extended dissipative analysis for neural networks with time varying delays in this brief an extended dissipativity analysis was conducted for a neural network with time varying delays the concept of the extended dissipativity can be used to solve for the h l2 l passive and dissipative performance by adjusting the weighting matrices in a new performance index in addition the activation function dividing method is modified by introducing a tuning parameter examples are provided to show the effectiveness and less conservatism of the proposed method

the mixed problem in lipschitz domains with general decompositions of the boundary this paper continues the study of the mixed problem for the laplacian we consider a bounded lipschitz domain rn n 2 with boundary that is decomposed as d n d and n disjoint we let denote the boundary of d relative to and impose conditions on the dimension and shape of and the sets n and d under these geometric criteria we show that there exists p0 1 depending on the domain such that for p in the interval 1 p0 the mixed problem with neumann data in the space lp n and dirichlet data in the sobolev space w 1 p d has a unique solution with the non tangential maximal function of the gradient of the solution in lp we also obtain results for p 1 when the dirichlet and neumann data comes from hardy spaces and a result when the boundary data comes from weighted sobolev spaces

asymptotic stabilization of passive systems without damping injection a sampled integral technique passivity in physical systems is a restatement of energy balancing and therefore is a ubiquitous property in engineering applications under some weak conditions the unique equilibrium state of passive systems is stable however to ensure asymptotic stability strict output passivity and a detectability property are required although strict output passivity may be enforced via a damping injection that feeds back the passive output this signal may be noisy or unmeasurable the paradigmatic example being velocity in mechanical systems in this paper a sampled integral stabilization sis technique for the asymptotic regulation of passive systems that requires only the knowledge of the time integral of the passive output i e position in mechanical systems is proposed as a generalization of the previous result it is shown that sis is applicable to cascade connections of passive systems measuring only the storage function of the second one several examples including a planar elbow manipulator and the rigid body dynamics are shown to satisfy the assumptions for the application of sis

the use of cornu spirals in drawing planar curves of controlled curvature abstract cornu spirals or clothoids have been used in highway design for many years in the past the spirals have been found manually by draftsmen the purpose of this paper is to show that it is practical to find these spirals with a micro computer the design curve will be made up of arcs of circles and segments of cornu spirals joined in such a way that the curvature is continuous throughout and takes its largest values on the arcs of circles thus the radii of the circles used will limit and control the curvature of the whole design curve

finite time stabilizability and instabilizability of delayed memristive neural networks with nonlinear discontinuous controller this paper is concerned about the finite time stabilizability and instabilizability for a class of delayed memristive neural networks dmnns through the design of a new nonlinear controller algebraic criteria based on m matrix are established for the finite time stabilizability of dmnns and the upper bound of the settling time for stabilization is estimated in addition finite time instabilizability algebraic criteria are also established by choosing different parameters of the same nonlinear controller the effectiveness and the superiority of the obtained results are supported by numerical simulations

greenʼs function for second order parabolic systems with neumann boundary condition abstract we study the neumann green s function for second order parabolic systems in divergence form with time dependent measurable coefficients in a cylindrical domain q where r n is an open connected set such that a multiplicative sobolev embedding inequality holds there such a domain includes for example a bounded sobolev extension domain a special lipschitz domain and an unbounded domain with compact lipschitz boundary we construct the neumann green s function in q under the assumption that weak solutions of the systems satisfy an interior holder continuity estimate we also establish global gaussian bounds for neumann green s function under an additional assumption that weak solutions with zero neumann data satisfy a local boundedness estimate in the scalar case such a local boundedness estimate is a consequence of de giorgi moser nash theory holds for equations with bounded measurable coefficients in sobolev extension domains while in the vectorial case one may need to impose further regularity assumptions on the coefficients of the system as well as on the domain to obtain such an estimate we present a unified approach valid for both the scalar and vectorial cases and discuss some applications of our results including the construction of neumann functions for second order elliptic systems with measurable coefficients in two dimensional domains

on global dissipativity of nonautonomous neural networks with multiple proportional delays this brief addresses the problem of global dissipativity analysis of nonautonomous neural networks with multiple proportional delays by using a novel constructive approach based on some comparison techniques for differential inequalities new explicit delay independent conditions are derived using m matrix theory to ensure the existence of generalized exponential attracting sets and the global dissipativity of the system the method presented in this brief is also utilized to derive a generalized exponential estimate for a class of halanay type inequalities with proportional delays finally three numerical examples are given to illustrate the effectiveness and improvement of the obtained results

