variational properties and orbital stability of standing waves for nls equation on a star graph we study standing waves for a model of nonlinear schr odinger equation on a graph the graph is obtained joining n halflines at a vertex i e it is a star graph at the vertex an interaction occurs due to a boundary condition of delta type with strength alpha leqslant 0 which includes the free or kirchhoff case alpha 0 there imposed the nonlinearity is of focusing power type the dynamics is given by an equation of the form i frac d dt psi t h psi t psi t 2 mu psi t where h is the s a operator which generates the linear schr odinger dynamics on the graph in the hilbert space l 2 gg we show the existence of several families of standing waves solutions of the form phi t e i omega t psi omega where psi omega is a vector amplitude parametrized by a frequency omega they exist for every sign of the coupling at the vertex attractive alpha 0 and for every omega frac alpha 2 n 2 the number of the families depends on the number n of the edges of the graph we moreover determine the ground state which is the standing wave the amplitude of which minimizes the action on the natural nehari constraint and order the various families of standing waves according to their increasing action thus determining a nonlinear spectrum of the problem finally we show that the ground state is orbitally stable for every allowed omega if the nonlinearity is subcritical or critical for supercritical nonlinearities there exists an omega frac alpha 2 n 2 such that the ground state is orbitally stable for frac alpha 2 n 2 omega omega action minimization requires technical subtleties in particular an adaptation of decreasing rearrangements on a star graph is developed with a generalization of the p olya szeg h o inequality

chaos synchronization of different chaotic systems subjected to input nonlinearity abstract in this paper a unified mathematical expression describing a class of synchronization systems is presented for which the problem of chaos synchronization between different chaotic systems with input nonlinearity has been studied based on lyapunov stability theory a sliding mode controller and some generic sufficient conditions for global asymptotic synchronization are designed such that the error dynamics of two different chaotic motions satisfy stability in the lyapunov sense in spite of the input nonlinearity this technique is applied to achieve chaos synchronization of three pairs of different chaotic systems lorenz chen chen liu and liu lorenz in drive response structure the numerical simulation results demonstrate the validity and feasibility of the proposed controller

fast and explicit wentzel kramers brillouin mode sum for the bottom interacting field including leaky modes a fast and explicit method is presented for calculating the bottom interacting field by means of a mode sum using the wentzel kramers brillouin approximation for the eigenfunctions and the tindle weston formula for eigenvalue spacing both trapped and leaky modes are automatically included requiring no numerical inversions for either eigenfunctions or eigenvalues examples are provided which demonstrate the speed and accuracy of the approach by comparison with reference solutions the importance of leaky modes especially in range dependent environments with variable water depth is demonstrated a simple criterion for neglecting leaky modes is developed

existence of a tree of stieltjes strings corresponding to two given spectra transversal vibrations of a plane rooted tree of stieltjes strings are considered with dirichlet boundary conditions at each pendant vertex continuity and kirchhoff conditions are imposed at each interior vertex except the root the dirichlet problem is that with the dirichlet condition at the root and the neumann problem is that with continuity and kirchhoff conditions at the root it is shown that strict interlacing is a sufficient condition for two sequences of real numbers to be the spectra of neumann and dirichlet problems generated by stieltjes string recurrent relations on any prescribed tree

a matched peak inversion approach for ocean acoustic travel time tomography a new approach for the inversion of travel time data is proposed based on the matching between model arrivals and observed peaks using the linearized model relations between sound speed and arrival time perturbations about a set of background states arrival times and associated errors are calculated on a fine grid of model states discretizing the sound speed parameter space each model state can explain identify a number of observed peaks in a particular reception lying within the uncertainty intervals of the corresponding predicted arrival times the model states that explain the maximum number of observed peaks are considered as the more likely parametric descriptions of the reception these model states can be described in terms of mean values and variances providing a statistical answer matched peak solution to the inversion problem a basic feature of the matched peak inversion approach is that each reception can be treated independently i e no constraints are posed from previous reception identification or inversion results accordingly there is no need for initialization of the inversion procedure and furthermore discontinuous travel time data can be treated the matched peak inversion method is demonstrated by application to 9 month long travel time data from the thetis 2 tomography experiment in the western mediterranean sea

