useful expressions with moderate analytical effort when specialized to the case of white gaussian noise the mcrvb yields results already available in the literature in fragmentary form and simplified contexts

the linear quadratic optimal control approach to feedback control design for systems with delay abstract a generalized linear quadratic optimal control problem for systems with delay is formulated the optimal solution is given as a state feedback form which requires a solution of coupled infinite dimensional riccati equations it is shown that the closed loop system formed by the optimal state feedback control has some desirable sensitivity and robustness properties the generalization exists in the state quadratic form of the cost functional which makes it possible to discuss a pole location problem within the framework of the linear quadratic optimal control problem it is also shown that the generalized cost functional contains a special class of cost functionals for which the optimal control can be realized by solving only a finite dimensional riccati equation based on these results about the generalized linear quadratic optimal control a design method of feedback controls is proposed and an illustrative example is then presented

multiscale computational homogenization methods with a gradient enhanced scheme based on the discontinuous galerkin formulation abstract when considering problems of dimensions close to the characteristic length of the material the size effects can not be neglected and the classical so called first order multiscale computational homogenization scheme fmch looses accuracy motivating the use of a second order multiscale computational homogenization smch scheme this second order scheme uses the classical continuum at the micro scale while considering a second order continuum at the macro scale although the theoretical background of the second order continuum is increasing the implementation into a finite element code is not straightforward because of the lack of high order continuity of the shape functions in this work we propose a smch scheme relying on the discontinuous galerkin dg method at the macro scale which simplifies the implementation of the method indeed the dg method is a generalization of weak formulations allowing for inter element discontinuities either at the c 0 level or at the c 1 level and it can thus be used to constrain weakly the c 1 continuity at the macro scale the c 0 continuity can be either weakly constrained by using the dg method or strongly constrained by using usual c 0 displacement based finite elements therefore two formulations can be used at the macro scale i the full discontinuous galerkin formulation fdg with weak c 0 and c 1 continuity enforcements and ii the enriched discontinuous galerkin formulation edg with high order term enrichment into the conventional c 0 finite element framework the micro problem is formulated in terms of standard equilibrium and periodic boundary conditions a parallel implementation in three dimensions for non linear finite deformation problems is developed showing that the proposed method can be integrated into conventional finite element codes in a straightforward and efficient way

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

error analysis of maximum likelihood estimates of physical parameters from one or more dispersive waves measurement of physical parameters from one or more dispersive waves propagating in a band of frequencies across a linear array of receivers is considered the waves propagate according to a known physical model having real valued parameters and have spatially uncorrelated white gaussian noise added to them the objective of the measurement is to estimate a specified subset of the physical parameters the remaining physical parameters are externally provided and have known error statistics existing maximum likelihood ml estimation and cramer rao cr bounds theory describes the measurement under the assumption of correct values for the externally provided parameters a review of this theory is presented for completeness then a bounding estimate on the total error on the estimated parameters is derived which takes into account both the cr bounds and errors in the externally provided parameters suggestions for the application of the theory to practical problems are provided a criterion is derived for determining whether additional unwanted nuisance parameters should be included in the estimate to improve the total error on the desired parameters

mixed finite element formulations of strain gradient elasticity problems theories on intrinsic or material length scales find applications in the modeling of size dependent phenomena in elasticity length scales enter the constitutive equations through the elastic strain energy function which in this case depends not only on the strain tensor but also on gradients of the rotation and strain tensors in the present paper the strain gradient elasticity theories developed by mindlin and co workers in the 1960s are treated in detail in such theories when the problem is formulated in terms of displacements the governing partial differential equation is of fourth order if traditional finite elements are used for the numerical solution of such problems then c 1 displacement continuity is required an alternative mixed finite element formulation is developed in which both the displacement and the displacement gradients are used as independent unknowns and their relationship is enforced in an integralsense a variational formulation is developed which can be used for both linear and non linear strain gradient elasticity theories the resulting finite elements require only c 0 continuity and are simple to formulate the proposed technique is applied to a number of problems and comparisons with available exact solutions are made 2002 elsevier science b v all rights reserved

receding horizon controls for input delayed systems this paper presents a receding horizon control rhc for an unconstrained input delayed system to begin with we derive a finite horizon optimal control for a quadratic cost function including two final weighting terms the rhc is easily obtained by changing the initial and final times of the finite horizon optimal control a linear matrix inequality lmi condition on two final weighting matrices is proposed to meet the cost monotonicity under which the optimal cost on the horizon is monotonically nonincreasing with time and hence the asymptotical stability is guaranteed only if an observability condition is met it is shown through simulation that the proposed rhc stabilizes the input delayed system effectively and its performance can be tuned by adjusting weighting matrices with respect to the state and the input

information capacity of stochastic pooling networks is achieved by discrete inputs stochastic pooling networks spn are sensor networks where multiple sensors make independently noisy and compressed measurements of the same information source which are combined via pooling examples of spns range from nanoelectronics to biological sensory neurons here it is shown that optimal information transmission in spns with nodes that quantize to a finite number of states requires the input signal distribution to be discrete this is illustrated numerically for a simple spn consisting of n binary quantizing sensors the resultant information capacity is shown to be independent of the noise distribution when the signal distribution can be freely chosen but to imply an optimal noise distribution if the signal distribution is fixed while larger than the best performance of previously studied continuously valued input signals the capacity does not scale faster than the previous best result of text log 2 sqrt n bits per channel use it is also shown that a plot of the optimal input distribution contains bifurcations as n increases and that suprathreshold stochastic resonance occurs when the mutual information is determined for a suboptimal noise distribution

