on the stabilization of a flexible beam with a tip mass we study the stability of a flexible beam that is clamped at one end and free at the other a mass is also attached to the free end of the beam to stabilize this system we apply a boundary control force at the free end of the beam we prove that the closed loop system is well posed and is exponentially stable we then analyze the spectrum of the system for a special case and prove that the spectrum determines the exponential decay rate for the considered case

exponential stabilisation of a simple tree shaped network of timoshenko beams system the stabilisation problem of a forked triple system of timoshenko beams which is a simple tree shaped network is considered in this article suppose that the root of the fork is clamped at the interior node of the fork the displacement and rotational angle of the beams are continuous the shearing force and bending moments of the beams satisfy the transmission conditions the feedback controllers are designed at the exterior tips to stabilise this system then the closed loop system is proved to be well posed by the eigenfrequency analysis together with the asymptotic technique the system is shown to satisfy the spectrum determined growth condition finally this closed loop system is proved to be exponentially stable furthermore a simulation is given to support these results

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

properties of a class of c0 semigroups on banach spaces and their applications abstract in this paper we investigate some properties of a class of c 0 semigroups on banach spaces suppose that the spectrum of the infinitesimal generator is discrete and there are only finitely many eigenvalues in each vertical strip we show that such semigroups can be expanded by their generalized eigenvectors under certain conditions as a consequence we assert that the semigroups with these conditions are eventually differentiable provided that the system of generalized eigenvectors is complete as an example we apply our results to a one dimensional wave control system

the damped string problem revisited abstract we revisit the damped string equation on a compact interval with a variety of boundary conditions and derive an infinite sequence of trace formulas associated with it employing methods familiar from supersymmetric quantum mechanics we also derive completeness and riesz basis results with parentheses for the associated root functions under less smoothness assumptions on the coefficients than usual using operator theoretic methods rather than detailed eigenvalue and root function asymptotics only

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

exponential bases in sobolev spaces in control and observation problems for the wave equation the fourier method in control systems reduces the study of controllability observability to the study of related exponential families in this paper we present examples of such systems specifically those for which we can prove that the related exponential families form a riesz basis in corresponding appropriately defined sobolev spaces this makes it possible to choose natural pairs of spaces the state space observability space and the control space state space depending on whether an observation or a control problem is studied respectively so that the observation and control operators are isomorphisms

output feedback stabilisation of a tree shaped network of vibrating strings with non collocated observation in this article the authors consider the simple tree shaped network of strings with non collocated observation suppose that the network consists of three strings and the displacements of these strings are continuous at the common vertex the sensors and actuators are required to be set at different vertices we propose an observer based output feedback controller to stabilise this network the exponential stability of the closed loop network is obtained based on the riesz basis approach together with estimates of the spectral distribution finally a numerical simulation is given to support these results

a complexity theory based on boolean algebra a projection of a boolean function is a function obtained by substituting for each of its variables a variable the negation of a variable or a constant reducibilities among computational problems under this relation of projection are considered it is shown that much of what is of everyday relevance in turing machine based complexity theory can be replicated easily and naturally in this elementary framework finer distinctions about the computational relationships among natural problems can be made than in previous formulations and some negative results are proved

ordinary differential equations in the oscillation theory of partial half linear differential equation abstract in the paper we study the damped half linear partial differential equation div a x u p 2 u b x u p 2 u c x u p 2 u 0 using radialization method we derive general oscillation results which allow to deduce new oscillation criteria for this equation from oscillation criteria for ordinary differential equations using careful radialization we improve several known oscillation criteria

an integrability condition on the resolvent for hyperbolicity of the semigroup abstract in this paper we present necessary and sufficient conditions on the resolvent of the generator of a strongly continuous semigroup in order that the corresponding semigroup is hyperbolic the proof is based on a new characterization of the growth bound in terms of the resolvent as an application we discuss three examples

riesz basis for strongly continuous groups given a hilbert space and the generator of a strongly continuous group on this hilbert space if the eigenvalues of the generator have a uniform gap and if the span of the corresponding eigenvectors is dense then these eigenvectors form a riesz basis or unconditional basis of the hilbert space furthermore we show that none of the conditions can be weakened

