contamination source determination in water distribution networks we consider a water distribution network where at a finite number of nodes contaminant injection can occur we consider the problem of the identification of the contaminations this problem can be considered as an optimal control problem with a networked system that is governed by a transport reaction equation the identification is based upon observations from a finite number of sensors the corresponding infinite dimensional optimization problem is defined in a hilbert space setting in order to guarantee that our optimization problem has a unique solution a quadratic regularization term is added in the objective function under certain assumptions on the relations of the travel times through the pipes we obtain a representation of this optimization problem that allows the computation of the solution on a discrete time grid by solving finite dimensional linear least squares problems on these time grids there is no discretization error since our approach is based upon an exact representation of the s

on the hyers ulam rassias stability of approximately additive mappings abstract in this paper using an idea from the paper of p gvruta j math anal appl 184 1994 431 436 the results of th m rassias j math anal appl 158 1991 106 113 shall be generalized

on the stability of functional equations on a square symmetric groupoid abstract let x be a square symmetric groupoid and y d a complete metric divisible square symmetric groupoid in this paper we obtain the hyers ulam stability problem of the functional inequality d g x y g x g y e x y for approximate mapping g x y of the functional equation f x y f x f y differing by e x 2 0 in particular we have investigated the case of f x f y h f x 1 t f y 1 t on some set y

global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws abstract this paper deals with the global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws with linearly degenerate characteristics it is shown that the system with nonlinear boundary conditions is globally exactly boundary controllable in the class of piecewise c 1 functions some physical and mechanical applications are given

hyers ulam stability of functional equations with a square symmetric operation abstract the stability of the functional equation f x y h f x f y x y s is investigated where h is a homogeneous function and is a square symmetric operation on the set s the results presented include and generalize the classical theorem of hyers obtained in 1941 on the stability of the cauchy functional equation

a self orthogonalizing efficient block adaptive filter this paper deals with the development of a unique self orthogonalizing block adaptive filter sobaf algorithm that yields efficient finite impulse response fir adaptive filter structures computationally the sobaf is shown to be superior to the least mean squares lms algorithm the consistent convergence performance which it provides lies between that of the lms and the recursive least squares rls algorithm but unlike the lms is virtually independent of input statistics the block nature of the sobaf exploits the use of efficient circular convolution algorithms such as the fft the rectangular transform rt the fermat number transform fnt and the fast polynomial transform fpt in performance the sobaf achieves the mean squared error mse convergence of a self orthogonalizing structure that is the adaptive filter converges under any input conditions at the same rate as an lms algorithm would under white input conditions furthermore the selection of the step size for the sobaf is straightforward as the range and the optimum value of the step size are independent of the input statistics

the mixed initial boundary value problem for reducible quasilinear hyperbolic systems with linearly degenerate characteristics in this paper we prove that the c0 boundedness of solution implies the global existence and uniqueness of c1 solution to the mixed initial boundary value problem for linearly degenerate reducible quasilinear hyperbolic systems with nonlinear boundary conditions and we show by an example that the c0 norm of solution may blow up in a finite time this gives the mechanism of the formation of singularities caused by the interaction of boundary conditions with nonlinear hyperbolic waves the same result is still valid for the quasilinear hyperbolic system of rich type

a unified approach to time and frequency domain realization of fir adaptive digital filters specific implementations of the finite impulse response fir block adaptive filter in the frequency domain are presented and some of their important properties are discussed the time domain block adaptive filter implemented in the frequency domain is shown to be equivalent to the frequency domain adaptive filter derived in the frequency domain provided data sectioning is done properly all of the known time and frequency domain adaptive filters 1 12 16 18 are contained in the set of possible block adaptive filter structures thus the block adaptive filter is generic and its formulation unifies the current theory of time and frequency domain fir adaptive filter structures a detailed analysis of overlap save and overlap add implementations shows that the former is to be preferred for adaptive applications because it requires less computation a fact that is not true for fixed coefficient filters