implicit gradient elasticity a new formulation of gradient elasticity is derived and implemented pade approximations are used to introduce an implicit relation between non local strains and displacements as a result the finite element interpolation requires only 0 continuous rather than 1 continuous shape functions the underlying energy functional is presented and it is found that the present formulation is of the mixed type whereby the non local strains act as the primary unknowns and the displacements as the auxiliary unknowns the implications on the interpolation are studied finally the influence of the additional length scale parameter on the global response is assessed copyright 2006 john wiley sons ltd

gradient elasticity in statics and dynamics an overview of formulations length scale identification procedures finite element implementations and new results in this paper we discuss various formats of gradient elasticity and their performance in static and dynamic applications gradient elasticity theories provide extensions of the classical equations of elasticity with additional higher order spatial derivatives of strains stresses and or accelerations we focus on the versatile class of gradient elasticity theories whereby the higher order terms are the laplacian of the corresponding lower order terms one of the challenges of formulating gradient elasticity theories is to keep the number of additional constitutive parameters to a minimum we start with discussing the general mindlin theory that in its most general form has 903 constitutive elastic parameters but which were reduced by mindlin to three independent material length scales further simplifications are often possible in particular the aifantis theory has only one additional parameter in statics and opens up a whole new field of analytical and numerical solution procedures we also address how this can be extended to dynamics an overview of length scale identification and quantification procedures is given finite element implementations of the most commonly used versions of gradient elasticity are discussed together with the variationally consistent boundary conditions details are provided for particular formats of gradient elasticity that can be implemented with simple linear finite element shape functions new numerical results show the removal of singularities in statics and dynamics as well as the size dependent mechanical response predicted by gradient elasticity

exponentiated beta distributions beta distributions are usually defined on the unit interval 0 1 for wider applicability we introduce six exponentiated beta distributions and derive several of their properties including the moment generating function expectation variance skewness kurtosis shannon entropy and the renyi entropy

optimal control for linear systems with multiple time delays in control input this note presents the optimal linear quadratic lq regulator for a linear system with multiple time delays in the control input optimality of the solution is proved in two steps first a necessary optimality condition is derived from the maximum principle then the sufficiency of this condition is established by verifying that it satisfies the hamilton jacobi bellman equation using an illustrative example the performance of the obtained optimal regulator is compared against the performance of the optimal lq regulator for linear systems without delays and some other feasible feedback regulators that are linear in the state variables finally the note establishes a duality between the solutions of the optimal filtering problem for linear systems with multiple time delays in the observations and the optimal lq control problem for linear systems with multiple time delays in the control input

chirality in isotropic linear gradient elasticity abstract chirality is generally speaking the property of an object that can be classified as left or right handed though it plays an important role in many branches of science chirality is encountered less often in continuum mechanics so most classical material models do not account for it in the context of elasticity for example classical elasticity is not chiral leading different authors to use cosserat elasticity to allow modelling of chiral behaviour gradient elasticity can also model chiral behaviour however this has received much less attention than its cosserat counterpart this paper shows how in the case of isotropic linear gradient elasticity a single additional parameter can be introduced that describes chiral behaviour this additional parameter directly linked to three dimensional deformation can be either negative or positive with its sign indicating a discrimination between the two opposite directions of torsion two simple examples are presented to show the practical effects of the chiral behaviour

robust fuzzy controller design for nonlinear multiple time delay systems by dithers this study presents a robustness design of fuzzy control for nonlinear systems with multiple time delays first the neural network nn model is employed to approximate the nonlinear multiple time delay nmtd plant then a linear differential inclusion ldi state space representation is established for the dynamics of the nn model according to the ldi state space representation a robustness design of fuzzy control is proposed to overcome the effect of modeling errors between the nmtd plant and the nn model if the designed fuzzy controller cannot stabilize the nmtd system a dither as an auxiliary of the fuzzy controller is simultaneously introduced to stabilize the nmtd system based on the relaxed method the nmtd system can be stabilized by regulating appropriately the parameters of dither if the frequency of dither is high enough the trajectory of the dithered system and that of its corresponding mathematical model the relaxed system can be made as close as desired this fact enables us to get a rigorous prediction of stability of the dithered system by establishing the stability of the relaxed system

some generalized functions for the size distribution of income many distributions have been used as descriptive models for the size distribution of income this paper considers two generalized beta distributions which include many of these models as special or limiting cases these generalized distributions have not been used as models for the distribution of income and provide a unified method of comparing many models previously considered

