positive solutions of nonlinear m point boundary value problems on time scales in this paper by using fixed point theorems in a cone and the associated green s function we study the existence of at least two and three positive solutions to the m point boundary value problem bvp on time scales u d t f t u t 0 email protected 0 1 t bu 0 email protected d 0 0 u 1 email protected email protected iu e i m 3 where t is a time scale email protected c l d 0 1 x 0 0 b email protected 0 a email protected 0 for i 1 2 m 2 and e i satisfy 0 e 1 e 2 e m 2 r 1

universal 1 w 1 tracking for a class of nonlinear systems an adaptive output feedback strategy incorporating gains of nussbaum type is described and shown to be a universal tracking controller for a class of nonlinearly perturbed minimum phase linear systems with reference signals r r rm of sobolev class w1

a simple adaptive pi controller for linear systems with constant disturbances it is known that an adaptive controller via high gain output feedback can globally stabilize a class of minimum phase systems with relative degree one however exact output regulation is difficult for systems with disturbances in this paper we consider linear single input single output siso systems with unknown constant disturbances we present a simple adaptive output feedback controller with an integral action and show that it can asymptotically stabilize those disturbed systems the proposed pi type adaptive controller can also deal with the output tracking problem of a step reference

geometric mesh partitioning implementation and experiments we investigate a method of dividing an irregular mesh into equal sized pieces with few interconnecting edges the method s novel feature is that it exploits the geometric coordinates of the mesh vertices it is based on theoretical work of miller teng thurston and vavasis who showed that certain classes of well shaped finite element meshes have good separators the geometric method is quite simple to implement we describe a sc matlab code for it in some detail the method is also quite efficient and effective we compare it with some other methods including spectral bisection

twin solutions of boundary value problems for ordinary differential equations and finite difference equations a new twin fixed point theorem is applied first to obtain the existence of at least two positive solutions for the right focal boundary value problem y f ity 0 0 t 1 y 0 y 1 0 it is applied later to obtain the existence of at least two positive solutions for the analogous discrete right focal boundary value problem 2u k g u k 0 k 0 n u 0 u n 1 0

adaptive stabilization with exponential decay abstract adaptive high gain stabilizers for classes of linear time invariant state space systems are presented the classes cover multi input multi output systems where the state dimension is not known only standard assumptions such as minimum phase and known respectively unknown sign are required the main result is that the adaptive control laws of byrnes and willems can be modified to produce a gurantee of exponentially decaying states

robust adaptive stabilization by high gain feedback and switching abstract a wide class of stabilizing adaptive control rules is investigated the feedback laws combine high gain adaptive procedures with switching functions and stabilize the systems without knowledge of the sign of the high frequency gain furthermore some non linear structural perturbations are tolerated

existence and nonexistence of positive solutions for a class of nth order three point boundary value problems in banach spaces by using the fixed point principle in cone and the fixed point index theory for strict set contraction operator this paper investigates the existence nonexistence and multiplicity of positive solutions for a class of nonlinear three point boundary value problems of nth order differential equations in ordered banach spaces in addition an example is included to demonstrate the main results

multiple positive solutions of multi point boundary value problem for second order impulsive differential equations this paper is devoted to study the existence of multiple positive solutions for the second order multi point boundary value problem with impulse effects the arguments are based upon fixed point theorems in a cone an example is worked out to demonstrate the main results

symmetric positive solutions for p laplacian fourth order differential equations with integral boundary conditions this paper investigates the existence and multiplicity of symmetric positive solutions for a class of p laplacian fourth order differential equations with integral boundary conditions the arguments are based upon a specially constructed cone and the fixed point theory for cones the nonexistence of a positive solution is also studied

on the existence of nonnegative solutions to an integral equation with applications to boundary value problems abstract by the use of a guo krasnoselskii theorem in cones existence of positive eigenvalues yielding nonnegative or positive solutions to an integral equation is studied the results are applied to a variety of boundary value problems concerning ordinary differential equations

