deformed shape invariance and exactly solvable hamiltonians with position dependent effective mass known shape invariant potentials for the constant mass schrodinger equation are taken as effective potentials in a position dependent effective mass pdem one the corresponding shape invariance condition turns out to be deformed its solvability imposes the form of both the deformed superpotential and the pdem a lot of new exactly solvable potentials associated with a pdem background are generated in this way a novel and important condition restricting the existence of bound states whenever the pdem vanishes at an end point of the interval is identified in some cases the bound state spectrum results from a smooth deformation of that of the conventional shape invariant potential used in the construction in others one observes a generation or suppression of bound states depending on the mass parameter values the corresponding wavefunctions are given in terms of some deformed classical orthogonal polynomials

on the communication complexity of distributed algebraic computation abstract we consider a situation where two processors p sub 1 and p sub 2 ar e to evaluate a collection of functions function 1 function 8 of two vector variables x y under the assumption that processor p sub 1 respectively p sub 2 has access only to the value of the variable x respectively y and the functional form of function 1 function 8 we provide some new bounds on the communication complexity the amount of information that has to be exchanged between the processors for this problem an almost optimal bound is derived for the case of one way communication when the functions function 1 function 8 are polynomials we also derive some new lower bounds for the case of two way communication which improve on earlier bounds by abelson a 80 as an application we consider the case where x and y are n x n matrices and f x y is a particular entry of the inverse of x y under certain restriction on the class of allowed communication protocols we obtain an omega n squared lower bound in contrast to the omega n lower bound obtained by applying abelson s results our results are based on certain tools from classical algebraic geometry and field extension theory

some aspects of fusion in estimation theory the problem of fusing or combining various estimates to obtain a single good estimate is investigated the problem of fusion in estimation theory is addressed and several examples using common distributions in which virtually any method of fusion would be useless in approximating the random variable of interest are presented a theorem which for a very general situation shows that fusion resulting in an almost surely exact approximation is always possible is presented in particular this result addresses the situation in which the data consists of the random variable of interest corrupted by additive gaussian noise and the random variable of interest could be any second order random variable finally an example which illustrates the utility of this result is presented

a graph theory approach to identify resonant and non resonant transmission paths in statistical modal energy distribution analysis statistical modal energy distribution analysis smeda extends classical statistical energy analysis sea to the mid frequency range by establishing power balance equations between modes in different subsystems this circumvents the sea requirement of modal energy equipartition and enables applying smeda to the cases of low modal overlap locally excited subsystems and to deal with complex heterogeneous subsystems as well yet widening the range of application of sea is done at a price with large models because the number of modes per subsystem can become considerable when the frequency increases therefore it would be worthwhile to have at one s disposal tools for a quick identification and ranking of the resonant and non resonant paths involved in modal energy transmission between subsystems it will be shown that previously developed graph theory algorithms for transmission path analysis tpa in sea can be adapted to smeda and prove useful for that purpose the case of airborne transmission between two cavities separated apart by homogeneous and ribbed plates will be first addressed to illustrate the potential of the graph approach a more complex case representing transmission between non contiguous cavities in a shipbuilding structure will be also presented

a new class of quasi exactly solvable potentials with a position dependent mass a new class of quasi exactly solvable potentials with a variable mass in the schrodinger equation is presented we have derived a general expression for the potentials including natanzon confluent potentials the general solution of the schrodinger equation is determined and the eigenstates are expressed in terms of the orthogonal polynomials

an exactly solvable schrodinger equation with finite positive position dependent effective mass the solution of the one dimensional schrodinger equation is discussed in the case of position dependent mass the general formalism is specified for potentials that are solvable in terms of generalized laguerre polynomials and mass functions that are positive and bounded on the whole real x axis the resulting four parameter potential is shown to belong to the class of implicit potentials closed expressions are obtained for the bound state energies and the corresponding wave functions including their normalization constants the constant mass case is obtained by a specific choice of the parameters it is shown that this potential contains both the harmonic oscillator and the morse potentials as two distinct limiting cases and that the original potential carries several characteristics of these two potentials possible generalizations of the method are outlined