degree independent sobolev extension on locally uniform domains abstract we consider the problem of constructing extensions l k p l k p r n where l k p is the sobolev space of functions with k derivatives in l p and r n is a domain in the case of lipschitz calderon gave a family of extension operators depending on k while stein later produced a single k independent operator for the more general class of locally uniform domains which includes examples with highly non rectifiable boundaries a k dependent family of operators was constructed by jones in this work we produce a k independent operator for all spaces l k p on a locally uniform domain

harmless delays in cohen grossberg neural networks without assuming monotonicity and differentiability of the activation functions and any symmetry of interconnections we establish some sufficient conditions for the globally asymptotic stability of a unique equilibrium for the cohen grossberg neural network with multiple delays lyapunov functionals and functions combined with the razumikhin technique are employed the criteria are all independent of the magnitudes of the delays and thus the delays under these conditions are harmless 2002 elsevier science b v all rights reserved msc 34d23 34k20 92b20

green s matrices of second order elliptic systems with measurable coefficients in two dimensional domains we study green s matrices for divergence form second order strongly elliptic systems with bounded measurable coefficients in two dimensional domains we establish existence uniqueness and pointwise estimates of green s matrices

stability analysis in lagrange sense for a non autonomous cohen grossberg neural network with mixed delays abstract the paper discusses the global exponential stability in the lagrange sense for a non autonomous cohen grossberg neural network cgnn with time varying and distributed delays the boundedness and global exponential attractivity of non autonomous cgnn with time varying and distributed delays are investigated by constructing appropriate lyapunov like functions moreover we provide verifiable criteria on the basis of considering three different types of activation function which include both bounded and unbounded activation functions these results can be applied to analyze monostable as well as multistable biology neural networks due to making no assumptions on the number of equilibria meanwhile the results obtained in this paper are more general and challenging than that of the existing references in the end an illustrative example is given to verify our results

event triggered generalized dissipativity filtering for neural networks with time varying delays this paper is concerned with event triggered generalized dissipativity filtering for a neural network nn with a time varying delay the signal transmission from the nn to its filter is completed through a communication channel it is assumed that the network measurement of the nn is sampled periodically an event triggered communication scheme is introduced to design a suitable filter such that precious communication resources can be saved significantly while certain filtering performance can be ensured on the one hand the event triggered communication scheme is devised to select only those sampled signals violating a certain threshold to be transmitted which directly leads to saving of precious communication resources on the other hand the filtering error system is modeled as a time delay system closely dependent on the parameters of the event triggered scheme based on this model a suitable filter is designed such that certain filtering performance can be ensured provided that a set of linear matrix inequalities are satisfied furthermore since a generalized dissipativity performance index is introduced several kinds of event triggered filtering issues such as h infty filtering passive filtering mixed h infty and passive filtering q s r dissipative filtering and mathcal l 2 mathcal l infty filtering are solved in a unified framework finally two examples are given to illustrate the effectiveness of the proposed method

on extended dissipativity of discrete time neural networks with time delay in this brief the problem of extended dissipativity analysis for discrete time neural networks with time varying delay is investigated the definition of extended dissipativity of discrete time neural networks is proposed which unifies several performance measures such as the h infty performance passivity l 2 l infty performance and dissipativity by introducing a triple summable term in lyapunov function the reciprocally convex approach is utilized to bound the forward difference of the triple summable term and then the extended dissipativity criterion for discrete time neural networks with time varying delay is established the derived condition guarantees not only the extended dissipativity but also the stability of the neural networks two numerical examples are given to demonstrate the reduced conservatism and effectiveness of the obtained results

an arc spline approximation to a clothoid the clothoid is a spiral used in highway and railway route design clothoids are transcendental functions and so have been approximated by polynomials by power series and continued fractions and by rational functions here the clothoid is approximated by an arc spline the chief advantage in doing so is that arc splines are very easy to lay out and to offset examples show that the approximation is of extremely high accuracy it is proved that if the arc spline has n arcs then the error in the approximation is of order o 1 n2