stochastic resonance in the mutual information between input and output spike trains of noisy central neurons abstract within the framework of information theory we investigate the phenomenon of stochastic resonance in a realistic stochastic model of central neurons the essential point is that for central neurons the input is not a continuous signal but a train of spikes which has in general a non periodic distribution the behavior of an individual neuron is modeled by a combination of an ornstein uhlenbeck diffusion process and a jump process corresponding to a discrete input spike train the input spike train is assumed to be given by a poisson distribution if the parameters are such that the input spike train provokes a membrane potential that hovers under the threshold the noise given by the diffusive part of the neuron model induces a maximum in the mutual information between the input and output spike trains thus the stochastic resonance effect results in a strategy for efficient information transmission of subthreshold signals

boundary element analysis of mode i and mixed mode i and ii crack problems of 2 d gradient elasticity abstract a boundary element method is developed for fracture analysis of gradient elastic planar solids under static loading a simple version of mindlin s general theory of gradient elastic materials is employed and the two required boundary integral equations one for the displacement vector and the other for its normal derivative are presented use is made of the fundamental solution of the problem and this leads to a formulation that requires only a boundary discretization two representative numerical examples are presented to illustrate the method demonstrate its accuracy and efficiency and assess the gradient effect on the response the first deals with a mode i crack while the second with a mixed mode i ii crack for the second case the proposed method is used in conjunction with the method of subregions the method is employed with regular and special near the crack tip boundary elements the gradient effect consists of modifying both the displacement and the stress field around the crack tip and resulting in a response which is more physically acceptable than the one coming from the classical theory of elasticity

multiple signal extraction by multiple interference attenuation in the presence of random noise in seismic array data a vector of digital filters is derived for the multichannel processing of the signals acquired by an array of sensors with the objective of extracting multiple desired signals by the attenuation of multiple interferences and random noise the signals and interferences are assumed to have arbitrary waveforms with no a priori knowledge of these waveforms the time duration of the recorded array data is assumed to be long enough to incorporate all time delayed propagated waveforms at the sensors of the array the derivation is for the general case of an arbitrary array geometric configuration and is not confined to the special case of a linear array of equispaced sensors the rationale adopted in the derivation of the filters is to give first priority at each discrete frequency to passing the signals a second priority to canceling the interferences and a third priority to attenuating the random noise this rationale well suits the case of seismic data that are dominantly corrupted by strong interferences rather than random noise solving a constrained minimization problem derives the vector of array filters the computation of this vector requires the application of a powerful matrix decomposition technique for the detection of any redundant and or inconsistent constraints at each discrete frequency the simulation results demonstrate the extraction ability of the derived filters in both the multiple input single output and the multiple input multiple output processing schemes

stochastic resonance in continuous and spiking neuron models with levy noise levy noise can help neurons detect faint or subthreshold signals levy noise extends standard brownian noise to many types of impulsive jump noise processes found in real and model neurons as well as in models of finance and other random phenomena two new theorems and the ito calculus show that white levy noise will benefit subthreshold neuronal signal detection if the noise process s scaled drift velocity falls inside an interval that depends on the threshold values these results generalize earlier forbidden interval theorems of neuronal stochastic resonance sr or noise injection benefits global and local lipschitz conditions imply that additive white levy noise can increase the mutual information or bit count of several feedback neuron models that obey a general stochastic differential equation sde simulation results show that the same noise benefits still occur for some infinite variance stable levy noise processes even though the theorems themselves apply only to finite variance levy noise the appendix proves the two ito theoretic lemmas that underlie the new levy noise benefit theorems

the solution of elastostatic and dynamic problems using the boundary element method based on spherical hankel element framework summary in this paper new spherical hankel shape functions are utilized to reformulate boundary element method for two dimensional 2d elastostatic and elastodynamic problems to this end the dual reciprocity dr boundary element method bem is reconsidered by employing new spherical hankel shape functions to approximate the state variables displacements and tractions of navier s differential equation using enrichment of a class of radial basis functions rbfs called spherical hankel rbfs hereafter the interpolation functions of a hankel boundary element framework has been derived for this purpose polynomial terms are added to the functional expansion that only uses spherical hankel rbf in the approximation in addition to polynomial function fields the participation of spherical bessel function fields has also increased robustness and efficiency in the interpolation it is very interesting that there is no runge phenomenon in equispaced hankel macroelements unlike equispaced classic lagrange ones several numerical examples are provided to demonstrate the effectiveness robustness and accuracy of the proposed hankel shape functions and in comparison with the classic lagrange ones they show much more accurate and stable results

gradient elasticity and nonstandard boundary conditions abstract gradient elasticity for a second gradient model is addressed within a suitable thermodynamic framework apt to account for nonlocality the pertinent thermodynamic restrictions upon the gradient constitutive equations are derived which are shown to include besides the field differential stress strain laws a set of nonstandard boundary conditions consistently with the latter thermodynamic requirements a surface layer with membrane stresses is envisioned in the strained body which together with the above nonstandard boundary conditions make the body constitutively insulated i e no long distance energy flows out of the boundary surface due to nonlocality the total strain energy is shown to include a bulk and surface strain energy a minimum total potential energy principle is provided for the related structural boundary value problem the toupin mindlin polar type strain gradient material model is also addressed and compared with the above one their substantial differences are pointed out particularly for what regards the constitutive equations and the boundary conditions accompanying the solving displacement equilibrium equations a gradient one dimensional bar sample in tension is considered for a few applications of the proposed theory

