asymptotic formulas for the eigenvalues of the timoshenko beam abstract asymptotic formulas are derived for the eigenvalues of a free ended timoshenko beam which has variable mass density and constant beam parameters otherwise these asymptotic formulas show how the eigenvalues and hence how the natural frequencies of such a beam depend on the material and geometric parameters which appear as coefficients in the timoshenko differential equations

the partition of unity method for the elastically supported beam abstract the partition of unity method pum is used to solve the timoshenko beam with elastic support some important features of this new method are addressed but the main concern is to overcome locking and to resolve boundary layer we prove that by a proper selection of the local basis functions the method is free of locking at the thin beam limit and exhibits no numerical boundary layer for strong elastic support optimal convergent rate is established in the energy norm and it is uniformly valid with respect to the thickness of the beam and toughness of the elastic support furthermore the computed shear stress is also convergent uniformly with optimal rate

rates of decay to non homogeneous timoshenko model with tip body abstract we consider the uniform stabilization of a hybrid elastic model consisting of a timoshenko beam and a tip load at the free end of the beam our main result proves that the semigroup e a t associated to this model is not exponentially stable moreover we prove that the semigroup decays polynomially to zero as t 1 2 when the damping mechanism is effective only on the boundary of the rotational angle the solution also decays polynomially as t 1 2 provided the wave speeds are equal otherwise it decays as t 1 4 for any initial data taken in d a

the pessimistic diagnosabilities of some general regular graphs the pessimistic diagnosis strategy is a classic strategy based on the pmc model a system is t t diagnosable if provided the number of faulty processors is bounded by t all faulty processors can be isolated within a set of size at most t with at most one fault free node mistaken as a faulty one the pessimistic diagnosability of a system g denoted by t p g is the maximal number of faulty processors so that the system g is t t diagnosable in this paper we study the pessimistic diagnosabilities of some general k regular k connected graphs g n the main result t p g n 2 k 2 g under some conditions is obtained where g is the maximum number of common neighbors between any two adjacent vertices in g n as applications of the main result every pessimistic diagnosability of many famous networks including some known results such as the alternating group networks an n the k ary n cubes q n k the star graphs s n the matching composition networks g g 1 g 2 m and the alternating group graphs ag n are obtained we study the pessimistic diagnosabilities of some general regular graphs under the pmc model the exact value of t p g n is obtained as applications the pessimistic diagnosability of an n q n k s n some mcn and ag n etc are obtained

an 0 n 2 5 fault identification algorithm for diagnosable systems consider a system composed of n independent processors each of which tests a subset of the others it is assumed that at most tp of these processors are permanently faulty and that the outcome of a test is reliable if and only if the processor which performed the test is fault free such a system is said to be tp diagnosable if given any complete collection of test results the set of faulty processors can be uniquely identified in this paper it is shown that tp diagnosable systems due to their robust interconnection structure possess heretofore unknown graph theoretic properties relative to vertex cover sets and maximum matchings an 0 n2 5 algorithm is given which exploits these properties to identify the set of faulty processors in a tp diagnosable system the algorithm is shown to be correct complete not based on any conjecture and superior to any other known fault identification algorithm for the general class of tp diagnosable systems

local convergence analysis of tensor methods for nonlinear equations tensor methods for nonlinear equations base each iteration upon a standard linear model augmented by a low rank quadratic term that is selected in such a way that the mode is efficient to form store and solve these methods have been shown to be very efficient and robust computationally especially on problems where the jacobian matrix at the root has a small rank deficiency this paper analyzes the local convergence properties of two versions of tensor methods on problems where the jacobian matrix at the root has a null space of rank one both methods augment the standard linear model by a rank one quadratic term we show under mild conditions that the sequence of iterates generated by the tensor method based upon an ideal tensor model converges locally and two step q superlinearly to the solution with q order 3 2 and that the sequence of iterates generated by the tensor method based upon a practial tensor model converges locally and three step q superlinearly to the solution with q order 3 2 in the same situation it is known that standard methods converge linearly with constant converging to 1 2 hence tensor methods have theoretical advantages over standard methods our analysis also confirms that tensor methods converge at least quadratically on problems where the jacobian matrix at the root is nonsingular

a newton method for systems of m equations in n variables the classical newton kantorovich method for solving systems of equations f x 0 uses the inverse of the jacobian of f at each iteration if the number of equations is dierent than the number of variables or if the jacobian cannot be assumed nonsingular a generalized inverse of the jacobian can be used in a newton method whose limit points are stationary points of kf x k 2 we study conditions for local convergence of this method prove quadratic convergence and implement an adaptive version this iterative method allowing a controlled increase of the ranks of the 2 inverses used in the iterations