stability and robustness properties of universal adaptive controllers for first order linear systems quite recently examples of non linear adaptive controllers have been found that adaptively stabilize any scalar first order linear system in this paper we describe two general classes of such universal adaptive stabilizers that include the previously proposed controllers as special cases different types of perturbations of these controllers are studied and we report on extensive simulation experiments our results demonstrate considerable qualitative differences in the dynamical behaviour of various adaptive universal stabilizers while the previously proposed controllers all exhibit the bursting phenomena we give an explicit example of a stabilizing controller that does not show bursting behaviour

positive solutions for a class of boundary value problem with integral boundary conditions in banach spaces this paper investigates the existence and multiplicity of positive solutions for a class of nonlinear boundary value problem of second order differential equations with integral boundary conditions in ordered banach spaces the arguments are based upon a specially constructed cone and the fixed point theory in a cone for strict set contraction operators the nonexistence of a positive solution is also studied

positive solution for m point boundary value problems in this paper we investigate an m point boundary value problem with sign changing nonlinearity the existence of an interval of parameters which ensures the problem has at least one positive solution is determined by constructing available operator and combining the method of lower solution with the method of topology degree moreover the associated green s function for the above problem is also given

on computing inverse entries of a sparse matrix in an out of core environment the inverse of an irreducible sparse matrix is structurally full so that it is impractical to think of computing or storing it however there are several applications where a subset of the entries of the inverse is required given a factorization of the sparse matrix held in out of core storage we show how to compute such a subset e ciently by accessing only parts of the factors when there are many inverse entries to compute we need to guarantee that the overall computation scheme has reasonable memory requirements while minimizing the cost of loading the factors this leads to a partitioning problem that we prove is np complete we also show that we cannot get a close approximation to the optimal solution in polynomial time we thus need to develop heuristic algorithms and we propose i a lower bound on the cost of an optimum solution ii an exact algorithm for a particular case iii two other heuristics for a more general case and iv hypergraph partitioning models for the most general setting we illustrate the performance of our algorithms in practice using the mumps software package on a set of real life problems as well as some standard test matrices we show that our techniques can improve the execution time by a factor of 50 key words sparse matrices direct methods for linear systems and matrix inversion multifrontal method graphs and hypergraphs

existence of solutions of boundary value problems with integral boundary conditions for second order impulsive integro differential equations in banach spaces this paper investigates the existence of solutions for a class of second order boundary value problems with integral boundary conditions of nonlinear impulsive integro differential equations in banach spaces the arguments are based upon the fixed point theorem of strict set contraction operators meanwhile an example is worked out to demonstrate the main results

on exact solutions of differential equations arising in universal adaptive stabilization in this paper we analyse non linear willems byrnes adaptive stabilization of first order linear systems x t ax t bu t x 0 r the willems byrnes control law is u h k x k x2 k 0 r and for each x 0 x0 k 0 k0 r x t 0 k t k x0 as t there are three cases according to whether h is smooth piecewise smooth or piecewise constant for each x0 r k x0 defines a limit pole a bh k x0 r we find that in all cases x0 r a bh k x0 0 is open and dense in the piecewise smooth constant case we solve explicitly the closed loop dynamical equation for x t and k t we find that a bh k x0 0 corresponds to solutions which decay only algebraically

symmetric positive solutions of boundary value problems with integral boundary conditions under conditions weaker than those used by ma we establish various results on the existence and nonexistence of symmetric positive solutions to fourth order boundary value problems with integral boundary conditions the arguments are based upon a specially constructed cone and the fixed point theory in a cone our results improve and extend that obtained in h ma symmetric positive solutions for nonlocal boundary value problems of fourth order nonlinear anal 68 2008 645 651 we illustrate our results by one example which cannot be handled using the existing results

solutions and green s functions for some linear second order three point boundary value problems in this paper we consider the green s functions for a second order linear ordinary differential equation with some three point boundary conditions we give exact expressions of the unique solutions for the linear three point boundary problems by the green s functions as applications we study the iterative solutions for some nonlinear singular second order three point boundary value problems