input output finite time mean square stabilization of nonlinear semi markovian jump systems this paper is concerned with the input output finite time mean square stabilization problem for a class of nonlinear semi markovian jump systems smjss with time varying delay both time varying factors of transition rates and states delay are considered to be bounded our main purpose is to derive some parameter dependent sufficient criteria by designing a state feedback controller to guarantee the input output finite time mean square stabilization for the underlying systems where the nonlinear term satisfies the conic sector constraint then the stabilization conditions are obtained by employing a novel lyapunov krasovskii functional differential form gronwall s inequality and an extra slack variable which is composed of the time varying transition rates finally a simulation example is provided to illustrate the effectiveness and merits of the proposed method

the linear quadratic optimal control problem with delays in state and control variables a state space approach this paper generalizes the results of vinter and kwong to a control operator with a more general delay structure than the one in a ichikawa and to delay systems with both finite and infinite memories the linear quadratic optimal control problem over both finite and infinite time horizons is treated several forms of associated abstract riccati differential and algebraic equations are presented the properties of the kernel of the solution are studied and a coupled set of matrix ordinary and partial differential equations is obtained

maximum likelihood localization of multiple sources by alternating projection an algorithm referred to as apm for computing the maximum likelihood estimator of the locations of simple sources in passive sensor arrays is presented the algorithm is equally applicable to the case of coherent signals and to the case of a single snapshot the algorithm is iterative the maximum of the likelihood function is computed by successive approximations the convergence of the algorithm to the global maximum is demonstrated for a variety of scenarios the key to this global convergence is the initialization scheme

a new formulation and 0 implementation of dynamically consistent gradient elasticity in his article a special form of gradient elasticity is presented that can be used to describe wave dispersion this new format of gradient elasticity is an appropriate dynamic extension of the earlier static counterpart of the gradient elasticity theory advocated in the early 1990s by aifantis and co workers in order to capture dispersion of propagating waves both higher order inertia and higher order stiffness contributions are included a fact which implies and is denoted as dynamic consistency the two higher order terms are accompanied by two associated length scales to facilitate finite element implementations the model is rewritten such that 0 continuity of the interpolation is sufficient an auxiliary displacement field is introduced which allows the original fourth order equations to be split into two coupled sets of second order equations positive definiteness of the kinetic energy requires that the inertia length scale is larger than the stiffness length scale the governing equations boundary conditions and the discretized system of equations are presented finally dispersive wave propagation in a one dimensional bar is considered in a numerical example copyright 2007 john wiley sons ltd

muntz legendre spectral collocation method for solving delay fractional optimal control problems abstract in this paper a numerical method is applied for solving delay fractional optimal control problems dfocps the fractional derivative is described in the caputo sense since the fractional derivative of muntz polynomials can be expressed in terms of the same polynomials those polynomials can accurately represent properties of fractional calculus in some situations such as in the frequency response based analysis of control systems containing a time delay it is necessary to substitute exponential function with an approximation in the form of a rational function the most common approximation is the pade approximation at the first step using pade approximation the delay problem is transformed to a non delay problem next using the operational matrix of the fractional derivative of muntz polynomials and pseudospectral method fractional optimal control problem focp is reduced to a nonlinear programming problem some numerical examples are given to illustrate the effectiveness of the proposed scheme

proceedings of the second international tampere conference in statistics keynote addresses anderson t w multivariate linear relations box g e p with r d meyer some aspects of statistical design in quality improvement hannan e j the statistical theory of linear systems rao c r estimation in linear models with mixed effects a unified theory invited papers atkinson a c robust regression and unmasking transformations baksalary j k algebraic characterizations and statistical implications ofthe commutativity of orthogonal projectors conradsen k with b k nielsen textural features useful in classification of digital images kariya t mtv model and its application to prediction of stock prices khatri c g quadratic forms and null robustness for elliptical distributions mustonen s editorial approach in statistical computing perlman m d with t w anderson consistency of invariant tests for the multivariate analysis of variance pratt j w dividing the indivisible using simple symmetry to partition variance explained pukelsheim f majorization orderings for linear regression designs pukkila t with a kalijnen on the order determination of time series models rissanen j complexity and information in contingency tables soctt a j generalized linear models with survey data sinha b k with r das robust optimum invariant unbiased tests for variance components speed t p generalized variance component models styan g p h with r e hartwig partially ordered idempotent matrices contributed papers anderson a j b fortran8x as a language forstatisticalcomputation baldessari b on regression analysisundertheintrinsicinference model for stratified dependent normal random variables brannas k control in the duration model framework danial e j and katti s k the asymptotic variances of the necessary and sufficient conditions for the infinite divisibility of discrete distributions through multivariate analysis danial e j and katti s k computing the maximum likelihood estimates of the hyper poisson parameters interactively through apl computer language diebold f x and nerlove m factor structure in a multivariate arch model of exchange ratefluctuations farebrother r w simultaneous confidence intervals when the regressor matrix is unbalanced feuerverger a some fourier procedures for time domain analysis of parametric and semi parametric time series models gelfand a e estimation of a restricted variance ratio de gooijer j g and heuts r m j higher order moments of bilinear time series processes with symmetrically distributed errors ignatov z g and kaishev v k on the computation of distributions of serial correlation coefficients through b splines jajuga k elliptically symmetric distributions and their application to classification and regression kollo t asymptotic distributions of functions of means and covariances konakov v d nonparametric density estimation l approach korhonen p and narula s c on subjectivity in statistics koukouvinos c and kounias s optimal designs in linear models and hadamard matrices latour d puntanen s and styan g p h equalities and inequalities for the canonical correlations associated with some partitioned generalized inverses of a covariance matrix liski e p identifying influential data in a growth curves model manly b f j and mcalevey l a randomization alternative to the bonferroni inequality with multiple f tests mejza s experiments in incomplete split plot designs merikoski j k underestimating the largest eigenvalue of a covariance matrix militkt j kvsmr k and cap j comparison of some influence measures in nonlinear regression nordstrom k and von rosen d algebra of subspaces with applications to problems in statistics ososkov g a robust regression for the heavy contaminated sample pynnonen s selection of variables in nonlinear discriminant analysis by information criteria salem a m and wahab s a on the determination of the amplitude of quasi stationary phenomena schaffrin b less sensitive tests by introducing stochastic linear hypotheses schall r and dunne t t on outliers and influence in the general multivariate normal linear model trenkler g stahlecker p schipp b and hering f iterative improvements of a partial minimax estimator in regression analysis wernecke k d kalb g and stdrzebecker e on classification strategies in medical functional diagnostics