tensor methods for nonlinear equations a new class of methods for solving systems of nonlinear equations called tensor methods is introduced tensor methods are general purpose methods intended especially for problems where the jacobian matrix at the solution is singular or ill conditioned they base each iteration on a quadratic model of the nonlinear function the standard linear model augmented by a simple second order term the second order term is selected so that the model interpolates function values from several previous iterations as well as the current function value and jacobian the tensor method requires no more function and derivative information per iteration and hardly more storage or arithmetic per iteration than a standard method based on newton s method in extensive computational tests a tensor algorithm is significantly more efficient than a similar algorithm based on the standard linear model both on standard nonsingular test problems and on problems where the jacobian at the solution is singular

an accelerated newton method for equations with semismooth jacobians and nonlinear complementarity problems we discuss local convergence of newton s method to a singular solution x of the nonlinear equations f x 0 for f mathbb r n rightarrow mathbb r n it is shown that an existing proof of griewank concerning linear convergence to a singular solution x from a starlike domain around x for f twice lipschitz continuously differentiable and x satisfying a particular regularity condition can be adapted to the case in which f is only strongly semismooth at the solution further newton s method can be accelerated to produce fast linear convergence to a singular solution by overrelaxing every second newton step these results are applied to a nonlinear equations reformulation of the nonlinear complementarity problem ncp whose derivative is strongly semismooth when the function f arising in the ncp is sufficiently smooth conditions on f are derived that ensure that the appropriate regularity conditions are satisfied for the nonlinear equations reformulation of the ncp at x

locking free optimal discontinuous galerkin methods for timoshenko beams in this paper we consider the so called hp version of discontinuous galerkin methods for timoshenko beams we prove that when the numerical traces are properly chosen the methods display optimal convergence uniformly with respect to the thickness of the beam these methods are thus free from shear locking we also prove that when polynomials of degree p are used all the numerical traces superconverge with a rate of order h 2p 1 p 2p 1 numerical experiments verifying the above mentioned theoretical results are shown

exponential stability of laminated timoshenko beams with boundary internal controls abstract for a laminated timoshenko system with slip along the interface we study existence and boundary interior stabilization of solutions our first main result using resolvent estimates in the frequency domain is to show that interior damping created by the interfacial slip in companion with boundary feedback controls acting on the complementary displacements traverse and rotation angle drives the solution to zero with exponential decay rate we impose neither conditions on the physical parameters of the model nor on the damping coefficients our second main result is to investigate the asymptotic behavior of solutions for partially dissipative problems assuming the condition that the waves travel at the same speed we prove the decay of solutions with exponential rate finally the same condition allows us to show that dissipative effect created by the interfacial slip is strong enough to exponentially stabilizes the solutions to zero

the expansion of a semigroup and a riesz basis criterion problems on the expansion of a semigroup and a criterion for being a riesz basis are discussed in the present paper suppose that a is the generator of a c0 semigroup on a hilbert space and a 1 a 2 a with 2 a is consisted of isolated eigenvalues distributed in a vertical strip it is proved that if 2 a is separated and for each 2 a the dimension of its root subspace is uniformly bounded then the generalized eigenvectors associated with 2 a form an l basis under different conditions on the riesz projection the expansion of a semigroup is studied in particular a simple criterion for the generalized eigenvectors forming a riesz basis is given as an application a heat exchanger problem with boundary feedback is investigated it is proved that the heat exchanger system is a riesz system in a suitable state hilbert space

a mixed multiscale finite element method for elliptic problems with oscillating coefficients the recently introduced multiscale finite element method for solving elliptic equations with oscillating coefficients is designed to capture the large scale structure of the solutions without resolving all the fine scale structures motivated by the numerical simulation of flow transport in highly heterogeneous porous media we propose a mixed multiscale finite element method with an over sampling technique for solving second order elliptic equations with rapidly oscillating coefficients the multiscale finite element bases are constructed by locally solving neumann boundary value problems we provide a detailed convergence analysis of the method under the assumption that the oscillating coefficients are locally periodic while such a simplifying assumption is not required by our method it allows us to use homogenization theory to obtain the asymptotic structure of the solutions numerical experiments are carried out for flow transport in a porous medium with a random log normal relative permeability to demonstrate the efficiency and accuracy of the proposed method

fault diagnosability of data center networks abstract a kind of generalization of diagnosability for a network g is g good neighbor diagnosability which is denoted by t g g let g g be the r g connectivity lin et al 2016 17 and xu et al 2017 29 gave the same problem independently that the relationship between the r g connectivity g g and t g g of a general graph g needs to be studied in the future in this paper this open problem is solved for general regular graphs we firstly establish the relationship of g g and t g g and obtain that t g g g g g under some conditions secondly we obtain the g good neighbor diagnosability of data center network d k n which are t g d k n g 1 k 1 n g for 1 g n 1 under the pmc model and the mm model respectively furthermore we show that d k n is tightly super n k 1 connected for n 2 and k 2 and we also prove that the largest connected component of the survival graph contains almost all of the remaining vertices in d k n when n 2 k 2 vertices removed