interpolation of two dimensional curves with euler spirals we propose an algorithm for the interpolation of two dimensional curves using euler spirals the method uses a lower order reconstruction to approximate solution derivatives at each sample point the computed tangents are then used to connect consecutive points with segments of euler spirals the resulting interpolation is g 1 in regions where the curve being interpolated is smooth the algorithm uses an adaptive stencil which allows it to construct an approximation free of oscillations near discontinuities in the function or its derivatives the approximation is based on geometrical shapes which makes it particularly suitable for two dimensional curves

further result on guaranteed h_ infty performance state estimation of delayed static neural networks this brief considers the guaranteed h infty performance state estimation problem of delayed static neural networks an arcak type state estimator which is more general than the widely adopted luenberger type one is chosen to tackle this issue a delay dependent criterion is derived under which the estimation error system is globally asymptotically stable with a prescribed h infty performance it is shown that the design of suitable gain matrices and the optimal performance index are accomplished by solving a convex optimization problem subject to two linear matrix inequalities compared with some previous results much better performance is achieved by our approach which is greatly benefited from introducing an additional gain matrix in the domain of activation function an example is finally given to demonstrate the advantage of the developed result

dissipativity based sliding mode control of switched stochastic systems this technical brief is concerned with dissipativity analysis and dissipativity based sliding mode control smc of continuous time switched stochastic systems firstly a sufficient condition is proposed to guarantee the mean square exponential stability and strict dissipativity for the switched stochastic system then an integral type sliding surface function is designed for establishing a sliding mode dynamics which can be formulated by a switched stochastic system with an external disturbance uncertainty dissipativity analysis and synthesis are both investigated for the sliding mode dynamics and consequently sufficient conditions are derived which pave the way for solving the dissipativity analysis and control problems moreover a smc law is synthesized to drive the system trajectories onto the predefined sliding surface in a finite time finally the efficiency of the theoretical findings is demonstrated by an illustrative example

a two point g1 hermite interpolating family of spirals a one parameter family of spirals that can match planar two point g 1 hermite data is presented these spirals can be used as an alternative to the biarc which is also a one parameter family of curves that can match two point g 1 hermite data some suggestions on choosing the free parameter of the family of spirals is given it is shown that there is a unique g 1 hermite interpolating spiral that passes through a given point in an allowable region three examples of the use of these spirals are given curve completion with spirals design with spirals and approximation of the clothoid by spirals

heat kernel for the elliptic system of linear elasticity with boundary conditions abstract we consider the elliptic system of linear elasticity with bounded measurable coefficients in a domain where the second korn inequality holds we construct heat kernel of the system subject to dirichlet neumann or mixed boundary condition under the assumption that weak solutions of the elliptic system are holder continuous in the interior moreover we show that if weak solutions of the mixed problem are holder continuous up to the boundary then the corresponding heat kernel has a gaussian bound in particular if the domain is a two dimensional lipschitz domain satisfying a corkscrew or non tangential accessibility condition on the set where we specify dirichlet boundary condition then we show that the heat kernel has a gaussian bound as an application we construct green s function for elliptic mixed problem in such a domain

asymptotic stability of cellular neural networks with multiple proportional delays proportional delay is a kind of unbounded time varying delay which is different from unbounded distributed delays in this paper asymptotic stability of the equilibrium point of cellular neural networks with multiple proportional delays is presented sufficient conditions for delay dependent global asymptotic stability and delay independent uniform asymptotic stability of the system are obtained by employing matrix theory and constructing lyapunov functional two examples are given to illustrate the effectiveness of the obtained results and less conservative than previously existing results

clothoid spline transition spirals highway and railway designers use clothoid splines planar g2 curves consisting of straight line segments circular arcs and clothoid segments as center lines in route location this paper considers the problem of finding a clothoid spline transition spiral which joins two given points and matches given curvatures and unit tangents at the two points conditions are given for the existence and uniqueness of the clothoid spline transition spirals and algorithms for finding them are outlined

existence and global asymptotic stability of positive periodic solution of delayed cohen grossberg neural networks abstract in this paper a class of periodic cohen grossberg neural networks with discrete and distributed time varying delays is considered by an extension of the lyapunov krasovskii functional method a novel criterion for the existence and uniqueness and global asymptotic stability of positive periodic solution is derived in terms of m matrix without any restriction on uniform positiveness of the amplification functions comparison and illustrative examples are given to illustrate the effectiveness of the obtained results

