correcting indefinite mass matrices due to substructure uncoupling abstract the transmission simulator method of experimental dynamic substructuring captures the interface forces and motions through a fixture called a transmission simulator the transmission simulator method avoids the need to measure connection point rotations facilitates substructuring for systems with continuous connections and enriches the modal basis of the substructure model to use this approach one first attaches the transmission simulator to the experimental substructure and then measures the free modes of the assembly a finite element model of the transmission simulator is then used to subtract the transmission simulator and to couple the experimental substructure to the assembly of interest unfortunately in several cases the process of subtracting the transmission simulator has caused the mass matrix for the experimental substructure to become indefinite making the substructure model difficult or impossible to use and potentially leading to erroneous results the authors previously developed metrics that could be used to identify which modes of the experimental model led to the indefinite mass matrix this work presents a method that utilizes those metrics with a sensitivity analysis to adjust the transmission simulator mass matrix so that the subtraction does not produce an indefinite mass matrix a second method is presented in which the mass matrix is made positive definite by coupling additional mass to the substructure the methods are evaluated using both numerical and experimental test cases showing promising results

remarks on the periodic boundary value problems for first order differential equations this paper is concerned with the existence of solutions and the monotone method of first order periodic boundary value problems when the lower and upper solutions and violate the boundary conditions 0 2 and 0 2 using the topological degree theory two existence theorems are established under weaker conditions than the one side lipschitz conditions an example is given which illustrates that pbvp may not have solutions between and without further restrictions to f t u the monotone method is also discussed with some new results

a receptance based method for predicting latent roots and critical points in friction induced vibration problems of asymmetric systems this paper studies the latent roots and critical points of friction induced vibration problems in which the stiffness matrix is asymmetric the asymmetric terms are represented by a parameter or parameters related to the friction coefficient as the parameter value increases some latent roots of the asymmetric system change and even become complex with positive real parts at a critical point indicating flutter instability a method is put forward for computing the latent roots and predicting the critical value of this parameter at the flutter instability boundary of the asymmetric system based on the receptance of the symmetric system when measured receptances of the symmetric system at those locations where friction forces would be acting in the corresponding asymmetric system are available the simulated numerical example shows that this method is efficient

quasi solutions vector lyapunov functions and monotone method the notion of quasi solution which was introduced earlier has been developed in this paper further the notion of coupled quasi solutions and coupled maximal and minimal solutions has been introduced it is shown that the idea of quasi solutions leads to isolated subsystems and has obtained error estimates between solutions and quasi solutions also monotone iterative techniques have been developed to obtain coupled maximal and minimal quasi solutions

periodic boundary value problems for a class of functional differential equations in this paper we show that the method of upper and lower solutions coupled with the monotone iterative technique is valid to obtain constructive proofs of existence of solutions for nonlinear periodic boundary value problems of functional differential equations without assuming properties of monotonicity in the nonlinear part

structural modification part 2 assignment of natural frequencies and antiresonances by an added beam in this paper the inverse structural modification problem is solved in order to determine the dimensions of the cross section of a beam that when added to an original structure will assign natural frequencies or antiresonances as specified in order for this to be accomplished rotational receptances must be measured as presented in the companion paper when the modification is cast as an additional forcing term on the original structure a system of multivariate polynomials in the parameters of the beam cross section are revealed the solution of this system yields the beam parameters that assign the specified vibration behaviour

measurement of force and moment mobilities using a finite difference technique measuring only force mobilities it is possible to derive a moment mobility without the need for an externally applied moment the method uses finite differences of both forces and velocities about a central point in this way pure forces and moments can be extracted as can pure velocities and angular velocities there are however errors associated with finite difference techniques in this case the purity of the extracted quantities depends on the area over which they are measured and its significance in terms of wavelength meanwhile experimental errors such as noise dictate that the area is sufficiently large to provide differences which are incorruptible the paper aims to quantify the finite difference error in a general way free of situation specifics

two techniques in the area of the star problem in trace monoids this paper deals with decision problems related to the star problem in trace monoids which means to determine whether the iteration of a recognizable trace language is recognizable due to a theorem by richomme in i privara et al eds mfcs 94 proc lecture notes in computer science vol 841 springer berlin 1994 pp 577 586 we know that the star problem is decidable in trace monoids which do not contain a submonoid of the form a c b d cf theory comput systems 34 3 2001 193 227 here we consider a more general problem is it decidable whether for some recognizable trace language r and some recognizable or finite trace language p the intersection r p is recognizable if p is recognizable then we show that this problem is decidable iff the underlying trace monoid does not contain a submonoid of the form a c b in the case of finite languages p this problem is decidable in a c b but undecidable in a c b d