boundary control of the timoshenko beam it is shown that the timoshenko beam can be uniformly stabilized by means of a boundary control a numerical study on the spectrum is also presented

application of an automatic hp adaptive finite element method for thin walled structures the paper investigates the possibility of solving beam and thin walled structures with an automatic hp adaptive finite element method for three dimensional linear elasticity this technique generates sequences of meshes with nonuniform distribution of element sizes h and their spectral orders p to minimize the interpolation error for the hypothetical exact solution with constant number of degrees of freedom the intent of using hp method for beam and thin walled structures is that it should automatically create fe meshes with adequate distribution of the approximation orders to prevent the numerical locking phenomenon and to provide accurate solutions the method also reduces the human work spent on building the numerical model to generation of the description of the geometry we discuss energy based and goal oriented versions of hp adaptivity the paper presents a broad spectrum of examples of engineering applications

a second order accurate difference scheme for the heat equation with concentrated capacity a numerical solution to the one dimensional heat equation with concentrated capacity is considered a second order accurate difference scheme is derived by the method of reduction of order on non uniform meshes the solvability stability and second order l convergence are proved a numerical example demonstrates the theoretical results

feedback stabilization of a timoshenko beam with an end mass the boundary feedback control problem of a timoshenko beam with an end mass is studied in this paper first under some nonlinear boundary feedback controls the asymptotic stability for the corresponding closed loop system is shown then with the energy perturbed approach it is proved under some specific linear feedback controls applied to the tip that the vibration of the beam decays uniformly finally in the case when feedback controls are applied to both the beam ends the uniform decay is also established

riesz basis property of serially connected timoshenko beams in this paper we study the riesz basis property of serially connected timoshenko beams with joint and boundary feedback controls suppose that the left end of the whole beam is clamped and the right end is free at intermediate nodes the displacement and rotational angle of beams are continuous but the shearing force and bending moment could be discontinuous the collocated velocity feedback of the beams at intermediate nodes and the right end are used to stabilize the system we prove that the operator determined by the closed loop system has compact resolvent and generates a c 0 semigroup in an appropriate hilbert space we also show that there is a sequence of the generalized eigenvectors of the operator that forms a riesz basis with parentheses hence the spectrum determined growth condition holds therefore if the imaginary axis is not an asymptote of the spectrum then the closed loop system is exponentially stable finally we give a conclusion remark to explain that our result can be applied not

analysis and modification of newton s method for algebraic riccati equations when newton s method is applied to find the maximal symmetric solution of an algebraic riccati equation convergence can be guaranteed under moderate conditions in particular the initial guess need not be close to the solution the convergence is quadratic if the frechet derivative is invertible at the solution in this paper we examine the behaviour of the newton iteration when the derivative is not invertible at the solution we find that a simple modification can improve the performance of the newton iteration dramatically

conditional diagnosability of alternating group graphs let an be the alternating group of degree n with n 3 set s 1 2 i 1 i 2 3 i n the alternating group graph denoted by agn is defined as the cayley graph on an with respect to s jwo et al networks 23 1993 315 326 introduced alternating group graph agn as an interconnection network topology for computing systems conditional diagnosability a new measure of diagnosability introduced by lai et al ieee transactions on computers 54 2 2005 165 175 can better measure the diagnosability of regular interconnection networks this paper determines that under pmc model the conditional diagnosability of agn is 4 for n 4 and 6n 18 for each n 5

locking free finite element method for a bending moment formulation of timoshenko beams in this paper we study a finite element formulation for timoshenko beams it is known that standard finite elements applied to this model lead to wrong results when the thickness of the beam is small here we consider a mixed formulation in terms of the transverse displacement rotation shear stress and bending moment by using the classical babuska brezzi theory it is proved that the resulting variational formulation is well posed we discretize it by continuous piecewise linear finite elements for the shear stress and bending moment and discontinuous piecewise constant finite elements for the displacement and rotation we prove an optimal linear order of convergence in terms of the mesh size for the natural norms and a double order quadratic in l 2 norms for the shear stress and the bending moment these estimates involve constants and norms of the solution that are proved to be bounded independently of the beam thickness which ensures the locking free character of the method numerical tests are reported in order to support our theoretical results