distribution theory for discontinuous test functions and differential operators with generalized coefficients investigation of the differential operators with the generalized coefficients having singular support on a disjoint set of points requires the consideration of the distribution theory with the set of discontinuous test functions such a distribution theory for test functions having discontinuity at one point is developed a four parameter family of schrodinger operators formed by the operators with singular potential singular metrics and singular gauge field is considered it is proved that this family of singular interactions describes all possible selfadjoint extensions of the second derivative operator defined on the functions vanishing in a neighbourhood of the point approximation by operators with smooth coefficients is discussed c 1996 academic press inc

synchronization of a chaotic finance system synchronization strategies of a three dimensional chaotic finance system are investigated in this paper based on lyapunov stability theory and routh hurwitz criteria some effective controllers are designed for the global asymptotic synchronization on different conditions when the system parameters are known the hybrid feedback control and a method based on special matrix structure are adopted respectively to realize the synchronization of the chaotic finance system when the parameters are unknown the active control is extended and introduced to realize the synchronization numerical simulations show the validity and feasibility of the synchronization schemes

integrable models from twisted half loop algebras this paper is devoted to the construction of new integrable quantum mechanical models based on certain subalgebras of the half loop algebra of various results about these subalgebras are proven by presenting them in the notation of the st petersburg school these results are then used to demonstrate the integrability and find the symmetries of two types of physical system twisted gaudin magnets and calogero type models of particles on several half lines meeting at a point

chaotic sliding mode controllers for uncertain time delay chaotic systems with input nonlinearity this paper presents a novel robust chaotic controller for stabilizing uncertain time delay chaotic systems with input nonlinearity based on dynamic output sliding mode control smc lyapunov theory and linear matrix inequality lmi technique the stability of overall uncertain time delay chaotic system with input nonlinearity under the proposed control scheme is guaranteed without the state predictor the selection of sliding surface and the design of control law are two important issues which have been addressed a priori knowledge of upper bounds of uncertainties is not required furthermore the proposed scheme ensures robustness against input nonlinearity time delays nonlinear real valued functions parameter uncertainties and disturbances simultaneously finally simulation results demonstrate the validity of the proposed control methodology

asymptotic behavior of jost functions near resonance points for wigner von neumann type potentials in this work are considered radial schrodinger operators v r e where v r a sin br r w r with w r bounded w r o r 2 at infinity a b real the asymptotic behavior of the jost function and the scattering matrix near the resonance point e0 b2 4 are studied if a b then this point may be an eigenvalue embedded in the continuous spectrum the leading behavior of the jost function for all values of a and b were determined somewhat surprisingly situations were found where the jost function becomes singular as e e0 even if e0 is an embedded eigenvalue moreover it was found that the scattering matrix is always discontinuous at e0 except in a few special cases it is also shown that the asymptotics for the jost function and the scattering matrix hold under weaker assumptions on w r in particular an angular momentum term l l 1 r 2 may be incorporated into w r the results were also applied to a whole line problem with a potential v x such that v x 0 for x 0 and v x of wigner von neumann

a hamiltonian method for finding broadband modal eigenvalues for shallow water waveguides over a layered elastic bottom modal eigenvalues can be determined by searching the locations in the complex plane of the horizontal wave number at which the complex phase function is a multiple of c t tindle and n r chapman j acoust soc am 96 1777 1782 1994 in this paper a hamiltonian method is introduced for tracing the path in the complex plane along which the phase function keeps real the hamiltonian method can also be extended to compute the broadband modal eigenvalues or the modal dispersion curves in the pekeris waveguide with fluid elastic bottoms for each proper or leaky normal mode a different hamiltonian is constructed in the complex plane and used to trace automatically the complex dispersion curve with the eigenvalue in a reference frequency as the initial value in contrast to the usual methods the dispersion curve for each mode is determined individually the hamiltonian method shows good performance by comparing with kraken

high energy analysis and levinson s theorem for the selfadjoint matrix schrodinger operator on the half line the matrix schrodinger equation with a selfadjoint matrix potential is considered on the half line with the general selfadjoint boundary condition at the origin when the matrix potential is integrable the high energy asymptotics are established for the related jost matrix the inverse of the jost matrix and the scattering matrix under the additional assumption that the matrix potential has a first moment levinson s theorem is derived relating the number of bound states to the change in the argument of the determinant of the scattering matrix