superintegrable systems with position dependent mass first order integrals of motion for schrodinger equations with position dependent masses are classified eighteen classes of such equations with non equivalent symmetries are specified they include integrable superintegrable and maximally superintegrable systems among them is a system invariant with respect to the lie algebra of lorentz group and a system whose integrals of motion form algebra so 4 three of the obtained systems are solved exactly

absolute and relative path measures in a discrete system by using two analytical methods this paper analytically examines two vibration paths rank ordering methods and critically investigates several path identification issues one method is the indirect interfacial path force estimation procedure that is employed in the well known experimental transfer path analysis the other method is path disconnect scheme that has been historically utilized in industry to empirically find a dominant or defective path in this article we utilize simplified but pedagogical discrete vibratory systems to clarify the underlying principles of both methods and to assess the path rank orders our analysis is limited to a linear time invariant system with only translating motions under harmonic excitation and three distinct parallel paths with or without masses are considered alternate formulations of the interfacial path forces based on direct and indirect methods are derived the indirect yet exact interfacial path force expressions could be used to estimate time averaged dissipated power and lagrangian energy spectra in various sub systems estimations using only the driving point frequency response functions are emphasized since they would ease the experimental burden next the path disconnect method is analytically formulated and related to the path connect scheme assuming one path at a time this analysis reveals some useful relations among the path measures and the way a particular path could be connected or disconnected a laboratory experiment validates the simplified massless path model which yields asymptotic trends finally all of the path rank orders are quantified and compared using many absolute and relative measures based on interfacial force receiver motion and sub system energy relationships direction for future work is briefly discussed

quantization of the lienard ii equation and jacobi s last multiplier in this paper the role of jacobi s last multiplier in mechanical systems with a position dependent mass is unveiled in particular we map the lienard ii equation to a position dependent mass system the quantization of the lienard ii equation is then carried out using the point canonical transformation method together with the von roos ordering technique finally we show how their eigenfunctions and eigenspectrum can be obtained in terms of associated laguerre and exceptional laguerre functions

generalized laguerre polynomials with position dependent effective mass visualized via wigner s distribution functions we construct analytically and numerically the wigner distribution functions for the exact solutions of the position dependent effective mass schrodinger equation for two cases belonging to the generalized laguerre polynomials using a suitable quantum canonical transformation expectation values of position and momentum operators are obtained analytically in order to verify the universality of heisenberg s uncertainty principle

a class of exactly solvable potentials related to the jacobi polynomials the author investigates a family of solvable potentials related to the jacobi polynomials this one dimensional potential family depends on three parameters and is restricted to the domain xo so it can be interpreted as the radial part of a central potential in three dimensions with l 0 closed expressions are obtained for the bound state energy spectrum and the wavefunctions the supersymmetric partner of this potential is also determined and it is found not to belong to the same potential family it is shown that this potential family is a special subclass of the general six parameter natanzon potential class and similarities with another subclass the ginocchio potentials are pointed out some aspects of supersymmetric quantum mechanics and shape invariance are also discussed in connection with the potential family under study

combining and updating of local estimates and regional maps along sets of one dimensional tracks in this paper we consider the problem of combining and updating estimates that may have been generated in a distributed fashion or may represent estimates generated at different times of the same process sample path the first of these cases has applications in decentralized estimation while the second has applications in updating maps of spatially distributed random quantities given measurements along several tracks the method of solution for the second problem uses the result of the first and the similarity in the formulation and solution of these problems emphasizes the conceptual similarity between many problems in decentralized control and in the analysis of random fields

graph theory applied to noise and vibration control in statistical energy analysis models a fundamental aspect of noise and vibration control in statistical energy analysis sea models consists in first identifying and then reducing the energy flow paths between subsystems in this work it is proposed to make use of some results from graph theory to address both issues on the one hand linear and path algebras applied to adjacency matrices of sea graphs are used to determine the existence of any order paths between subsystems counting and labeling them finding extremal paths or determining the power flow contributions from groups of paths on the other hand a strategy is presented that makes use of graph cut algorithms to reduce the energy flow from a source subsystem to a receiver one modifying as few internal and coupling loss factors as possible