on stability of a functional equation with n variables abstract generalized hyers ulam stability problems of the quadratic functional equation f i 1 n x i n 2 i 1 n f x i 1 i j n f x i x j shall be treated under the approximately even or odd condition and some behaviors of quadratic mappings and additive mappings shall be investigated

on the generalized hyers ulam rassias stability in banach modules over a c algebra abstract in this paper we will investigate the generalized hyers ulam rassias stability of an n dimensional quadratic functional equation in banach modules over a c algebra and unitary elements

on an equation characterizing multi additive quadratic mappings and its hyers ulam stability in this paper we unify the system of functional equations defining a multi additive quadratic mapping to obtain a single equation we also prove using the fixed point method the generalized hyers ulam stability of this equation thus generalizing some known results

realization of adaptive digital filters using the fermat number transform an efficient realization of the block least mean square adaptive digital filters using fast transforms is discussed the computational complexities of the fermat number transform realization and the fixed point fast fourier transform realization are compared and their convergence properties are studied through the computer simulation of practical applications

block realization of multirate adaptive digital filters in this paper we study multirate transversal adaptive digital filters adf s based on the block least mean square blms algorithms these include an adf with decimation adfd and an adf with interpolation adfi we first formulate these filters based on the block mean squared error bmse criterion and derive blms multi rate weight adjustment algorithms and then study efficient realization of those filters it is shown that the blms adfd can be realized efficiently in the direct form or in the filter bank structure both using the fast fourier transform fft and an appropriate sectioning procedure according to our analysis of computational complexity the fft realization of the blms adfd in the filter bank structure is more efficient than in the direct form and the two structures using the fft become more efficient in comparison to the lms adfd as the number of weights increases unlike the direct form realization the filter bank realization of the blms adfd using the fft becomes more efficient as the decimation ratio increases similar results have been obtained for the blms adfi finally we investigate by computer simulation the effects of different weight adjustment algorithms and several system parameters on the performances of adfd s the results of simulation indicate that as expected the convergence speed of the blms adfd can be significantly improved by self orthogonalization of weight adjustment in the frequency domain furthermore the convergence factor of the self orthogonalizing blms adfd can be chosen such that the steady state performance of the new adfd is the same as that of the existing lms adfd

observability and controllability of piecewise affine and hybrid systems we prove in a constructive way the equivalence between piecewise affine systems and a broad class of hybrid systems described by interacting linear dynamics automata and propositional logic by focusing our investigation on the former class we show through counterexamples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems instead we propose practical numerical tests based on mixed integer linear programming

boundary feedback control in networks of open channels this article deals with the regulation of water flow in open channels modelled by saint venant equations by means of a riemann invariants approach we deduce stabilizing control laws for a single horizontal reach without friction the stability condition is extended to a general class of hyperbolic systems which can describe canal networks with more general topologies a control law design based on this condition is illustrated with a simple case study two reaches in cascade the proof of the main stability theorem is based on a previous result from li ta tsien concerning the existence and decay of classical solutions of hyperbolic systems

on a cauchy jensen functional equation and its stability abstract in this paper we obtain the general solution and stability of the cauchy jensen functional equation 2 f x y z w 2 f x z f x w f y z f y w

on the interrelationships among a class of convolutions in this paper some interrelationships among a class of circular operations are investigated based on matrix formulation it is shown that a class of convolutions representing forward backward and convolution correlation of two periodic sequences may be related to each other in terms of discrete transforms having the circular convolution property the results obtained are useful in efficient realization of adaptive digital filters using fast transforms

a fixed point method for perturbation of bimultipliers and jordan bimultipliers in c ternary algebras let a be a c ternary algebra a c bilinear t a a a is called a c ternary algebra bi multiplier if it satisfies t abc d t a b cd t a bcd abt c d for all a b c d a also the mapping t a a a is a called c ternary algebra jordan bimultiplier if it satisfies t aaa a t a a aa t a aaa aat a a for all a a using the fixed point method we investigate the generalized hyers ulam rassias stability of bimultipliers and jordan bimultipliers in c ternary algebras the concept of hyers ulam rassias stability originated from the th m rassias stability theorem that appeared in his paper th m rassias proc am math soc 72 297 1978