star graphs and seba billiards we derive an exact expression for the two point correlation function for quantum star graphs in the limit as the number of bonds tends to infinity this turns out to be identical to the corresponding result for certain eba billiards in the semiclassical limit the reasons for this are discussed the formula we derive is also shown to be equivalent to a series expansion for the form factor the fourier transform of the two point correlation function previously calculated using periodic orbit theory

the free dirac operator on compact and noncompact graphs the free dirac operator defined on composite one dimensional structures consisting of finitely many half lines and intervals is investigated the influence of the connection points between the constituents is modeled by transition conditions for the wave functions or equivalently by different self adjoint extensions of the dirac operator general relations between the parameters of the extensions and the eigenvalues resp the scattering coefficients are derived and then applied to the cases of a bundle of half lines a point defect a branching line and an eye shaped structure

four parameter point interaction in 1d quantum systems the author constructs a four parameter point interaction for a nonrelativistic particle moving on a line as the limit of a short range interaction with a range tending toward zero for particular choices of the parameters one can obtain a delta interaction or the so called delta interaction the hamiltonian corresponding to the four parameter point interaction is shown to correspond to the four parameter self adjoint hamiltonian of the free particle moving on the line with the origin excluded

quantum graphs with singular two particle interactions we construct quantum models of two particles on a compact metric graph with singular two particle interactions the hamiltonians are self adjoint realizations of laplacians acting on functions defined on pairs of edges in such a way that the interaction is provided by boundary conditions in order to find such hamiltonians closed and semi bounded quadratic forms are constructed from which the associated self adjoint operators are extracted we provide a general characterization of such operators and furthermore produce certain classes of examples we then consider identical particles and project to the bosonic and fermionic subspaces finally we show that the operators possess purely discrete spectra and that the eigenvalues are distributed following an appropriate weyl asymptotic law

dispersion for the schrodinger equation on networks in this paper we consider the schrodinger equation on a network formed by a tree with the last generation of edges formed by infinite strips we give an explicit description of the solution of the linear schrodinger equation with constant coefficients this allows us to prove dispersive estimates which in turn are useful for solving the nonlinear schrodinger equation the proof extends also to the laminar case of positive step function coefficients having a finite number of discontinuities

index theorems for quantum graphs in geometric analysis an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned sometimes using the heat kernels of two higher order differential operators as an intermediary in this paper the case of quantum graphs is addressed a quantum graph is a graph considered as a singular one dimensional variety and equipped with a second order differential hamiltonian h a laplacian with suitable conditions at vertices for the case of scale invariant vertex conditions i e conditions that do not mix the values of functions and of their derivatives the constant term of the heat kernel expansion is shown to be proportional to the trace of the internal scattering matrix of the graph this observation is placed into the index theory context by factoring the laplacian into two first order operators h a a and relating the constant term to the index of a an independent consideration provides an index formula for any differential operator on a finite quantum graph in terms of the vertex conditions it is also found that the algebraic multiplicity of 0 as a root of the secular determinant of h is the sum of the nullities of a and a

on δ like potential scattering on star graphs we discuss the potential scattering on the noncompact star graph the schrodinger operator with the short range potential localized in a neighborhood of the graph vertex is considered we study the asymptotic behavior of the corresponding scattering matrix in the zero range limit it has been known for a long time that in dimension 1 there is no non trivial hamiltonian with the distributional potential i e the potential acts as a totally reflecting wall several authors have in recent years studied the scattering properties of the regularizing potentials e 2q x e approximating the first derivative of the dirac delta function a non zero transmission through the regularized potential has been shown to exist as e 0 we extend these results to star graphs with the point interaction which is an analog of the potential on the line we prove that generically such a potential on the graph is opaque we also show that there exists a countable set of resonant intensities for which a partial transmission through the potential occurs this set of resonances is referred to as the resonant set and is determined as the spectrum of an auxiliary sturm liouville problem associated with q on the graph

bound states in point interaction star graphs we discuss the discrete spectrum of the hamiltonian describing a two dimensional quantum particle interacting with an infinite family of point interactions we suppose that the latter are arranged into a star shaped graph with n arms and a fixed spacing between the interaction sites we prove that the essential spectrum of this system is the same as that of the infinite straight polymer but in addition there are isolated eigenvalues unless n 2 and the graph is a straight line we also show that the system has many strongly bound states if at least one of the angles between the star arms is small enough examples of eigenfunctions and eigenvalues are computed numerically