rational approximations for the fresnel integrals a class of simple rational polynomial approximations for the fresnel integrals is given with maximum errors from 1 7 x 10 3 down to 4 x 10 8 the domain 0 oo is not subdivided the format is particularly convenient for programmable hand calculators and microcomputer subroutines the best known algorithms for computer evaluation of the fresnel integrals 1 c x is x j exp ip t2 dt 0 are those of hastings 1 41 and of boersma 2 the former is of very limited precision the latter is relatively cumbersome and is subject to nonobvious underflow subtraction errors as is direct evaluation of the standard maclaurin and asymptotic series an extensive set of rational polynomial approximations has been given by cody 3 these are efficient for very high precision work but tedious for intermediate levels of precision because the domain is subdivided into five intervals our approach follows hastings but recasts the formulas into the polar form 2 c x 2ri x sinf1pr ajk x x2 i 3 s x 2 rim x cos 7t ajk x x2 where the rim and ajk functions are rational approximations of the form i m2 4 r 01 l c1xi e dix i o i 0 i k s ajk e a x e b x o i o the domain of x is positive real numbers from zero to infinity we consider error functions of the form 6 sr rim ro 7 sa 7tro ak ao where r0 and ao are exact values these functions represent orthogonal errors in the plane of the cornu spiral with the coefficient inserted in 7 to make the magnitudes received may 2 1983 revised january 9 1984 1980 mathematics subject classification primary 65d20 secondary 33a20 41a50 78a50

gaussian estimates for fundamental solutions of second order parabolic systems with time independent coefficients auscher mcintosh and tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on r n in particular in the case when n 2 they obtained gaussian upper bound estimates for the heat kernel without imposing further assumption on the coefficients we study the fundamental solutions of the systems of second order parabolic equations in the divergence form with bounded measurable time independent coefficients and extend their results to the systems of parabolic equations

exponential stability on stochastic neural networks with discrete interval and distributed delays this brief addresses the stability analysis problem for stochastic neural networks snns with discrete interval and distributed time varying delays the interval time varying delay is assumed to satisfy 0 d1 d t d2 and is described as d t d 1 h t with 0 h t d 2 d 1 based on the idea of partitioning the lower bound d 1 new delay dependent stability criteria are presented by constructing a novel lyapunov krasovskii functional which can guarantee the new stability conditions to be less conservative than those in the literature the obtained results are formulated in the form of linear matrix inequalities lmis numerical examples are provided to illustrate the effectiveness and less conservatism of the developed results

a comprehensive review of stability analysis of continuous time recurrent neural networks stability problems of continuous time recurrent neural networks have been extensively studied and many papers have been published in the literature the purpose of this paper is to provide a comprehensive review of the research on stability of continuous time recurrent neural networks including hopfield neural networks cohen grossberg neural networks and related models since time delay is inevitable in practice stability results of recurrent neural networks with different classes of time delays are reviewed in detail for the case of delay dependent stability the results on how to deal with the constant variable delay in recurrent neural networks are summarized the relationship among stability results in different forms such as algebraic inequality forms m matrix forms linear matrix inequality forms and lyapunov diagonal stability forms is discussed and compared some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed concluding remarks and future directions of stability analysis of recurrent neural networks are given

a note on finding clothoids the clothoid is a spiral that is used as transition curve in highway and railway route design although its defining formulas are transcendental functions recent work has shown that it can be used fairly easily on small computers a single nonlinear equation must be solved in each of four common arrangements of the clothoid the purpose of this work is to give starting intervals for which newton s root finding method applied to those equations is guaranteed to converge

global exponential stability of nonautonomous neural network models with continuous distributed delays for a family of non autonomous differential equations with distributed delays we give sufficient conditions for the global exponential stability of an equilibrium point this family includes most of the delayed models of neural networks of hopfield type with time varying coefficients and distributed delays for these models we establish sufficient conditions for their global exponential stability the existence and global exponential stability of a periodic solution is also addressed a comparison of results shows that these results are general news and add something new to some earlier publications