diagnosability of hypercubes and enhanced hypercubes under the comparison diagnosis model a sengupta and a dahbura 1992 discussed how to characterize a diagnosable system under the comparison diagnosis model proposed by j maeng and m malek 1981 and a polynomial algorithm was given to identify the faulty processors provided that the system s diagnosability is known however for a general system the determination of its diagnosability is not algorithmically easy this paper proves that for the important hypercube structured multiprocessor systems n cubes the diagnosability under the comparison model is n when n spl ges 5 the paper also studies the diagnosability of enhanced hypercube which is obtained by adding 2 sup n 1 more links to a regular hypercube of 2 sup n processors it is shown that the augmented communication ability among processors also increases the system s diagnosability under the comparison model we prove that the diagnosability is n 1 for an enhanced hypercube when n spl ges 6

the optimal convergence rate of the p version of the finite element method optimal error estimates for the p version of the finite element method in two dimensions are proven for the case when u in h k omega or u has singularities induced by the corners of the domain the case of nonhomogenous essential boundary conditions is also analyzed

a priori error estimations of hp finite element approximations for hierarchical models of plate and shell like structures a priori error estimates of hp finite element approximations for hierarchical models of the thin elastic plate and shell like structures are derived the error in the approximations of a hierarchical model consists of the modelling error due to assumptions on displacement or stress fields and the finite element approximation error of discretizations of such a model also non uniformity with respect to the thickness owing to numerical locking is included in the present error estimates numerical results are given supporting the theoretical results

a second order accurate linearized difference scheme for the two dimensional cahn hilliard equation the cahn hilliard equation is a nonlinear evolutionary equation that is of fourth order in space in this paper a linearized finite difference scheme is derived by the method of reduction of order it is proved that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete l2 norm the coefficient matrix of the difference system is symmetric and positive definite so many well known iterative methods e g gauss seidel sor can be used to solve the system

the lack of exponential stability of the hybrid bresse system abstract in this paper we consider the dissipative bresse system with an attached hollow tip body that contains granular material the resulting model being called hybrid system our main result is to show that the corresponding model is not exponentially stable moreover we show that the solution decays polynomially to zero as 1 t 1 2 when t

conditional diagnosability of arrangement graphs under the pmc model abstract processor fault diagnosis has played an important role in measuring the reliability of a multiprocessor system and the diagnosabilities of many well known multiprocessor systems have been investigated the conditional diagnosability has been widely accepted as a measure of diagnosability by assuming an additional condition that any fault set can t contain all the neighbors of any node in a multiprocessor system this paper considers the conditional diagnosability of an n k arrangement graph a n k a flexible interconnection network model for multiprocessor systems under the classical pmc diagnostic model and determines that the conditional diagnosability of a n k k 2 n k 2 is 4 k 4 n k 3 which is about four times its traditional diagnosability

finite element methods for timoshenko beam circular arch and reissner mindlin plate problems in this paper some finite element methods for timoshenko beam circular arch and reissner mindlin plate problems are discussed to avoid locking phenomenon the reduced integration technique is used and a bubble function space is added to increase the solution accuracy the method for timoshenko beam is aligned with the petrov galerkin formulation derived in loula et al 1987 and can be naturally extended to solve the circular arch and the reissner mindlin plate problems optimal order error estimates are proved uniform with respect to the small parameters numerical examples for the circular arch problem shows that the proposed method compares favorably with the conventional reduced integration method

fault diagnosability of arrangement graphs the growing size of the multiprocessor system increases its vulnerability to component failures it is crucial to locate and to replace the faulty processors to maintain a system s high reliability the fault diagnosis is the process of identifying faulty processors in a system through testing in this paper we show that the largest connected component of the survival graph contains almost all of the remaining vertices in the n k arrangement graph a n k when the number of moved faulty vertices is up to twice or three times the traditional connectivity using this fault resiliency we establish the conditional diagnosability of a n k under the comparison model and prove that the conditional diagnosability of a n k is 3k 2 n k 3 for k 4 n k 2 and the conditional diagnosability of a n n 1 is 3n 7 for n 5

the g good neighbor diagnosability of n k star graphs many large scale multiprocessor or multi computer systems take interconnection networks as underlying topologies fault diagnosis is especially important to identify fault tolerability of such systems the g good neighbor conditional diagnosability such that every fault free node has at least g fault free neighbors is a novel measure of diagnosability in this paper we show that the g good neighbor diagnosability of the n k star graph s n k under the pmc model 2 k n 1 and 1 g n k and the comparison model 2 k n 1 and 2 g n k is n g k 1 1 respectively in addition we derive that 1 good neighbor diagnosability of s n k under the comparison model is n k 2 for 3 k n 1 and n 4 as a supplement we also derive that the g good neighbor diagnosability of the n 1 star graph s n 1 1 g n 2 1 and n 4 under the pmc model and the comparison model is n 2 1 respectively we explore fault diagnosability of multiprocessor systems based on combinatorial network theory we establish the g good neighbor diagnosability of the n k star graph s n k under the pmc model we establish the g good neighbor diagnosability of the n k star graph s n k under the comparison model