a factorization of the scattering matrix for the schrodinger equation and for the wave equation in one dimension for the one dimensional schrodinger equation with a potential decaying at both ends of the real axis the scattering matrix of the potential is given explicitly in terms of the scattering matrices corresponding to the fragments of this potential a similar result also holds for the wave equation in a nonhomogeneous nondispersive medium where the wave speed has the same asymptotics at both ends of the real line

comment on factorization of scattering matrices due to partitioning of potentials in one dimensional schrodinger type equations j math phys 37 5897 1996

appendix resonances on a simple graph we study the scattering problem on a graph consisting of a line with a finite length appendix the two parts are coupled through boundary conditions depending on three parameters the motion on the line is free while the appendix supports a potential the appendix bound states give rise to a ladder of resonances we construct the resolvent and solve the corresponding pole condition for a weak coupling in general the condition only admits an analytic solution in particular cases we find the pole positions numerically for a linear potential and show that the poles eventually return to the real axis when the coupling strength increases

on multiplicity of a quantum graph spectrum the sturm liouville equations on the edges of a metric connected graph together with the boundary and matching conditions at the vertices generate a spectral problem for a self adjoint operator it is shown that if the graph is not cyclically connected then the maximal multiplicity of an eigenvalue of such an operator is gt ptin where is the cyclomatic number of the graph and gt and ptin are the number of edges and the number of interior vertices respectively for the tree obtained by contracting all the cycles of the graph into vertices if the graph is cyclically connected then the maximal multiplicity of an eigenvalue is 1

green function approach for general quantum graphs we present a recursive prescription to calculate the exact green function for general quantum graphs for the closed case the expression for the poles of g which gives the individual eigenstates has the structure of a semiclassical formula where the sum over the periodic orbit is already performed as applications we discuss eigenstate localization for a three arm closed star and filter like mechanisms for transmission throughout an open trident graph

ocean acoustic tomography based on peak arrivals the recently introduced notion of peak arrivals athanassoulis and skarsoulis j acoust soc am 97 3575 3588 1995 defined as the significant local maxima of the arrival pattern is studied here as a modeling basis for performing ocean tomography peak arrivals constitute direct theoretical counterparts of experimentally observed peaks and offer a complete modeling of experimental observables even in cases where ray or modal arrivals cannot be resolved the coefficients of the resulting peak inversion system relating travel time with sound speed perturbations are explicitly calculated in the case of range independent environments using normal mode theory to apply the peak inversion scheme to tomography the peak identification and tracking problem is examined from a statistical viewpoint maximum likelihood and least square solutions are derived and discussed the particular approach adopted treats the identification and tracking problem in close relation to the inversion procedure all possibi

consistency and accuracy of perturbative inversion methods for group travel time data perturbation theory for ocean acoustic modal group speed responses to small environmental changes is investigated with regard to its applicability to ocean acoustic tomography assuming adiabaticity the inverse problem for each vertical eigenmode is an integral equation whose kernel involves the eigenfunction and its frequency derivative a proof is given for the equivalence of two dissimilar forms of the integral equation numerical examples are given for the inversion kernel for four types of sound speed profiles and then the parameter range amplitude and scale size in which perturbation theory is accurate is examined it is found that the range of validity is determined not only by the amplitude of the perturbations but also by their vertical scale size

second order perturbations of peak arrival times due to sound speed variations the concept of peak arrivals is used to study the second order arrival time behavior of broadband tomographic signals due to sound speed variations peak arrivals defined as the local maxima of the pressure amplitude at the receiver in the time domain are the exact theoretical counterparts of the experimental observables in ocean acoustic tomography and they offer a uniform description of all the peaks in the arrival pattern independent of whether they can be resolved as ray modal arrivals or not closed form expressions for the first and second sound speed derivatives of peak arrival times are derived in terms of sound speed derivatives of the green s function using normal mode theory the sound speed derivatives of the green s function are analytically expressed for the case of a range independent medium in terms of eigenvalues and eigenfunctions at the reference state numerical examples are given for range independent environments motivated from the thetis 2 experiment showing different kinds of

a multilevel sampling method for detecting sources in a stratified ocean waveguide in the reconstruction process of sound waves in a 3d stratified waveguide a key technique is to effectively reduce the huge computational demand in this work we propose an efficient and simple multilevel reconstruction method to locate the accurate position of a point source in a stratified ocean the proposed method can be viewed as a direct sampling method since no solutions of optimizations or linear systems are involved the novel method exhibits several strengths fast convergence robustness against noise advantages in computational complexity and applicability for a very small number of receivers