structural modification part 1 rotational receptances abstract the inverse problem of assigning natural frequencies and antiresonances by a modification to the stiffness mass and damping of a structure is addressed very simple modifications such as the addition of masses and grounded springs can be easily accommodated and require the measurement of translational receptances at the connection coordinates realistic modifications of practical usefulness such as a modification by an added beam require the measurement of rotational as well as translational receptances such data are difficult to obtain because of the practical problems of applying a pure moment one method the so called t block approach has received considerable attention in the literature but the accompanying problem of ill conditioning has not been fully addressed until now the t block is attached to the structure at the modification point so that a force applied to the t block generates a moment together with a force at the connection point between the t block and the parent structure forces and linear displacements measured on the t block together with a mass and stiffness model of the t block itself allow the problem to be cast as a special case of excitation by multiple inputs the resulting equations are generally ill conditioned but can be regularized by using a small number of independent measurements the methodology and signal processing techniques required to estimate the rotational receptances are described an experimental example is used to demonstrate the practical application of the method

on boundary value problems for singular second order functional differential equations abstract positive solutions to the boundary value problem y f x y w x 0 y x y x x a x 0 y x y x x 1 x b are obtained by applying the schauder fixed point theorem where w x is a continuous function defined on 0 1 and f x y is a function defined on 0 1 0 which satisfies certain restrictions and may have singularity at y 0 the result corrects and improves an existence theorem due to erbe and kong j comput appl math 53 1994 377 388

second order functional differential equations with past present and future dependence abstract in this paper we obtain a result on existence of extremal quasisolutions and solutions for second order functional differential equations with functional boundary conditions and past present and future dependence in order to do that we develop a generalized monotone method in presence of lower and upper solutions some examples of application are provided too

monotone method for first order functional differential equations we study periodic boundary value problems relative to a general class of first order functional differential equations for this class of problems we develop the monotone iterative technique our formulation is very general including delay differential equations functional differential equations with maxima and integro differential equations but the case where the operator defining the functional dependence is not necessarily lipschitzian is also considered

recognizable closures and submonoids of free partially commutative monoids abstract the main result of this paper is the presentation of two sufficient conditions for the closure x of x and the closure x of x respectively in any free partially commutative monoid for any regular language x to be recognizable several previously obtained sufficient conditions for x to be recognizable can be seen to imply one of those two conditions

existence of positive solutions for second order functional differential equations we afford a existence criterion of positive solutions of a boundary value problem concerning a second order functional differential equation by using the krasnoselskii fixed point theorem on cones in banach spaces moreover we also apply our results to establish several existence theorems of multiple positive solutions for some functional differential equations

recognizable subsets of some partially abelian monoids we show that in a free partially abelian monoid generated by a finite alphabet a the subset x of a containing all the words equivalent to a product of words of x is rational if x is a finite set of words each word containing at least one occurrence of any letter of a we suppose that the graph the vertices of which are letters of a and the edges of which correspond to noncommuting pairs of letters is connected

solvability of three point boundary value problems for second order differential equations with deviating arguments the monotone iterative technique is used to boundary problems for second order ordinary differential equations with deviating arguments corresponding results are formulated when the problem has extremal solutions or weakly coupled extremal quasi solutions

quasi solutions for generalized second order differential equations with deviating arguments this paper deal with boundary value problems for generalized second order differential equations with deviating arguments existence of quasi solutions and solutions are proved by monotone iterative method examples with numerical results are added

positive solutions of three point boundary value problems for second order impulsive differential equations with advanced arguments in this paper we discuss three point boundary value problems for second order impulsive differential equations with advanced arguments we establish sufficient conditions under which such problems have positive solutions to obtain the results we use the fixed point index

positive solutions to a multi point boundary value problem with delay abstract the paper is concerned with the existence of positive solutions for the nonlinear multi point boundary value problems of a class of second order delay differential equations our results improve some recent results obtained in d q jiang multiple positive solutions for boundary value problems of second order delay differential equations appl math lett 15 2002 575 583 dingyong bai yuantong xu existence of positive solutions for boundary value problems of second order delay differential equations appl math lett 18 2005 621 630

on recognizable subsets of free partially commutative monoids on montre que dans un mono de partiellement commutatif libre engendre par un alphabet fini a le sous ensemble x de a forme des mots equivalents a un des mots de x est reconnaissable si x est reconnaissable et si tout facteur iterant de x a un graphe de non commutation connexe

periodic boundary value problem for the second order impulsive functional differential equations this paper considers the existence of extreme solutions of the periodic boundary value problem for second order functional differential equations by using the method of lower and upper solutions coupled with monotone iterative technique

multi point boundary value problems for second order functional differential equations this paper is concerned with the existence of extreme solutions of multi point boundary value problem for a class of second order functional differential equations we introduce a new concept of lower and upper solutions by using the method of upper and lower solutions and monotone iterative technique we obtain the existence of extreme solutions