how delays affect neural dynamics and learning we investigate the effects of delays on the dynamics and in particular on the oscillatory properties of simple neural network models we extend previously known results regarding the effects of delays on stability and convergence properties we treat in detail the case of ring networks for which we derive simple conditions for oscillating behavior and several formulas to predict the regions of bifurcation the periods of the limit cycles and the phases of the different neurons these results in turn can readily be applied to more complex and more biologically motivated architectures such as layered networks in general the main result is that delays tend to increase the period of oscillations and broaden the spectrum of possible frequencies in a quantifiable way simulations show that the theoretically predicted values are in excellent agreement with the numerically observed behavior adaptable delays are then proposed as one additional mechanism through which neural systems could tailor their own dynamics accordingly we derive recurrent backpropagation learning formulas for the adjustment of delays and other parameters in networks with delayed interactions and discuss some possible applications

finite time stability of a class of non autonomous neural networks with heterogeneous proportional delays in this paper the problem of finite time stability analysis for a class of non autonomous neural networks with heterogeneous proportional delays is considered by introducing a novel constructive approach we derive new explicit conditions in terms of matrix inequalities ensuring that the state trajectories of the system do not exceed a certain threshold over a pre specified finite time interval as a result we also obtain conditions for the power rate global stability of the system numerical examples are given to demonstrate the effectiveness and less restrictiveness of the results obtained in this paper

new approaches on stability criteria for neural networks with interval time varying delays abstract this paper concerns the problem of delay dependent stability criteria for neural networks with interval time varying delays first by constructing a newly augmented lyapunov krasovskii functional and combining with a reciprocally convex combination technique less conservative stability criterion is established in terms of linear matrix inequalities lmis which will be introduced in theorem 1 second by taking different interval of integral terms of lyapunov krasovskii functional utilized in theorem 1 further improved stability criterion is proposed in theorem 2 third a novel approach which divides the bounding of activation function into two subinterval are proposed in theorem 3 to reduce the conservatism of stability criterion finally through two well known numerical examples used in other literature it will be shown the proposed stability criteria achieves the improvements over the existing ones and the effectiveness of the proposed idea

well posedness and regularity for the elasticity equation with mixed boundary conditions on polyhedral domains and domains with cracks we prove a regularity result for the anisotropic linear elasticity equation p u rm div left boldmath mathsf c cdot nabla u right f with mixed displacement and traction boundary conditions on a curved polyhedral domain omega subset mathbb r 3 in weighted sobolev spaces mathcal k m 1 a 1 omega for which the weight is given by the distance to the set of edges in particular we show that there is no loss of mathcal k m a regularity our curved polyhedral domains are allowed to have cracks we establish a well posedness result when there are no neighboring traction boundary conditions and a 0 that depends on p on the boundary conditions and on the domain our results extend to other strongly elliptic systems and higher dimensions

dynamical behavior of nonautonomous stochastic reaction diffusion neural network models this brief investigates nonautonomous stochastic reaction diffusion neural network models with s type distributed delays first the existence and uniqueness of mild solution are studied under the lipschitz condition without the linear growth condition due to the existence of a nonautonomous reaction diffusion term and the infinite dimensional wiener process the criteria for the well posedness of the models are established based on the evolution system theory then the s type distributed delay which is an infinite delay is handled by the truncation method and sufficient conditions for the global exponential stability are obtained by constructing a simple lyapunov krasovskii functional candidate finally neural network examples and an illustrative example are given to show the applications of the obtained results

corrigenda rational approximations for the fresnel integrals math comp 44 1985 no 170 459 461 mr0777277 86b 65017

on the g2 hermite interpolation problem with clothoids abstract the g 2 hermite interpolation problem with clothoid curves requires to find the interpolating clothoid that matches initial and final positions tangents and curvatures also known as g 2 hermite data in the paper we prove that this problem does not always admit solution with only one clothoid segment nor with two as some counterexamples show the general fitting scheme herein proposed requires three arcs determined via the solution of a nonlinear system of 8 equations in 10 unknowns we discuss how it is possible to recast this system to 2 equations and how to efficiently solve it by means of the newton method the choice of the clothoid is crucial because it exhibits the curvature which is linear with the arc length an important property in many applications ranging from path planning for autonomous vehicles road design manufacturing and graphics the algorithm is tested on a fine hypercube of all possible configurations of angles and curvatures it always converges and in the worst case it requires 5 standard newton iterations