the number of eigenvalues of the matrix schrodinger operator on the half line with general boundary conditions we prove a bound of the bargmann birman schwinger type on the number of eigenvalues of the matrix schrodinger operator on the half line with the most general self adjoint boundary condition at the origin and with selfadjoint matrix potentials that are integrable and have a finite first moment

on the number of states bound by one dimensional finite periodic potentials bound states and zero energy resonances of one dimensional finite periodic potentials are investigated by means of levinson s theorem for finite range potentials supporting no bound states a lower bound for the reduced time delay at threshold is derived

a numerical method for acoustic normal modes for shear flows abstract the normal modes and their propagation numbers for acoustic propagation in wave guides with flow are the eigenvectors and eigenvalues of a boundary value problem for a non standard sturm liouville problem it is non standard because it depends non linearly on the eigenvalue parameter in the classical problem for ducts with no flow the problem depends linearly on the eigenvalue parameter in this paper a method is presented for the fast numerical solution of this problem it is a generalization of a method that was developed for the classical problem a finite difference method is employed that combines well known numerical techniques and a generalization of the sturm sequence method to solve the resulting algebraic eigenvalue problem then a modified richardson extrapolation method is used that dramatically increases the accuracy of the computed eigenvalues the method is then applied to two problems they correspond to acoustic propagation in the ocean in the presence of a current and to acoustic propagation in shear layers over flat plates

high frequency numerical analytic approximations for the separable acoustic wave equation abstract an algorithm which employs a combination of asymptotic and numerical methods to solve a sturm liouville problem arising from a separable acoustic wave equation is presented error criteria for switching between methods are derived implementation requires a decomposition of the index of refraction profile into separable subprofiles computing times and accuracies are compared with conventional methods

uniform existence of the integrated density of states for random schrodinger operators on metric graphs over zd abstract we consider ergodic random schrodinger operators on the metric graph z d with random potentials and random boundary conditions taking values in a finite set we show that normalized finite volume eigenvalue counting functions converge to a limit uniformly in the energy variable this limit the integrated density of states can be expressed by a closed shubin pastur type trace formula it supports the spectrum and its points of discontinuity are characterized by existence of compactly supported eigenfunctions among other examples we discuss random magnetic fields and percolation models

global synchronization of chaotic systems via linear balanced feedback control global synchronization of two identical chaotic systems by the linear balanced feedback control and the gerschgorin theorem is studied in this paper linear feedback control method based on lyapunov stability theory and extreme approach is introduced to design controller to synchronize two identical chaotic systems two techniques are applied to four scroll chaotic systems for determining the balanced feedback gains a numerical example is given to illuminate the design procedure and advantage of the results derived

factorization of scattering matrices due to partitioning of potentials in one dimensional schrodinger type equations the one dimensional schrodinger equation and two of its generalizations are considered as they arise in quantum mechanics wave propagation in a nonhomogeneous medium and wave propagation in a nonconservative medium where energy may be absorbed or generated generically the zero energy transmission coefficient vanishes when the potential is nontrivial but in the exceptional case this coefficient is nonzero resulting in tunneling through the potential it is shown that any nontrivial exceptional potential can always be fragmented into two generic pieces furthermore any nontrivial potential generic or exceptional can be fragmented into generic pieces in infinitely many ways the results remain valid when dirac delta functions are included in the potential and other coefficients are added to the schrodinger equation for such schrodinger equations factorization formulas are obtained that relate the scattering matrices of the fragments to the scattering matrix of the full problem

a method for approximating acoustic field amplitude uncertainty caused by environmental uncertainties in underwater acoustics the accuracy of computational field predictions is commonly limited by uncertainty in environmental parameters an approximate technique for determining the probability density function pdf of computed field amplitude a from known environmental uncertainties is presented here the technique can be applied to several n uncertain parameters simultaneously requires n 1 field calculations and can be used with any acoustic field model the technique implicitly assumes independent input parameters and is based on finding the optimum spatial shift between field calculations completed at two different values of each uncertain parameter this shift information is used to convert uncertain environmental parameter distributions into pdf a the technique s accuracy is good when the shifted fields match well its accuracy is evaluated in range independent underwater sound channels via an l1 error norm defined between approximate and numerically converged results for pdf a in 50 m a