a fixed point technique for investigating the stability of α β γ derivations on lie c algebras abstract we apply a fixed point theorem to investigate some new stability results for derivations on lie c algebras associated with the generalized cauchy jensen type additive functional equation i 1 n f x i 1 n 1 j 1 j i n x j 2 i 1 n f x i

dynamic output feedback linearization and global stabilization abstract we present a class of single input single output nonlinear systems which are globally transformable by a dynamic output feedback control and a time varying state space transformation into a linear observable and minimum phase system we then show how those systems can be globally stabilized by a dynamic output feedback nonlinear control and how global output tracking can be achieved as well

output feedback stabilization of an unstable wave equation we consider the problem of stabilization of a one dimensional wave equation that contains instability at its free end and control on the opposite end in contrast to classical collocated boundary damper feedbacks for the neutrally stable wave equations with one end satisfying a homogeneous boundary condition the controllers and the associated observers designed in the paper are more complex due to the open loop instability of the plant the controller and observer gains are designed using the method of backstepping which results in explicit formulae for the gain functions we prove exponential stability and the existence and uniqueness of classical solutions for the closed loop system we also derive the explicit compensators in frequency domain the results are illustrated with simulations

on the stability of functional equations in banach spaces the paper is devoted to some results on the problem of s m ulam for the stability of functional equations in banach spaces the problem was posed by ulam 60 years ago

generalized hyers ulam rassias stability of n sesquilinear quadratic mappings on banach modules over c algebras assume that x is a left banach module over a unital c algebra a it is shown that almost every n sesquilinear quadratic mapping h xxxxx n a is an n sesquilinear quadratic mapping when h rx y z 1 z n h x ry z 1 z n h x y rz 1 z 2 z n h x y z 1 z 2 rz n rh x y z 1 z 2 z n r 0 r 1 holds for all x y z 1 z email protected x moreover we prove the generalized hyers ulam rassias stability of an n sesquilinear quadratic mapping on a left banach module over a unital c algebra

performance of transform domain lms adaptive digital filters in this paper we analyze the performance particularly the convergence behavior of the transform domain least mean square lms adaptive digital filter adf using the discrete fourier transform and discrete orthogonal transforms such as discrete cosine and sine transforms we first obtain the optimum wiener solution and the minimum mean squared error mse in the transform domain it is shown that the two minimum mse s in the time and transform domains are identical independently of the transforms used we then study the convergence conditions and the steady state excess mse s of the transform domain lms trlms algorithms both for the cases of having a constant and a time varying convergence factors when a constant convergence factor is used the convergence behaviors of the lms and trlms adf s appear to be almost identical provided that each has an appropriate value of the convergence factor depending on the transform used also based on the concept of a self orthogonalizing algorithm in the transform domain it is shown that the convergence speed of the trlms adf can be improved significantly for the same excess mse as that of the lms adf in addition we compare the computational complexities of the lms and trlms adf s finally we investigate by computer simulation the effects of system parameter values and different transforms on the convergence behavior of the trlms adf

on the cauchy rassias stability of a generalized additive functional equation let x and y be banach spaces and f x y an odd mapping we solve the following generalized additive functional equation rf j 1dxjr j 0 1 j 1d j lrf j 1d 1 j xjr cld 1 cl 1d 1 1 j 1df xj for all x1 xd x moreover we deal with the above functional equation in banach modules over a c algebra and obtain generalizations of the cauchy rassias stability the concept of cauchy rassias stability for the linear mapping was originated from th m rassias s stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

a generalization of the hyers ulam rassias stability of approximately additive mappings abstract in this paper we prove a generalization of the stability of approximately additive mappings in the spirit of hyers ulam and rassias