a class of three point boundary value problems for second order impulsive integro differential equations in banach spaces abstract in this paper we consider the following boundary value problems for second order three point nonlinear impulsive integro differential equation of mixed type in a real banach space e x t f t x t x t a x t b x t t j t t k x t t k i k x t k x t t k i k x t k x t k k 1 2 m x 0 x 1 x where is the zero element of e a x t 0 t g t s x s d s b x t 0 1 h t s x s d s g c d r d t s j j t s h c j j r and x t t k denotes the jump of x t at t t k x t t k denotes the jump of x t at t t k some new results are obtained for the existence and multiplicity of positive solutions of the above problems by using the fixed point index theory and fixed point theorem in the cone of strict set contraction operators meanwhile an example is worked out to demonstrate the main results

domain decomposition type methods for computing the diagonal of a matrix inverse this paper presents two methods based on domain decomposition concepts for determining the diagonal of the inverse of specific matrices the first uses a divide and conquer principle and the sherman morrison woodbury formula and assumes that the matrix can be decomposed into a 2 times 2 block diagonal matrix and a low rank matrix the second method is a standard domain decomposition approach in which local solves are combined with a global correction both methods can be successfully combined with iterative solvers and sparse approximation techniques the efficiency of the methods usually depends on the specific implementation which should be fine tuned for different test problems preliminary results for some two dimensional 2d problems are reported to illustrate the proposed methods

fixed sign solutions for a system of singular focal boundary value problems we consider a system of focal boundary value problems where the nonlinearities may be singular in the independent variable and may also be singular in the dependent arguments using schauder fixed point theorem we establish criteria such that the system of boundary value problems has at least one fixed sign solution

positive solutions for a class of boundary value problems with integral boundary conditions this paper investigates the existence and multiplicity of positive solutions for a class of nonlinear boundary value problems of fourth order differential equations with integral boundary conditions the arguments are based upon a specially constructed cone and the fixed point theory in cone the nonexistence of positive solutions is also studied

robust control design for nonlinear uncertain systems with an unknown time varying control direction a continuous robust control design approach is proposed for first order nonlinear systems whose dynamics contain both nonlinear uncertainty and an unknown time varying control direction the so called control direction is the multiplier of the control term in the dynamic equation and it effectively represents the direction of motion under any given control a nonlinear robust control is designed to online and continuously identify sign changes of the unknown control direction and to guarantee stability of uniform ultimate boundedness the proposed robust control design requires only three conditions the nominal system is stable the control direction is smooth and the uncertainty in the system is bounded by a known function the necessity of these conditions is established in this paper continuity of the proposed robust control is achieved by using a so called shifting law that changes smoothly the sign of robust control and tracks the change of the unknown control direction analysis and design is shown by using lyapunov s direct method

adaptive stabilization using a variable sampling rate it is observed that digital versions of globally stable adaptive stabilization algorithms are at best locally stable due to incompatibilities between the gain adaptation algorithms and the choice of sampling rate this fact suggests the problem of retrieving global asymptotic stability for such difficulties by modifications to the stabilization algorithms to include sampling rates as control variables and the inclusion of extra plant information to relate sampling rates to gain evolutions in this contribution the theoretical problem of adaptive stabilization of single input single output siso linear systems s a b c in rnis approached using the sampling rate as the basic adaptive mechanism a wide range of sample interval adaptation schemes is derived that guarantees global asymptotic stability of the sampled outputs from the plant for any minimum phase siso systems satisfying the relative degree one constraint cb 0 the control laws are universal in the sense that stabilization is achieved des

permuting sparse rectangular matrices into block diagonal form we investigate the problem of permuting a sparse rectangular matrix into block diagonal form block diagonal form of a matrix grants an inherent parallelism for solving the deriving problem as recently investigated in the context of mathematical programming lu factorization and qr factorization to represent the nonzero structure of a matrix we propose bipartite graph and hypergraph models that reduce the permutation problem to those of graph partitioning by vertex separator and hypergraph partitioning respectively our experiments on a wide range of matrices using the state of the art graph and hypergraph partitioning tools metis and patoh revealed that the proposed methods yield very effective solutions both in terms of solution quality and runtime

a universal adaptive stabilizer for a class of nonlinear systems abstract an adaptive stabilizer is described which is universal for a class of single input nonlinear systems modelled as a controlled differential inclusion on r n the stabilizer has a discontinous feedback structure and incorporates a gain of nussbaum type the analysis draws on an extension to differential inclusions of lasalle s principle for ordinary differential equations