leaky quantum graphs approximations by point interaction hamiltonians we prove an approximation result showing how operators of the type x in where is a graph can be modelled in the strong resolvent sense by point interaction hamiltonians with an appropriate arrangement of the potentials the result is illustrated on finding the spectral properties in cases when is a ring or a star furthermore we use this method to indicate that scattering on an infinite curve which is locally close to a loop shape or has multiple bends may exhibit resonances due to quantum tunnelling or repeated reflections

a numerical method for bottom interacting ocean acoustic normal modes in this paper we present a finite difference method to numerically determine the normal modes for the sound propagation in a stratified ocean resting on a stratified elastic bottom the compound matrix method is used for computing an impedance condition at the ocean elastic bottom interface the impedance condition is then incorporated as a boundary condition into the finite difference equations in the ocean yielding an algebraic eigenvalue problem for each fixed mesh size this eigenvalue problem is solved by a combination of efficient numerical methods the richardson mesh extrapolation procedure is then used to substantially increase the accuracy of the computation two applications are given to demonstrate the speed accuracy and efficiency of the method

boundary conditions at the derivative of a delta function the author derives the joining conditions on psi at a point where the potential is the nth derivative of a dirac delta function

chaos synchronization between two different chaotic systems via nonlinear feedback control this work presents chaos synchronization between two different chaotic systems via nonlinear feedback control on the basis of a converse lyapunov theorem and balanced gain scheme control gains of controller are derived to achieve chaos synchronization for the unified chaotic systems numerical simulations are shown to verify the results

a numerical method for ocean acoustic normal modes the method of normal modes is frequently used to solve acoustic propagation problems in stratified oceans the propagation numbers for the modes are the eigenvalues of the boundary value problem to determine the depth dependent normal modes errors in the numerical determination of these eigenvalues appear as phase shifts in the range dependence of the acoustic field such errors can severely degrade the accuracy of the normal mode representation particularly at long ranges in this paper we present a fast finite difference method to accurately determine these propagation numbers and the corresponding normal modes it consists of a combination of well known numerical procedures such as sturm sequences the bisection method newton s and brent s methods richardson extrapolation and inverse iteration we also introduce a modified richardson extrapolation procedure that substantially increases the speed and accuracy of the computation

a note on the relationship between finite difference and shooting methods for ode eigenvalue problems finite difference methods and shooting methods are two standard classes of techniques for solving ordinary differential equation eigenvalue problems we first show that a sturm sequence method often used for solving the finite difference eigenvalue problem may be interpreted in the shooting framework then we find that the sturm sequence procedure is easily extended to more complicated problems this enables the shooting method to guarantee convergence to specified subsets of the modes of the problem without the usual requirement of an initial guess for the eigenvalues

rational operators for filtering the parabolic equation pe method has been applied to approximate the wave equation construct radiation conditions solve scattering problems construct initial conditions and derive energy flux conditions a new application of the pe method filters based on rational approximations of depth operators is described and tested the rational approximation is designed to act as the identity operator on the desired part of the spectrum of the depth separated wave equation and to annihilate other parts of the spectrum this approach does not require explicit knowledge of the spectrum the applications of the filter include directly solving eigenvalue problems annihilating components of the wave number spectrum generating initial conditions at the source range and eliminating gibbs oscillations that arise in energy conserving pe solutions

kirchhoff s rule for quantum wires we formulate and discuss one particle quantum scattering theory on an arbitrary finite graph with n open ends and where we define the hamiltonian to be minus the laplace operator with general boundary conditions at the vertices this results in a scattering theory with n channels the corresponding on shell s matrix formed by the reflection and transmission amplitudes for incoming plane waves of energy e 0 is given explicitly in terms of the boundary conditions and the lengths of the internal lines it is shown to be unitary which may be viewed as the quantum version of kirchhoff s law we exhibit covariance and symmetry properties it is symmetric if the boundary conditions are real also there is a duality transformation on the set of boundary conditions and the lengths of the internal lines such that the low energy behaviour of one theory gives the high energy behaviour of the transformed theory finally we provide a composition rule by which the on shell s matrix of a graph is factorizable in terms of the s matrices of its subgraphs all proofs use only known facts from the theory of self adjoint extensions standard linear algebra complex function theory and elementary arguments from the theory of hermitian symplectic forms