a novel approach to output feedback control of fuzzy stochastic systems this paper investigates the problem of hankel norm output feedback controller design for a class of t s fuzzy stochastic systems the full order output feedback controller design technique with the hankel norm performance is proposed by the fuzzy basis dependent lyapunov function approach and the conversion on the hankel norm controller parameters sufficient conditions are established to design the controllers such that the resulting closed loop system is stochastically stable and satisfies a prescribed performance the desired output feedback controller can be obtained by solving a convex optimization problem which can be efficiently solved by standard numerical algorithms finally a henon map system is used to illustrate the effectiveness of the proposed techniques

error bars for sonic slowness measurements semblance provides a quality indicator for beam former array processing methods such as slowness time coherence stc and dispersive stc dstc semblance does not indicate the slowness variance because the array design the processing time bandwidth parameters and the signal spectral content are not taken into account for the classical case of a single propagating wave with added gaussian noise semblance is distributed according to the noncentral beta distribution this distribution is parameterized by the number of receivers m the processing time bandwidth product bt and signal to noise ratio given m and bt the measured semblance can be inverted to give a high quality estimate of the signal to noise ratio the cramer rao lower bounds on slowness variance for the classical case of signals in added gaussian noise depend on the array dimensions the signal power spectrum and the signal to noise ratio estimates of the cramer rao bounds can be calculated from the estimated signal to noise ratio an

robust stochastic resonance for simple threshold neurons simulation and theoretical results show that memoryless threshold neurons benefit from small amounts of almost all types of additive noise and so produce the stochastic resonance or sr effect input output mutual information measures the performance of such threshold systems that use subthreshold signals the sr result holds for all possible noise probability density functions with finite variance the only constraint is that the noise mean must fall outside a forbidden threshold related interval that the user can control a new theorem shows that this condition is also necessary a corollary and simulations show that the sr effect occurs for right sided beta and weibull noise as well these sr results further hold for the entire uncountably infinite class of alpha stable probability density functions alpha stable noise densities have infinite variance and infinite higher order moments and often model impulsive noise environments the stable noise densities include the special case of symmetric bell curve densities with thick tails such as the cauchy probability density the sr result for alpha stable noise densities shows that the sr effect in threshold and thresholdlike systems is robust against occasional or even frequent violent fluctuations in noise regression analysis reveals both an exponential relationship for the optimal noise dispersion as a function of the alpha bell curve tail thickness and an approximate linear relationship for the sr maximal mutual information as a function of the alpha bell curve tail thickness

an optimization based approach to sampled data control of networked control systems with multiple delays a networked control system ncs is a control system in which plants sensors controllers and actuators are connected through communication networks in this paper the optimal sampled data control problem of linear systems with multiple time delays which is one of the fundamental problems in ncss is considered where multiple time delays and the sampling period are uncertain first the problem is transformed into the optimal control problem of discrete time uncertain linear systems where the intersample behavior is considered in the cost function next under a certain assumption the obtained problem is further transformed into a convex quadratic programming problem finally a numerical simulation is presented

modelling of localisation and scale effect in thick walled cylinders with gradient elastoplasticity we model the progressive localisation of deformation which causes failure around thick walled cylinders under external radial pressure the study is based on a second gradient elastoplastic model developed to regularise the ill posedness caused by material strain softening behaviour the stress increment is related to both the strain increment and its laplacian the gradient terms introduce an internal length scale to the material allowing robust modelling of its post peak behaviour the numerical implementation is based on a c 1 finite element displacement formulation mesh insensitivity in terms of load displacement and failure mechanism is demonstrated the internal length in the constitutive equations enables modelling of the scale effect in thick walled cylinders according to which the load required to induce failure appears to be much larger for small holes than for large holes