a box type scheme for fractional sub diffusion equation with neumann boundary conditions combining order reduction approach and l1 discretization a box type scheme is presented for solving a class of fractional sub diffusion equation with neumann boundary conditions a new inner product and corresponding norm with a sobolev embedding inequality are introduced a novel technique is applied in the proof of both stability and convergence the global convergence order in maximum norm is o t 2 a h 2 the accuracy and efficiency of the scheme are checked by two numerical tests

numerical analysis of a multi symplectic scheme for a strongly coupled schrodinger system abstract in this paper we analyze a multi symplectic scheme for a strongly coupled nonlinear schrodinger equations we derive a general box scheme which is equivalent to the multi symplectic scheme by reduction method based on the general box scheme we prove that the multi symplectic scheme preserves not only the multi symplectic structure of the equation but also conservation law of mass in general the multi symplectic schemes are not conservative to energy in the nonlinear case so it is difficult to obtain the estimates of numerical solutions in norm hence proofs of convergence and stability are difficult for multi symplectic schemes of nonlinear equations a deduction argument and the energy analysis method are used to prove that the numerical solution is stable for initial values and second order convergent to the exact solutions in 2 norm a fixed point theorem is introduced and used to prove the unique solvability of the numerical solutions

a shamanskii like acceleration scheme for nonlinear equations at singular roots on applique une variante de la methode de shamanskii pour realiser une methode a convergence superlineaire de resolution d une classe d equations non lineaires ayant une derivee de frechet singuliere a la racine

the 2 good neighbor diagnosability of cayley graphs generated by transposition trees under the pmc model and mm model diagnosability is an important metric for measuring the reliability of multiprocessor systems in 2012 peng et al proposed a new measure for fault diagnosis of the system which is called g good neighbor diagnosability that restrains every fault free node containing at least g fault free neighbors as a favorable topology structure of interconnection networks the cayley graph c n generated by the transposition tree n has many good properties in this paper we give that the 2 good neighbor diagnosability of c n under the pmc model and mm model is g n 2 1 where n 4 and g is the girth of c n

convergence rates for newton s method at singular points if newton s method is employed to find a root of a map from a banach space into itself and the derivative is singular at that root the convergence of the newton iterates to the root is linear rather than quadratic in this paper we give a detailed analysis of the linear convergence rates for several types of singular problems for some of these problems we describe modifications of newton s method which will restore quadratic convergence

a new acceleration method for newton s method at singular points when newton s method is used to find a root of a map from a banach space into itself and the derivative is singular at that root convergence of the newton sequence is in general linear in this paper we give a modification of newton s method that under certain conditions converges superlinearly our method is applicable under more general conditions than other techniques in particular it may be used for certain quadratic problems and problems in which the dimension of the null space of the derivative is larger than one

fault tolerance of n k star networks this paper considers a refined measure s h for the fault tolerance of a network and for the generalized star network s n k determines s h s n k n h k 2 1 for 2 k n 1 and 0 h n k which implies that at least n h k 2 1 vertices of s n k have to be removed to get a disconnected graph without vertices of degree less than h this work generalizes some known results when the n k star graph is used to model the topological structure of a large scale parallel processing system this result can provide a more accurate measure for the fault tolerance of the system

convergence acceleration for newton s method at singular points if newton s method is employed to find a root of a map from a banach space into itself and the derivative is singular at that root linear convergence of the newton sequence to the root is the best

on the robustness of the h and p versions of the finite element method abstract the classical h version of the finite element method achieves accuracy by refining the mesh and keeping p the degree of polynomials used at a fixed low level we compare the robustness of such algorithms to that of the more recent p version which uses a fixed mesh and increases p we consider two physical parameter dependent problems that can lead to poor approximations near a limiting value of the parameter locking our results show that p type algorithms are generally more robust with respect to the parameter values than h type ones

on solving nonlinear equations with simple singularities or nearly singular solutions the paper begins with a review of the convergence theory for newton s method near simple and other regular singularities followed by a brief discussion of the inherent difficulty of singular problems and the effect of rounding errors on the achievable solution accuracy then several ways to accelerate the slow convergence of newton s method are described in some detail these are richardson extrapolation overrelaxation bordering by a singularity condition and appending the usual linear model by a quadratic term the last two approaches require limited second derivative information which can be obtained analytically by differencing or through secant updating numerical comparisons reported in the final sections lead to the conclusion that the collection of the additional information pays off in terms of speed and accuracy