oscillation criteria for second order forced elliptic differential equations with mixed nonlinearities in the case of oscillatory potentials we establish some oscillation criteria for the second order forced elliptic differential equation with mixed nonlinearities div a x y c x y e x when n 1 our results extend those of kong q kong interval criteria for oscillation of second order linear ordinary differential equations j math anal appl 229 1999 258 270 for certain second order linear ordinary differential equations sun and meng y g sun f w meng interval criteria for oscillation of second order differential equations with mixed nonlinearities appl math comput 2007 doi 10 10 1016 j amc 2007 08 042 for certain second order differential equations with mixed nonlinearities yang q yang interval oscillation criteria for a second order nonlinear ordinary differential equations with oscillatory potential appl math comput 135 2003 49 64 for a forced second order superlinear ordinary differential equation when n 2 our theorems are more general and improve the oscillation criteria of zhuang r k zhuang annual oscillation criteria for second order nonlinear elliptic differential equations j comput anal math 2007 doi 10 1016 j cam 2007 06 031 for a forced second order undamped elliptic differential equation

completeness and non completeness results with respect to read once projections several models of restricted branching programs or binary decision diagrams have a lot of applications in hardware verification these models are investigated here from a complexity theoretical viewpoint because of depth restrictions projections are not suitable as reduction type and have to be restricted to read once projections several types of polynomial size binary decision diagrams have complete problems with respect to polynomial read once projections on the contrary it can be proved that the classes of polynomial size decision trees and polynomial size read once branching programs or free binary decision diagrams do not have such complete problems

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

abstract second order hyperbolic system and applications to controlled network of strings in this paper we study an abstract second order hyperbolic system valued in mathbb c n with appropriate boundary conditions we prove that the system is well posed and associates with a c 0 semigroup in a hilbert state space under certain conditions we show that the spectra of the system operator are located in the vertical strip and that there is a sequence of eigenvectors and generalized eigenvectors that forms a riesz basis with parentheses for the hilbert state space and hence that the system satisfies the spectrum determined growth assumption as applications we investigate the exponential stability of a controlled tree shaped network of 7 strings and a network of n connected strings

efficient boolean manipulation with obdd s can be extended to fbdd s obdd s are the state of the art data structure for boolean function manipulation basic tasks of boolean manipulation such as equivalence test satisfiability test tautology test and single boolean synthesis steps can be performed efficiently in terms of fixed ordered obdd s the bottleneck of most obdd applications is the size of the represented boolean functions since the total computation merely remains tractable as long as the obdd representations remain of reasonable size since it is well known that obdd s are restricted fbdd s free bdd s i e bdd s that test on each path each input variable at most once and that fbdd representations are often much more sometimes even exponentially more concise than obdd representations we propose to work with a more general fbdd based data structure we show that fbdd s of a fixed type provide similar as obdd s of a fixed variable ordering canonical representations of boolean functions and that basic tasks of boolean manipulation can be performed in terms of fixed typed fbdd s similarly efficient as in terms of fixed ordered obdd s in order to demonstrate the power of the fbdd concept we show that the verification of the circuit design for the hidden weighted bit function proposed bryant can be carried out efficiently in terms of fbdd s while this is for principal reasons impossible in terms of obdd s

global attractivity of a synchronized periodic orbit in a delayed network abstract we consider an artificial neural network where the signal transmission is of a digital mcculloch pitts nature and is delayed due to the finite switching speed of neurons amplifiers for a particular connection topology we show that all solutions starting from nonoscillatory initial states will be eventually synchronized and stabilized at a unique limit cycle and hence such a network can be used as a synchronized oscillator

riesz basis property and exponential stability of controlled euler bernoulli beam equations with variable coefficients this paper studies the basis property and the stability of a distributed system described by a nonuniform euler bernoulli beam equation under linear boundary feedback control it is shown that there is a sequence of generalized eigenfunctions of the system which forms a riesz basis for the state hilbert space the asymptotic distribution of eigenvalues the spectrum determined growth condition and the exponential stability are concluded the results are applied to a nonuniform beam equation with viscous damping of variable coefficient as a generalization of existing results for the uniform beam

state reconstruction of a distributed parameter system with exact observability abstract we study the problem of state reconstruction for exactly observable systems here we present two approaches for state reconstruction the riesz basis approach and the dual hilbert uniqueness method hum based on an iteration algorithm the riesz basis approach gives an explicit representation of the initial state of the system whereas the hum dual method gives an efficient approximation of the initial state

graph driven bdds a new data structure for boolean functions abstract ordered binary decision diagrams obdds are used as a data structure for boolean functions in the logical synthesis process for verification and test pattern generation and as part of cad tools for several important functions like arithmetical and logical units with quite different functions the indirect storage access function or the hidden weighted bit function obdds have exponential size for any ordering of the variables since an ordering of the variables may be stored as a list obdds may also be called list driven bdds two new generalized models of graph driven bdds are presented the above mentioned and many other functions can be represented in small polynomial size in this model and the usual operations on obdds can be performed efficiently also for graph driven bdds