theoretical analysis of a class of mixed c0 continuity formulations for general dipolar gradient elasticity boundary value problems abstract mixed weak formulations with two or three main tensor variables are stated and theoretically analyzed for general multi dimensional dipolar gradient elasticity biharmonic boundary value problems the general structure of constitutive equations is considered with and without coupling terms the mixed formulations are based on various generalizations of the so called ciarlet raviart technique hence c 0 continuity conforming basis functions may be employed in the finite element approximations or even c 1 basis functions for the cauchy stress variable all the complicated boundary conditions especially in the multi dimensional scenario are naturally considered the main variables are the displacement vector the double stress tensor and the cauchy stress tensor the latter variable may be eliminated in some of the formulations depending on the structure of the constitutive equations the standard continuous and discrete babuska brezzi inf sup conditions for the constraint equation as well as solution uniqueness for both the continuous statements and discrete approximations are established in all cases for the purpose of completeness two one dimensional mixed formulations are also analyzed the respective constitutive equations possess general structure with coupling terms for the 1 d formulations all the inf sup conditions are satisfied for both the continuous and discrete statements assuming proper selection of the polynomial spaces for the main variables hence the general babuska brezzi theory results in quasi optimality and stability for multi dimensional problems the difficulty of deducing the inf sup condition on the kernel is examined certain aspects of methodologies employed to theoretically by pass this problem are also discussed

large strain finite element analysis of a local second gradient model application to localization summary a large strainnite element formulation based on a local second gradient plasticity model is presented the corresponding constitutive equations were developed as a direct extension of microstructured siam j appl math 1973 25 3 556 575 arch rational mech anal 1964 16 51 78 or micromorphic in mechanics of generalized continua iutam symposium kroner ed springer berlin 1968 18 35 j math mech 1966 15 6 909 924 continua in which a mathematical constraint between the micro kinematics description and the usual macrodeformation gradienteld has been introduced this constraint is enforced in a weak sense by the use of lagrange multipliers in order to avoid diculties with the c 1 continuity for thenite element method correspondingnite elements are then constructed involving the lagrange multiplierseld a geometrically non linear 2 dnite element code is developed within a framework of an incremental method for every step a full newton raphson involving a numerical consistent tangent stiness operator for the complete model i e the second gradient terms as well as the classical ones is done and some numerical tests allow to validate the method and to discuss the inuence of the geometrical non linearity copyright 2002 john wiley sons ltd

a method for creating a class of triangular c1 finite elements finite elements providing a c1 continuous interpolation are useful in the numerical solution of problems where the underlying partial differential equation is of fourth order such as beam and plate bending and deformation of strain gradient dependent materials although a few c1 elements have been presented in the literature their development has largely been heuristic rather than the result of a rational design to a predetermined set of desirable element properties therefore a general procedure for developing c1 elements with particular desired properties is still lacking this paper presents a methodology by which c1 elements such as the tuba 3 element proposed by argyris et al can be constructed in this method which to the best of our knowledge is the first one of its kind a class of finite elements is first constructed by requiring a polynomial interpolation and prescribing the geometry the location of the nodes and the possible types of nodal dofs a set of necessary conditions is then imposed to obtain appropriate interpolations generic procedures are presented which determine whether a given potential member of the element class meets the necessary conditions the behaviour of the resulting elements is checked numerically using a benchmark problem in strain gradient elasticity

information transmission in parallel threshold arrays suprathreshold stochastic resonance the information transmitted through a parallel summing array of noisy threshold elements with a common threshold is considered in particular using theoretical and numerical analysis a recently reported n g stocks phys rev lett 84 2310 2000 form of stochastic resonance termed suprathreshold stochastic resonance ssr is studied in detail ssr is observed to occur in arrays with two or more elements and unlike stochastic resonance sr in a single element gives rise to noise induced information gains that occur independent of the setting of the threshold or the size of the signal the transmitted information is maximized when all thresholds are set to coincide with the signal mean in this situation and for large arrays the noise can enhance performance up to approximately half the theoretical noiseless channel capacity the theory is tested against digital simulation

the robust covariation based music roc music algorithm for bearing estimation in impulsive noise environments this paper presents a new subspace based method for bearing estimation in the presence of impulsive noise which can be modeled as a complex symmetric alpha stable s spl alpha s process we define the covariation matrix of the array sensor outputs and show that eigendecomposition based methods such as the music algorithm can be applied to the sample covariation matrix to extract the bearing information from the measurements a consistent estimator for the marginals of the covariation matrix is presented and its asymptotic performance is studied the improved performance of the proposed source localization method in the presence of a wide range of impulsive noise environments is demonstrated via monte carlo experiments

optimal controller for uncertain stochastic polynomial systems with deterministic disturbances this article presents the optimal quadratic gaussian controller for uncertain stochastic polynomial systems with unknown coefficients and matched deterministic disturbances over linear observations and a quadratic criterion the optimal closed form controller equations are obtained through the separation principle whose applicability to the considered problem is substantiated as intermediate results this article gives closed form solutions of the optimal regulator controller and identifier problems for stochastic polynomial systems with linear control input and a quadratic criterion the original problem for uncertain stochastic polynomial systems with matched deterministic disturbances is solved using the integral sliding mode algorithm performance of the obtained optimal controller is verified in the illustrative example against the conventional quadratic gaussian controller that is optimal for stochastic polynomial systems with known parameters and without deterministic disturbances simulation gr