analytical and computational assessment of locking in the hp finite element method locking is the phenomenon by which the numerical approximation of parameter dependent problems deteriorates for values of the parameter close to a limiting value in this paper we give a definition of locking and develop precise computable and analytic ways to quantify it using the example of nearly incompressible elasticity we show by means of computational and theoretical results the difference between the h version and php version in combatting locking our results establish the superiority of high order elements both h p and hp when the standard variational form is used we also discuss other issues such as curved elements mixed methods and locking phenomena for problems over anisotropic materials and over thin domains

the g good neighbor conditional diagnosability of hypercube under pmc model abstract processor fault diagnosis plays an important role in multiprocessor systems for reliable computing and the diagnosability of many well known networks has been explored for example hypercubes crossed cubes mobius cubes and twisted cubes of dimension n all have diagnosability n the conditional diagnosability of n dimensional hypercube q n is proved to be 4 n 2 1 under the pmc model in this paper we study the g good neighbor conditional diagnosability of q n under the pmc model and show that it is 2 g n g 2 g 1 for 0 g n 3 the g good neighbor conditional diagnosability of q n is several times larger than the classical diagnosability

asymptotic behavior of timoshenko beam with dissipative boundary feedback abstract this paper is concerned with the stabilization problem of timoshenko beam in the presence of linear dissipative boundary feedback controls using c 0 semigroups theory we establish the existence and the uniqueness of solution of the proposed closed loop system in order to consider the asymptotic behavior of the closed loop system we first discuss the existence of nonzero solution of a closely related boundary value problem then we derive various necessary and sufficient conditions for the system to be asymptotically stable finally we prove the equivalence between the exponential stability and the asymptotic stability for the closed loop system

discretization by finite elements of a model parameter dependent problem the discretization by finite elements of a model variational problem for a clamped loaded beam is studied with emphasis on the effect of the beam thickness which appears as a parameter in the problem on the accuracy it is shown that the approximation achieved by a standard finite element method degenerates for thin beams in contrast a large family of mixed finite element methods are shown to yield quasioptimal approximation independent of the thickness parameter the most useful of these methods may be realized by replacing the integrals appearing in the stiffness matrix of the standard method by gauss quadratures

direct strain feedback control of flexible robot arms new theoretical and experimental results this paper addresses control problems for flexible robot arms by using direct strain feedback the purpose is to make clear why direct strain feedback can damp out vibration of flexible arms satisfactorily we concentrate on one link flexible robot arms whose dynamic models can be represented by linear partial differential equations with appropriate boundary conditions which have been well examined in a number of papers a key contribution of this paper is the introduction of the concept of strict a dependent operators which allows us to prove rigorously the closed loop stability of direct strain feedback and the existence and uniqueness of nonstandard second order abstract differential equations in hilbert spaces several control experiments are performed verifying the main theoretical points of this paper demonstrating satisfactory control results of direct strain feedback and leading to potential application of this simple control method for flexible robot control

discretization of implicit odes for singular root finding problems this paper addresses the use of dynamical system theory to tackle singular root finding problems the use of continuous time methods leads to implicit differential systems when applied to singular nonlinear equations the analysis is based on a taxonomy of singularities and uses previous stability results proved in the context of quasilinear implicit odes the proposed approach provides a framework for the systematic formulation of quadratically convergent iterations to singular roots the scope of the work includes also the introduction of discrete time analysis techniques for singular problems which are based on continuous time stability and numerical stability some numerical experiments illustrate the applicability of the proposed techniques

discretization of the timoshenko beam problem by thep and theh p versions of the finite element method in this paper the discretization of the timoshenko beam problem by thep and theh p versions of the finite element method is considered optimal error estimates are established the locking phenomenon disappears as the thickness of the beam decreases

a novel semi discrete scheme preserving uniformly exponential stability for an euler bernoulli beam abstract in this paper a novel space semi discretized numerical scheme which is based on finite volume method is proposed for approximation of uniformly exponential decay of euler bernoulli beam system which turns out to be an alternative of finite difference scheme from order reduction point of view the new scheme is constructed on equidistant grid points without using any numerical viscosity terms the uniformly exponential decay is proved by the lyapunov function method and the energy multiplier technique with construction of a new gradient recovery function the numerical solution is proved to be convergent to the weak solution of the original continuous system compared with the existing literature the proposed approach has potentially achieved the following objectives a it removes the introduction of the numerical viscosity term to achieve uniform convergence b it can deal with any type of boundary conditions without help of the spectral analysis which is limited only for some special boundary conditions c the convergence proof is simplified significantly with the similar techniques in dealing with the continuous counterpart