isomorphisms between c ternary algebras in this paper we prove the hyers ulam rassias stability of homomorphisms in c ternary algebras and of derivations on c ternary algebras for the following generalized cauchy jensen additive mapping 2f j 1pxj2 j 1dyj j 1pf xj 2 j 1df yj this is applied to investigate isomorphisms between c ternary algebras the concept of hyers ulam rassias stability originated from the rassias stability theorem that appeared in his paper on the stability of the linear mapping in banach spaces see proc amr math soc 72 297 300 1978

on a problem of g isac and th m rassias concerning the stability of mappings abstract we give an answer to a problem of g isac and th m rassias concerning hyers ulam rassias stability of the linear mappings a new characterization of additive mappings is also given

stability of a functional equation deriving from quadratic and additive functions in quasi banach spaces abstract in this paper we establish the general solution of the functional equation f 2 x y f 2 x y f x y f x y 2 f 2 x 2 f x and investigate the hyers ulam rassias stability of this equation in quasi banach spaces

asymptotic behavior of generalized derivations on c algebras with applications we consider generalized derivations on c algebra and we will first study the conditions for a linear generalized derivation on c algebra then we prove some theorems involving approximate linear generalized derivations on c algebra so approximate linear generalized derivations on c algebra are characterized

a functional equation having monomials as solutions for each n 1 2 3 we obtain the general solution and the stability of the functional equation f 2x y f 2x y 2 n 2 f x y f x y 6f x and we obtain the general solution and the stability of the functional equation f 2x y f 2x y 6f y 4 f x y f x y 6f x using the fixed point method we prove the generalized hyers ulam stability of these functional equations

ulam stability problem for quadratic mappings of euler lagrange abstract the purpose of this paper is to solve the stability problem of ulam for an approximate mapping f a b of the following quadratic functional equation of euler lagrange a b aq x a b bq y q ax by abq x y for all x y a with a and b linear spaces

on approximate solutions of the linear functional equation of higher order abstract we show that under some assumptions every approximate solution of the linear functional equation of higher order in single variable generates a solution of the equation that is close to it we also give a description of a procedure that yields such a solution estimate the distance between those approximate and exact solutions to the equation and discuss the problem of uniqueness moreover as a consequence we obtain some results concerning the hyers ulam stability of the equation

on the hyers ulam rassias stability of an additive functional equation in quasi banach spaces abstract in this paper we investigate the hyers ulam rassias stability of the following functional equation i 1 m f m x i j 1 j i m x j f i 1 m x i 2 f i 1 m m x i m n m 2 in quasi banach spaces

on the modelling and stabilization of flows in networks of open canals in this paper we present a model for the controlled flow of a fluid through a network of canals using a coupled system of st venant equations we then generalize in a variety of ways recent results of coron d andrea novel and bastin concerning the stabilizability around equilibrium of the flow through a single channel this work is based on the theory of quasilinear hyperbolic systems and in particular on a delicate result of li ta tsien concerning the existence and decay of global classical solutions

analysis and stabilization for networked linear hyperbolic systems of rationally dependent conservation laws in this paper for a networked linear hyperbolic partial differential equations pdes system of conservation laws the propagation periods of which are rationally dependent with coupled boundary conditions we propose a novel approach to analyze its controllability and observability in addition we propose a design method of a stabilizing controller where a boundary input with boundary valued feedback is considered first we characterize the control properties such as controllability of such a pde system in terms of the corresponding ones of a finite dimensional discrete time system defined on the boundaries of the pde system which is derived by fully exploiting the method of characteristics since the obtained discrete time system is low dimensional its analysis is relatively easier next we propose a design method of a stabilizing controller based on this discrete time system finally numerical simulations are presented to show that the proposed method is effective

isomorphisms between c ternary algebras abstract in this paper we prove the hyers ulam rassias stability of homomorphisms in c ternary algebras and of derivations on c ternary algebras for the following cauchy jensen additive mappings 0 1 f x y 2 z f x y 2 z f x 2 f z 0 2 f x y 2 z f x y 2 z f y 0 3 2 f x y 2 z f x f y 2 f z these are applied to investigate isomorphisms between c ternary algebras the concept of hyers ulam rassias stability originated from the th m rassias stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