finite element formulations of strain gradient theory for microstructures and the c0 1 patch test based on finite element formulations for the strain gradient theory of microstructures a convergence criterion for the c0 1 patch test is introduced and a new approach to devise strain gradient finite elements that can pass the c0 1 patch test is proposed the displacement functions of several plane triangular elements which satisfy the c0 continuity and weak c1 continuity conditions are evaluated by the c0 1 patch test the difference between the proposed c0 1 patch test and the c0 constant stress and c1 constant curvature patch tests is elucidated an 18 dof plane strain gradient triangular element rct9 rt9 which passes the c0 1 patch test and has no spurious zero energy modes is proposed numerical examples are employed to examine the performance of the proposed element by carrying out the c0 1 patch test and eigenvalue test the proposed element is found to be without spurious zero energy modes and it possesses higher accuracy compared with other strain gradient elements copyright 2004 john wiley sons ltd

noise can speed convergence in markov chains a new theorem shows that noise can speed convergence to equilibrium in discrete finite state markov chains the noise applies to the state density and helps the markov chain explore improbable regions of the state space the theorem ensures that a stochastic resonance noise benefit exists for states that obey a vector norm inequality such noise leads to faster convergence because the noise reduces the norm components a corollary shows that a noise benefit still occurs if the system states obey an alternate norm inequality this leads to a noise benefit algorithm that requires knowledge of the steady state an alternative blind algorithm uses only past state information to achieve a weaker noise benefit simulations illustrate the predicted noise benefits in three well known markov models the first model is a two parameter ehrenfest diffusion model that shows how noise benefits can occur in the class of birth death processes the second model is a wright fisher model of genotype drift in population genetics the third model is a chemical reaction network of zeolite crystallization a fourth simulation shows a convergence rate increase of 64 for states that satisfy the theorem and an increase of 53 for states that satisfy the corollary a final simulation shows that even suboptimal noise can speed convergence if the noise applies over successive time cycles noise benefits tend to be sharpest in markov models that do not converge quickly and that do not have strong absorbing states

a three dimensional c1 finite element for gradient elasticity in gradient elasticity strain gradient terms appear in the expression of virtual work leading to the need for c1 continuous interpolation in finite element discretizations of the displacement field only employing such interpolation is generally avoided in favour of the alternative methods that interpolate other quantities as well as displacement due to the scarcity of c1 finite elements and their perceived computational cost in this context the lack of three dimensional c1 elements is of particular concern in this paper we present a new c1 hexahedral element which to the best of our knowledge is the first three dimensional c1 element ever constructed it is shown to pass the single element and patch tests and to give excellent rates of convergence in benchmark boundary value problems of gradient elasticity it is further shown that c1 elements are not necessarily more computationally expensive than alternative approaches and it is argued that they may be more efficient in providing good quality solutions copyright 2008 john wiley sons ltd

an advanced boundary element method for solving 2d and 3d static problems in mindlin s strain gradient theory of elasticity an advanced boundary element method bem for solving two 2d and three dimensional 3d problems in materials with microstructural effects is presented the analysis is performed in the context of mindlin s form ii gradient elastic theory the fundamental solution of the equilibrium partial differential equation is explicitly derived the integral representation of the problem consisting of two boundary integral equations one for displacements and the other for its normal derivative is developed the global boundary of the analyzed domain is discretized into quadratic line and quadrilateral elements for 2d and 3d problems respectively representative 2d and 3d numerical examples are presented to illustrate the method demonstrate its accuracy and efficiency and assess the gradient effect on the response the importance of satisfying the correct boundary conditions in gradient elastic problems is illustrated with the solution of simple 2d problems copyright 2010 john wiley sons ltd

relation between optimal nonlinearity and non gaussian noise enhancing a weak signal in a nonlinear system in the study of stochastic resonance it is often mentioned that nonlinearity can enhance a weak signal embedded in noise in order to give a systematic proof of the signal enhancement in nonlinear systems we derive an optimal nonlinearity that maximizes a signal to noise ratio snr the obtained optimal nonlinearity yields the maximum unbiased signal estimation performance which is known in the context of information theory it is found that a linear system is optimal for a gaussian noise but for a non gaussian noise there exist nonlinear systems that can achieve an snr higher than that obtained from linear systems this analysis refers to a system subjected to an additive non gaussian noise with a small signal input

a boundary element method for solving 2 d and 3 d static gradient elastic problems part ii numerical implementation the boundary element formulation for the static analysis of two dimensional 2 d and three dimensional 3 d solids and structures characterized by a gradient elastic material behavior developed in the first part of this work is treated numerically in this second part for the creation of a highly accurate and efficient boundary element solution tool the discretization of the body is restricted only to its boundary and is accomplished by the use of quadratic isoparametric three noded line and eight noded quadrilateral boundary elements for the 2 d and 3 d cases respectively advanced algorithms are presented for the accurate and efficient numerical computation of the singular integrals involved numerical examples involving a cylindrical bar in tension and a cylinder and a sphere in radial deformation are solved by the proposed boundary element method and the results are found in excellent agreement with the derived by the authors analytical solutions the bar and sphere problems are solved in a 3 d context while the cylinder problem is solved in a 2 d context plane strain both the exterior and interior versions of the cylinder and sphere problems are considered