a finite difference scheme for solving the timoshenko beam equations with boundary feedback in this study we derive a finite difference for a timoshenko beam with boundary feedback by the method of reduction of order on uniform meshes it is proved by the discrete energy method that the scheme is uniquely solvable unconditionally stable and second order convergent in l norm numerical results demonstrate the theoretical results

stabilisation of timoshenko beam system with a tip payload under the unknown boundary external disturbances this paper is concerned with the boundary stabilisation of a timoshenko beam with a tip payload under the boundary external disturbances nonlinear feedback control laws are designed to reduce the effects of the external disturbances since the controlled system is nonlinear the well posedness of the nonlinear closed loop system is investigated using the theory of nonlinear maximal monotone operators and the variational principle in addition we show the exponential stability of the nonlinear controlled system using the lyapunov direct method in the end the numerical simulations are displayed to illustrate the effectiveness of the proposed boundary controls

the conditional fault diagnosability of n k star graphs abstract the growing size of the multiprocessor system increases its vulnerability to component failures it is crucial to locate and replace the faulty processors to maintain a system s high reliability the fault diagnosis is the process of identifying faulty processors in a system through testing this paper shows that the largest connected component of the survival graph contains almost all the remaining vertices when a lot of faulty vertices occur in the n k star graph s n k n 5 k 3 n k 2 based on this fault resiliency it establishes the conditional fault diagnosability of s n k under the comparison model

boundary control of a timoshenko beam attached to a rigid body planar motion a flexible spacecraft modelled as a rigid body which rotates in an inertial space is considered a light flexible beam is clamped to the rigid body at one end and free at the other end the equations of motion are obtained by using the geometrically exact beam model for the flexible beam and it is then shown that under planar motion assumption linearization of this model yields the timoshenko beam model it is shown that suitable boundary controls applied to the free end of the beam and a control torque applied to the rigid body stabilize the system the proof is obtained by using a lyapunov functional based on the energy of the system

least squares finite element approximations to the timoshenko beam problem in this paper a least squares finite element method for the timoshenko beam problem is proposed and analyzed the method is shown to be convergent and stable without requiring extra smoothness of the exact solutions for sufficiently regular exact solutions the method achieves optimal order of convergence in the h 1 norm for all the unknowns displacement rotation shear moment uniformly in the small parameter which is generally proportional to the ratio of thickness to length thus the locking phenomenon disappears as the parameter tends to zero a sharp a posteriori error estimator which is exact in the energy norm and equivalent in the h 1 norm is also briefly discussed

the conditional diagnosability of k ary n cubes under the comparison diagnosis model processor fault diagnosis plays an important role in measuring the reliability of multiprocessor systems and diagnosing many well known interconnection networks conditional diagnosability is a novel measure of diagnosability that adds the additional condition that any faulty set cannot contain all of the neighbors of any vertex in a system this study investigates some topological properties of k ary n cubes where k 4 and n 4 and shows that the conditional diagnosability of k ary n cubes under the comparison diagnosis model is 6n 5

newton s method for singular problems when the dimension of the null space is 1 a theorem is proved concerning the convergence of newton s method when the dimension of the null space of the jacobian matrix is 1 it improves on previous results of decker and kelley siam j numer anal 17 1980 pp 66 70 and reddien comput math appl 5 1980 pp 79 86

on the convergence of finite difference schemes for the heat equation with concentrated capacity we investigate the convergence of difference schemes for the one dimensional heat equation when the coefficient at the time derivative heat capacity is c left x right 1 k delta left x xi right k const 0 represents the magnitude of the heat capacity concentrated at the point x xi an abstract operator method is developed for analyzing this equation estimates for the rate of convergence in special discrete energetic sobolev s norms compatible with the smoothness of the solution are obtained

exponential stability of uniform euler bernoulli beams with non collocated boundary controllers a b s t r a c t we study the stability of a robot system composed of two euler bernoulli beams with noncollocated controllers by the detailed spectral analysis we prove that the asymptotical spectra of the system are distributed in the complex left half plane and there is a sequence of the generalized eigenfunctions that forms a riesz basis in the energy space since there exist at most finitely many spectral points of the system in the right half plane to obtain the exponential stability we show that one can choose suitable feedback gains such that all eigenvalues of the system are located in the left half plane hence the riesz basis property ensures that the system is exponentially stable finally we give some simulation for spectra of the system