gas flow in fan shaped networks classical solutions and feedback stabilization we analyze the subcritical gas flow through fan shaped networks of pipes that is through tree shaped networks with exactly one node where more than two pipes meet the gas flow in pipe networks is modeled by the isothermal euler equations a hyperbolic pde system of balance laws for this system we analyze stationary states and classical nonstationary solutions locally around a stationary state on a finite time interval furthermore we present a lyapunov function and boundary feedback laws to stabilize a fan shaped network around a given stationary state

unconstrained frequency domain adaptive filter an unconstrained frequency domain least mean squares uflms algorithm is presented the algorithm is based on the overlap save technique used in frequency domain filtering the proposed algorithm converges to the wiener solution without the time domain constraint on the impulse response as proposed by ferrara for a large number of taps geq32 the uflms algorithm offers a significant reduction in computation another advantage is its fast convergence for highly correlated input signals the performance of the algorithm is illustrated by a simulation

stability of the multi jensen equation abstract in this paper we study the stability in the sense of th m rassias of multi jensen equation

persistently damped transport on a network of circles in this paper we address the exponential stability of a system of transport equations with intermittent damping on a network of n geq 2 circles intersecting at a single point o the n equations are coupled through a linear mixing of their values at o described by a matrix m the activity of the intermittent damping is determined by persistently exciting signals all belonging to a fixed class the main result is that under suitable hypotheses on m and on the rationality of the ratios between the lengths of the circles such a system is exponentially stable uniformly with respect to the persistently exciting signals the proof relies on an explicit formula for the solutions of this system which allows one to track down the effects of the intermittent damping

boundary control of an anti stable wave equation with anti damping on the uncontrolled boundary abstract much of the boundary control of wave equations in one dimension is based on a single principle passivity under the assumption that control is applied through neumann actuation on one boundary and the other boundary satisfies a homogeneous dirichlet boundary condition we have recently expanded the scope of tractable problems by allowing destabilizing anti stiffness a robin type condition on the uncontrolled boundary where the uncontrolled system has a finite number of positive real eigenvalues in this paper we go further and develop a methodology for the case where the uncontrolled boundary condition has anti damping which makes the real parts of all the eigenvalues of the uncontrolled system positive and arbitrarily high i e the system is anti stable exponentially stable in negative time using a conceptually novel integral transformation we obtain extremely simple explicit formulae for the gain functions for the case with only boundary sensing available at the same end with actuation we design backstepping observers which are dual to the backstepping controllers and have explicit output injection gains we then combine the control and observer designs into an output feedback compensator and prove the exponential stability of the closed loop system

hyers ulam rassias stability of homomorphisms in quasi banach algebras associated to the pexiderized cauchy functional equation abstract in this paper we prove the hyers ulam rassias stability of homomorphisms in quasi banach algebras associated to the pexiderized cauchy functional equation this is applied to investigate homomorphisms between quasi banach algebras the concept of hyers ulam rassias stability originated from th m rassias stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

hyers ulam rassias stability of an equation of davison abstract in this work the hyers ulam rassias stability of the davison functional equation f xy f x y f xy x f y is proved

brief paper arbitrary decay rate for two connected strings with joint anti damping by boundary output feedback in this paper we are concerned with the boundary stabilization of two connected strings with middle joint anti damping for which all eigenvalues of the control free system are located on the right complex plane we first design an explicit state feedback controller to achieve exponential stability for the closed loop system consequently we design the output feedback by using infinite dimensional observer the backstepping approach is adopted in investigation it is shown that by using one boundary stabilizer only the output feedback can make the closed loop system exponentially stable with arbitrary decay rate

controllability of nonlinear discrete time systems a lie algebraic approach this paper presents a geometric study of controllability for discrete time nonlinear systems various accessibility properties are characterized in terms of lie algebras of vector fields some of the results obtained are parallel to analogous ones in continuous time but in many respects the theory is substantially different and many new phenomena appear