isoparametric hermite elements isoparametric hermite elements are created using bogner fox schmit rectangles on a reference domain and mapping these numerically onto the computational domain the difficulties involved in devising explicit c1 shape functions for isoparametric elements are thus avoided and the resulting elements have all the benefits of full c1 continuity the simplicity of the bogner fox schmit element and the geometrical flexibility expected from higher order isoparametric elements the numerical mapping consists in the finite element solution of a linear boundary value problem which is inexpensive and is carried out as a preprocessing operation the required derivatives of the mapping then being supplied to the main analysis as data some care is required in defining the differential boundary conditions and guidance on this is provided examples are given showing the success of the mapping procedure and the use of the resulting elements in the solution of some boundary value problems the numerical results confirm a convergence analysis provided for the new isoparametric hermite element

aperiodic stochastic resonance stochastic resonance sr is a phenomenon wherein the response of a nonlinear system to a weak periodic input signal is optimized by the presence of a particular level of noise recently we presented a method and theory for characterizing sr type behavior in excitable systems with aperiodic i e broadband input signals phys rev e 52 r3321 1995 we coined the term aperiodic stochastic resonance asr to describe this general type of behavior in that earlier study we demonstrated asr in the fitzhugh nagumo neuronal model here we demonstrate asr in three additional systems a bistable well system an integrate and fire neuronal model and the hodgkin huxley hh neuronal model we present computational and theoretical results for each system in the context of the hh model we develop a general theory for asr in excitable membranes this work clearly shows that sr type behavior is not limited to systems with periodic inputs thus in general noise can serve to enhance the response of a nonlinear system to a weak input signal regardless of whether the signal is periodic or aperiodic textcopyright 1996 the american physical society

noise enhanced hypothesis testing in the restricted bayesian framework performance of some suboptimal detectors can be enhanced by adding independent noise to their observations in this paper the effects of additive noise are investigated according to the restricted bayes criterion which provides a generalization of the bayes and minimax criteria based on a generic m ary composite hypothesis testing formulation the optimal probability distribution of additive noise is investigated also sufficient conditions under which the performance of a detector can or cannot be improved via additive noise are derived in addition simple hypothesis testing problems are studied in more detail and additional improvability conditions that are specific to simple hypotheses are obtained furthermore the optimal probability distribution of the additive noise is shown to include at most m mass points in a simple m ary hypothesis testing problem under certain conditions then global optimization analytical and convex relaxation approaches are considered to obtain the optimal noise distribution finally detection examples are presented to investigate the theoretical results

theory of the stochastic resonance effect in signal detection part ii variable detectors in part i of this paper ldquotheory of the stochastic resonance effect in signal detection part i fixed detectors rdquo ieee transactions on signal processing vol 55 no 7 pt 1 pp 3172 3184 the mechanism of the stochastic resonance sr effect for a fixed detector has been examined this paper analyzes the stochastic resonance sr effect under the condition that the detector structure or its parameters can also be changed the detector optimization problem with sr noise under both neyman pearson and bayesian criteria is examined in the bayesian approach when the prior probabilities are unknown the minimax approach is adopted the form of the optimal noise pdf along with the corresponding detector as well as the maximum achievable performance are determined the developed theory is then applied to a general class of weak signal detection problems under the assumptions that the sample size n is large enough and the test statistics satisfies the conditions of central limit theorem the optimal sr noise is shown to be a constant vector and independent of the signal strength for both neyman pearson and bayesian criteria illustrative examples are presented where performance comparisons are made between the original detector and the optimal sr noise modified detector for different types of sr noise

finite elements for elasticity with microstructure and gradient elasticity we present a general finite element discretisation of mindlin s elasticity with microstructure a total of twelve isoparametric elements are developed and presented six for plane strain conditions and six for the general case of three dimensional deformation all elements interpolate both the displacement and microdeformation fields the minimum order of integration is determined for each element and they are all shown to pass the single element test and the patch test numerical results for the benchmark problem of one dimensional deformation show good convergence to the closed form solution the behaviour of all elements is also examined at the limiting case of vanishing relative deformation where elasticity with microstructure degenerates to gradient elasticity an appropriate parameter selection that enforces this degeneration in an approximate manner is presented and numerical results are shown to provide good approximation to the respective displacements and strains of a gradient elastic solid

a radar application of a modified cramer rao bound parameter estimation in non gaussian clutter in this paper we derive a lower bound on the error covariance matrix for any unbiased estimator of the parameters of a signal composed of a mixture of spherically invariant random processes sirps the proposed approach represents a special case of the global cramer rao bound for hybrid random and deterministic parameters estimation and it is particularly useful when the data conditioned on a vector of unwanted random parameters nuisance parameters with a priori known probability density function can be modeled as a gaussian vector the case of signal composed of a mixture of k distributed clutter gaussian clutter and thermal noise belongs to this set and it is regarded as a realistic radar scenario in the radar problem considered here this bound can be numerically computed in closed form whereas the computation of the true marginal cramer rao bound turns out to be infeasible the performance of some practical estimators are compared with it for two study cases