the p version of the finite element method in the p version of the finite element method the triangulation is fixed and the degree p of the piecewise polynomial approximation is progressively increased until some desired level of precision is reached in this paper we first establish the basic approximation properties of some spaces of piecewise polynomials defined on a finite element triangulation these properties lead to an a priori estimate of the asymptotic rate of convergence of the p version the estimate shows that the p version gives results which are not worse than those obtained by the conventional finite element method called the h version in which h represents the maximum diameter of the elements when quasi uniform triangulations are employed and the basis for comparison is the number of degrees of freedom furthermore in the case of a singularity problem we show under conditions which are usually satisfied in practice that the rate of convergence of the p version is twice that of the h version with quasi uniform mesh inve

the p and h p versions of the finite element method basic principles and properties in the classical form of the finite element method called the hversion piecewise polynomials of fixed degree p are used and the mesh size h is decreased for accuracy in this paper we discuss the fundamental theoretical ideas behind the relatively recent p version and h p version in the p version a fixed mesh is used and p is allowed to increase the h p version combines both approaches the authors describe and explain the basic properties and characteristics of these newer versions especially in areas where their behavior is significantly different from that of the h version simplified proofs of key concepts are included and computational illustrations of several results are provided a benchmark comparison between the various versions in included

stability of singular equilibria in quasilinear implicit differential equations abstract this paper addresses stability properties of singular equilibria arising in quasilinear implicit odes under certain assumptions local dynamics near a singular point may be described through a continuous or directionally continuous vector field this fact motivates a classification of geometric singularities into weak and strong ones stability in the weak case is analyzed through certain linear matrix equations a singular version of the lyapunov equation being especially relevant in the study weak stable singularities include singular zeros having a spherical domain of attraction which contains other singular points regarding strong equilibria stability is proved via a lyapunov schmidt approach under additional hypotheses the results are shown to be relevant in singular root finding problems

boundary feedback exponential stabilization of a timoshenko beam with both ends free in the present paper we consider the boundary feedback stabilization of a timoshenko beam with both ends free we propose boundary feedback control law that makes the closed loop system dissipative using asymptotic analysis techniques we give explicit asymptotic formula of eigenvalues of the closed loop system and prove the riesz basis property of eigenvectors and generalized eigenvectors by a detailed analysis of spectrum of the closed loop system we show that the closed system is exponentially stable

locking and robustness in the finite element method for circular arch problem in this paper we discuss locking and robustness of the finite element method for a model circular arch problem it is shown that in the primal variable i e the standard displacement formulation the p version is free from locking and uniformly robust with order p k and hence exhibits optimal rate of convergence on the other hand the h version shows locking of order h 2 and is uniformly robust with order h p 2 for p 2 which explains the fact that the quadratic element for some circular arch problems suffers from locking for thin arches in computational experience if mixed method is used both the h version and the p version are free from locking furthermore the mixed method even converges uniformly with an optimal rate for the stress

on locking and robustness in the finite element method a numerical scheme for the approximation of a parameter dependent problem is said to exhibit locking if the accuracy of the approximations deteriorates as the parameter tends to a limiting value a robust numerical scheme for the problem is one that is essentially uniformly convergent for all values of the parameter precise mathematical definitions for these terms are developed their quantitative characterization is given and some general theorems involving locking and robustness are proven a model problem involving heat transfer is analyzed in detail using this mathematical framework and various related computational results are described applications to some different problems involving locking are presented

on the convergence of difference schemes for hyperbolic problems with concentrated data hyperbolic equations with unbounded coefficients and even generalized functions in particular dirac delta functions occur both naturally and artificially and must be treated in numerical schemes an abstract operator method is proposed for studying these equations for finite difference schemes approximating several one dimensional initial boundary value problems convergence rate estimates in special discrete energetic sobolev s norms compatible with the smoothness of the solutions are obtained

g good neighbor conditional diagnosability measures for 3 ary n cube networks the diagnosability of a parallel system is defined as the maximum number of faulty processors or nodes that the system can guarantee to identify in this study we investigate the g good neighbor conditional diagnosability which indicates that every fault free node in a system contains at least g fault free neighbors compared with the conventional diagnosability g good neighbor conditional diagnosability improves accuracy in measuring the reliability of interconnection networks in heterogeneous environments we apply the pmc and mm models to study the g good neighbor conditional diagnosability of 3 ary n cube networks which represent a family of popular parallel systems such as ibm s blue gene and cray t3d the findings made in this study facilitate accurate reliability measurements in modern parallel systems powered by 3 ary n cube networks specifically our results show that the g good neighbor conditional diagnosability of 3 ary n cube is g 2 2 n g 1 1 and g 1 2 4 n 2 g 1 1 when the g value is even and odd respectively the r g connectivity of 3 ary n cube networks was determined for n 3 and 0 g n 1 applying the pmc model and the mm model we investigated and measured the g good neighbor conditional diagnosability of 3 ary n cube networks for n 4 and 0 g n 1