triple solutions for second order three point boundary value problems abstract we establish the existence of at least three positive solutions to the second order three point boundary value problem u f t u 0 u 0 0 u u 1 where 0 lt f 0 1 0 0 is continuous we accomplish this by making growth assumptions on f which can apply to many more cases than the sublinear and superlinear ones discussed in recent works

high gain robust adaptive controllers for multivariable systems abstract this paper extends the switching free high gain stabilizing adaptive control rules of byrnes and willems to a wide class of adaptive schemes capable of tolerating nonlinear state feedback perturbations

robust tracking control of uncertain nonlinear systems with unknown control directions a global robust tracking control design procedure is proposed for a class of uncertain nonlinear systems the key point is that the signs of multiplicative uncertainties the so called control directions are not assumed to be known a priori the class of systems can be of arbitrary dynamic order and the unmatched additive uncertainties need not satisfy the global lipschitz condition it is proved that under the proposed control all closed loop states are bounded and the tracking error converges to any prescribed small neighborhood of the origin the results of this paper enlarge the class of uncertain nonlinear systems for which global robust tracking control can be designed

on computing the inverse of a sparse matrix the gauss jordan inversion algorithm requires 0 n3 arithmetic operations in some practical applications like state estimation or short circuit calculation in power systems the given matrix is sparse and only part of the inverse is needed most frequently in the diagonal dominant case this is the diagonal there are two ways to exploit sparsity to determine elements of the inverse 1columnwise inversion via the solution of sparse linear systems with columns of the unit matrix as right hand sides 2application of the algorithm of takahashi et al6 the latter algorithm arises very naturally from multiplying the left and right hand factors of the zollenkopf bifactorization in reverse order we indicate how computing time can be gained in the important symmetric diagonal dominant case if only part of the diagonal is needed and compare computing times of the method of takahasi et al 6 with several variants of columnwise inversion whereas most of the theory holds for general matrices experiments are performed on the symmetric diagonal dominant case for band matrices the operation count is 0 n both for computing a column of the inverse by columnwise inversion and the diagonal by the algorithm of takahashi et al6

existence results for nonlinear boundary value problems with integral boundary conditions in banach spaces abstract this paper investigates the multiplicity of positive solutions for a class of nonlinear boundary value problems of fourth order differential equations with integral boundary conditions in ordered banach spaces the arguments are based upon a specially constructed cone and the fixed point index theory in cone for strict set contraction operator the nonexistence of positive solution is also studied meanwhile an example is worked out to demonstrate the main results

nonnegative solutions to nonlocal boundary value problems for systems of second order differential equations dependent on the first order derivatives abstract in this paper we consider nonlocal boundary value problems for systems of second order differential equations with dependence on the first order derivatives and deviating arguments by using a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three nonnegative solutions to such problems we investigate our problem both for delayed and advanced arguments i i and also for the case when i t i t t t 0 1 in all cases arguments i i can change the character on 0 1 so in some subinterval i of 0 1 they can be delayed in i and advanced in 0 1 i some remarks concern also the case when differential equations do not depend on the first order derivatives examples illustrate some results

improving the robustness of nussbaum type regulators by the use of σ modification local results abstract the bursting phenomenon in a nussbaum type regulator is discussed its cause is associated with some properties of the equilibrium manifold a modification factor is introduced and the resulting equilibrium set is completely characterized using linearization techniques local robustness against bounded disturbances is proved by malkin s theorem and verified by simulation

multiple positive solutions for discrete nonlocal boundary value problems in this paper we investigate a second order nonlinear difference equation with sign changing nonlinearity subject to two different sets of nonlocal boundary conditions the explicit expressions of the associated green s functions are presented by using a recently developed fixed point theorem we establish sufficient conditions for the existence of multiple positive solutions of the boundary value problem

remarks on the adaptive control of linear plants with unknown high frequency gain abstract adaptive control of first order linear systems of the form x ax bu with the sign of b unknown is considered it is shown that stabilizing adaptive controllers exist that have globally bounded gain and prespecified terminal dynamics