pragmatical adaptive chaos control from a new double van der pol system to a new double duffing system a new pragmatical adaptive control method for different chaotic systems is proposed traditional chaos control is limited to decrease chaos of one chaotic system this method enlarges the effective scope of chaos control we can control a chaotic system e g a new chaotic double van der pol system to a given chaotic or regular system e g a new chaotic double duffing system or to a damped simple harmonic system by a pragmatical theorem of asymptotical stability based on an assumption of equal probability of initial point an adaptive control law is derived such that it can be proved strictly that the common zero solution of error dynamics and of parameter dynamics is asymptotically stable numerical simulations are given to show the effectiveness of the proposed scheme

two body scattering on a graph and application to simple nanoelectronic devices the two body system on a graph with one junction is considered the effective three body scattering problem turns out to be exactly solvable for pointwise interactions additional degrees of freedom corresponding to a dynamics of some structure e g an atomic cluster located in the junction point of common contact of three thin electrodes are considered these degrees of freedom bring effective energy dependent interaction into the effective schrodinger equation in the scattering channel the wave function of the system is constructed in the explicit form using the extension theory methods the obtained results are applied to the qualitative description of a simple three electrode nanoelectronic device the perturbation theory approach based on the analysis of the liouville equation is suggested for calculation of the conductivity for such a device in terms of the obtained wave function

source localization in a waveguide using polynomial rooting source localization in acoustic waveguides involves a multidimensional search procedure we propose a new algorithm in which the search in the depth direction is replaced by polynomial rooting using the proposed algorithm range and depth estimation by a vertical array requires a 1 d search procedure for a 3 d localization problem i e range depth and direction of arrival doa estimation the algorithm involves a 2 d search procedure consequently the proposed algorithm requires significantly less computation than other methods that are based on a brute force search procedure over the source location parameters in order to evaluate the performance of the algorithm an error analysis is carried out and monte carlo simulations are performed the results are compared with the cramer rao bound crb and to the maximum likelihood ml simulation performance the algorithm is shown to be efficient while being computationally simpler than the ml or the bartlett processors the disadvantage of the algorithm is that its snr threshold occurs in lower snr than in the ml algorithm

classifying the general family of 1d point interactions a scattering approach we propose a classification scheme for the complete family of 1d point interactions to do so we first review the solutions of the wavefunctions and green functions of the problem second we derive the exact time dependent propagators in such a way that we can write the expressions for the k s in a very compact form as they should such expressions do reduce to the known results in the literature according to the potential parameter values then we analyse in general terms how the different point interactions scatter off arbitrary initially localized wave packets finally we show that the physical features associated with the scattering process can be used to establish a classification procedure moreover these physical characteristics are directly related to the potential parameters leading to the many formulae for the k s as an application we present numerical calculations for gaussian wave packets

estimates for the lowest eigenvalue of a star graph we derive new estimates for the lowest eigenvalue of the schrodinger operator associated with a star graph in r2 we achieve this by a variational method and a procedure for identifying test functions which are sympathetic to the geometry of the star graph

adaptive complete synchronization of the noise perturbed two bi directionally coupled chaotic systems with time delay and unknown parametric mismatch in this paper we design an adaptive feedback controller to synchronize a class of noise perturbed two bi directionally coupled chaotic systems with time delay and unknown parametric mismatch based on invariance principle of stochastic time delay differential equations some sufficient conditions of adaptive complete synchronization are given comparing with other papers here we consider the effect of internal noise time delay and parametric mismatch in the synchronized process as the illustrative examples the famous lorenz system and rossler system are considered here in order to validate the proposed scheme numerical simulations are performed and the numerical results show that our scheme is very effective

exponential synchronization of chaotic systems subject to uncertainties in the control input a sliding mode control technique is introduced for exponential synchronization of chaotic systems these systems are described by a general form including matched and unmatched nonlinear functions a new hitting free switching surface of proportional integral type is proposed this type of switching surface is without the hitting process if the attraction of sliding manifold is ensured this property makes it easy to exponentially synchronize the master slave chaotic systems based on this switching surface a robust sliding mode controller smc is derived to guarantee the attraction of sliding manifold even when the system is subjected to input uncertainties an example is included to illustrate the results developed in this paper