existence of multiple quasifixed points of mixed monotone operators by iterative techniques fixed point theorems of mixed monotone operators by iterative technique in a banach space with the ordering relative to cone k the notion of coupled quasi fixed points is introduced and the main result shows their existence

existence and approximation of solutions for nonlinear functional differential equations with periodic boundary value conditions abstract this paper is concerned with the existence and approximation of solutions for a class of first order functional differential equations with periodic boundary conditions we present a new comparison result and extend previous results

remarks on periodic boundary value problems for functional differential equations we extend some results on existence and approximation of solution for a class of first order functional differential equations with periodic boundary conditions we show the validity of the monotone iterative technique under weaker hypotheses and present some examples

periodic boundary value problems for delay differential equations with impulses existence and approximation of solutions for an impulsive delay differential equation with periodic boundary value conditions are presented we use comparison principles and monotone iterative techniques

existence results to delay fractional differential equations with nonlinear boundary conditions this paper concerns boundary value problems for delay fractional differential equations we formulate sufficient conditions under which such problems have extremal solutions in the corresponding region delay differential inequalities are also discussed examples are given to illustrate the effectiveness of the results

decidability undecidability and pspace completeness of the twins property in the tropical semiring we solve a problem already investigated by mohri in 1997 we show that the twins property for weighted finite automata over the tropical semiring is decidable and pspace complete we also point out that it is undecidable whether two given states are twins

periodic boundary value problems for the second order functional differential equations this paper considers the existence of extreme solutions of the periodic boundary value problems for second order functional differential equations a new concept of lower and upper solutions is introduced and we present a new comparison principle meanwhile we extend previous results

coupled fixed points of nonlinear operators with applications a partir de quasi solutions couplees des problemes aux valeurs initiales pour des equations differentielles ordinaires on introuit le concept de points fixes couples abstraits pour certains operateurs on donne des theoremes d existence

first and second order discontinuous functional differential equations with impulses at fixed moments abstract we give sufficient conditions for the existence of extremal solutions to discontinuous and functional differential equations with impulses our main results are new even for ordinary differential equations without impulses

coupled fixed points of multivalued operators and first order odes with state dependent deviating arguments abstract we establish a coupled fixed point theorem for a meaningful class of mixed monotone multivalued operators and then we use it to derive some results on the existence of quasisolutions and unique solutions to first order functional differential equations with state dependent deviating arguments our results are very general and can be applied to functional equations featuring discontinuities with respect to all of their arguments but we emphasize that they are new even for differential equations with continuously state dependent delays

existence theorems for a class of nonlocal differential equations abstract a class of nonlocal second order ordinary differential equations of the form y x f x y x y x y x for continuous f and is studied the equation is supplemented with none one or two robin boundary conditions depending on whether the interval of interest i is finite semi infinite or infinite the only other restriction on the function is that it maps i into itself sufficient conditions for the existence of a solution are found which include the assumption of the existence of upper and lower solutions the upper and lower solutions provide bounds for the solution on i

active vibration suppression by pole zero placement using measured receptances the paper addresses the problem of pole zero assignment using the receptance method in active vibration control and has applications particularly in vibration absorption and detuning of structures to avoid resonance an output feedback approach is described that makes use of measured receptances there being no requirement at all for the m c k matrices usually obtained by finite elements therefore in the controller design the approximations assumptions and other modelling errors are largely eliminated in addition the method does not require the use of model reduction techniques or the estimation of unmeasured states by an observer an advantage of the output feedback method over state feedback is that collocated actuator sensor arrangements become possible however this is achieved at the expense of creating characteristic equations nonlinear in the control gains numerical examples are provided to illustrate the working of the method this is followed by a series of experimental tests carried out using collocated accelerometers and inertial actuators on a t shaped plate in a series of experiments poles and zeros are assigned separately and simultaneously stability robustness is demonstrated by applying a constraint to the singular values of the matrix return difference

boundary value problems for singular second order functional differential equations abstract we consider general linear boundary value problems for equations of the form y f x y x 0 0 x x is continuous and f x y has a singularity at y 0 the results improve and extend earlier results for the case x x due to taliaferro 1979 and gatica 1989

existence of solutions of boundary value problems for differential equations with delayed arguments we study the existence and approximation of solution of boundary value problems for differential equations with delayed arguments sufficient conditions are established for the existence of a unique solution or extremal ones of the given problem a monotone iterative technique is applied

nonlinear boundary value problems for second order differential equations with causal operators in this paper we deal with second order differential equations with causal operators to obtain sufficient conditions for existence of solutions we use a monotone iterative method we investigate both differential equations and differential inequalities an example illustrates the results obtained

on monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations abstract in this paper we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions of first and second order periodic boundary value problems and periodic solutions of functional differential equations we obtain some new results relative to the lower solution and upper solution with

boundary value problems for first order impulsive delay differential equations with a parameter in this paper by means of the method of upper and lower solutions and monotone iterative technique the existence of maximal and minimal solutions of the boundary value problems for first order impulsive delay differential equations is established

monotone iterative method for first order functional difference equations with nonlinear boundary value conditions in this paper we show that the method of monotone iterative coupled with the upper and lower solutions is valid to obtain constructive proofs to the existence of solutions for first order functional difference equations with nonlinear boundary value conditions an example is given to illustrate the results obtained

new results on the star problem in trace monoids we prove that if it is decidable whether x is recognizable for a recognizable subset x of a free partially commutative monoid then it is decidable whether a recognizable subset of a free partially commutative monoid possesses the finite power property we prove that if any trace of a set x is connected we can decide whether x possesses the finite power property finally we also show that if x is a finite set containing at most four traces or at most two connected traces it is decidable whether x is recognizable

existence of positive solutions to second order four point impulsive differential problems with deviating arguments in this paper we discuss four point boundary value problems for impulsive second order differential equations with deviating arguments we investigate separately cases when arguments are of delayed or advanced types we formulate sufficient conditions under which our problems have at least one or two positive solutions to obtain our results we apply the fixed point index

periodic boundary value problems of second order impulsive differential equations abstract this paper discusses periodic boundary value problems of second order impulsive differential equations by using schaeffer s fixed point theorem and monotone iterative technique some existence results are obtained

existence theorems of coupled fixed points abstract by associating with a mixed monotone operator a monotone operator on product space several existence theorems of coupled fixed points are proved

advanced differential equations with nonlinear boundary conditions we investigate the existence of solutions for advanced differential equations with nonlinear boundary conditions sufficient conditions when the problem has extremal solutions or a unique solution are formulated linear advanced differential inequalities are also discussed

positive solutions for three point one dimensional p laplacian boundary value problems with advanced arguments this paper considers the existence of positive solutions for advanced differential equations with one dimensional p laplacian to obtain the existence of at least three positive solutions we use a fixed point theorem due to avery and peterson

existence of positive solutions for boundary value problem of second order fde abstract we use a fixed point theorem in cones to investigate the existence of positive solutions for boundary value problem of a second order functional differential equation fde with the form y t r t y t 0 0 y t y t t r t 0 y t y t n t 1 t 1 a where y t y t for a we allow that r t has the singularity at the endpoints t 0 and t 1 of 0 1 our results include the situations that f is either superlinear or sublinear

on some equations in free partially commutative monoids abstract we characterize the solutions of all the equations in two unknowns in the free partially commutative monoids and we show that the connected solutions are cyclic next we define the transposition relation m and n are transposed iff m xy and n yx and the conjugacy relation m and n are conjugate iff m n we show that the conjugacy is the transitive closure of the transposition and that the set of conjugacy factors is a recognizable subset of the free partially commutative monoid

monotone iterative technique for second order delayed periodic problem in banach spaces in this paper we deal with the existence of periodic solutions for second order functional differential equation with delay in e u t f t u t u t t r where e is an ordered banach space f r e e e is a continuous function which is periodic in t and 0 is a constant we first build a new maximum principle for the periodic solutions of the corresponding linear equation with delay with the aid of this maximum principle under the assumption that the nonlinear function is quasi monotonicity we study the existence of the minimal and maximal periodic solutions for abstract delayed equation by combining perturbation method and monotone iterative technique of the lower and upper solutions

the star problem and the finite power property in trace monoids we deal with the star problem in trace monoids which means to decide whether the iteration of a recognizable trace language is recognizable we consider trace monoids kn a1 b1 an bn our main result asserts that the star problem is decidable in some trace monoid m iff it is decidable in the biggest kn submonoid m consequently future research on the star problem can focus on the trace monoids kn we develop the main results of the paper for the finite power problem then we establish the link to the star problem by applying the recently shown decidability equivalence between the star problem and the finite power problem d kirsten and g richomme 2001 theory comput systems34 193 227

maximal serializability of iterated transactions abstract the serializability condition is usually considered in order to maintain the consistency of a database in the presence of conflicting accesses to the database performed by concurrent transactions this serializability condition is considered herein as a general synchronization problem among transactions or processes which can be iterated infinitely often the behaviour of such a system of transactions is represented by an infinite word over the alphabet of the operations performed by the transactions then a characterization of the prefixes of such behaviours is given and it is shown that satisfying the serializability condition so called correct behaviours is given and it is shown that the set of all correct behaviours can be controlled by a finite automaton as an example the classical dining philosophers problem is shown to be entirely modelled and solved as a serializability problem