distributed estimation algorithms for nonlinear systems in this paper we consider the problem of combining the local conditional distributions of a random variable which have been generated by local observers having access to their private information sufficient statistics for the local distributions are communicated to a coordinator who attempts to reconstruct the global centralized distribution using only the communicated statistics we obtain a distributed processing algorithm which recovers exactly the centralized conditional distribution the results can be applied in designing distributed hypothesis testing algorithms for event driven systems

unified treatment of the coulomb and harmonic oscillator potentials in d dimensions quantum mechanical models and practical calculations often rely on some exactly solvable models like the coulomb and the harmonic oscillator potentials the d dimensional generalized coulomb potential contains these potentials as limiting cases thus it establishes a continuous link between the coulomb and harmonic oscillator potentials in various dimensions we present results which are necessary for the utilization of this potential as a model and practical reference problem for quantum mechanical calculations we define a hilbert space basis the generalized coulomb sturmian basis and calculate the green s operator on this basis and also present an su 1 1 algebra associated with it we formulate the problem for the one dimensional case too and point out that the complications arising due to the singularity of the one dimensional coulomb problem can be avoided with the use of the generalized coulomb potential

a bochner type characterization theorem for exceptional orthogonal polynomials abstract it was recently conjectured that every system of exceptional orthogonal polynomials is related to a classical orthogonal polynomial system by a sequence of darboux transformations in this paper we prove this conjecture which paves the road to a complete classification of all exceptional orthogonal polynomials in some sense this paper can be regarded as the extension of bochner s result for classical orthogonal polynomials to the exceptional class as a supplementary result we derive a canonical form for exceptional operators based on a bilinear formalism and prove that every exceptional operator has trivial monodromy at all primary poles

on the quasi decentralized estimation and control of linear stochastic systems abstract it is shown that the quasi decentralized estimation and control of linear stochastic systems have extremely simple and computationally very efficient solutions in the domain of nonoptimal local filters these solutions reduce both off line and on line computation requirements the optimal global estimate is obtained simply by the addition of nonoptimal local estimates

the trigonometric rosen morse potential in the supersymmetric quantum mechanics and its exact solutions the analytic solutions of the one dimensional schrodinger equation for the trigonometric rosen morse potential reported in the literature rely upon the jacobi polynomials with complex indices and complex arguments we first draw attention to the fact that the complex jacobi polynomials have non trivial orthogonality properties which make them uncomfortable for physics applications instead we here solve the above equation in terms of real orthogonal polynomials the new solutions are used in the construction of the quantum mechanical superpotential

estimation of interfacial forces in time domain for linear systems abstract a structural path rank ordering process under transient excitations requires a good knowledge of the interfacial path forces which are difficult to directly measure four time domain methods to estimate the interfacial forces are proposed and comparatively evaluated with application to linear time invariant proportionally damped discrete systems first the transient response is derived by modal analysis and a direct time domain technique to calculate the interfacial forces is outlined next the frequency domain estimation methods based on the sub system concept are reviewed and an inverse fourier transform scheme is introduced an indirect method of estimating interfacial force in transient state is then developed through an inverse procedure of modal analysis the sub system approach is employed to obtain the interfacial forces based on the forced vibration response of the original system and modal data of the sub system finally an approximate time domain scheme is suggested that could be used only if the system properties are known or precisely estimated although the proposed indirect methods are designed for eventual experimental applications this article provides numerical feasibility studies via a simple source path receiver system with parallel vibration paths that has five translational degrees of freedom the proposed methods are compared under ideal impulse force excitation input and a periodic sawtooth load without and with gaussian noise to observe the starting transients as well as subsequent motions and interfacial forces preliminary comparisons with a laboratory experiment are very promising

isospectral hamiltonian for position dependent mass for an arbitrary quantum system and coherent states by means of the unitary transformation a new way for discussing the ordering prescription of the schrodinger equation with a position dependent mass pdm for isospectral hamiltonian operators is presented we show that the ambiguity parameter choices in the kinetic part of the hamiltonian can be explained through an exact susy qm symmetry as well as a consequence of an accidental symmetry under the z2 action by making use of the unitary transformation we construct coherent states for a family of pdm isospectral hamiltonians from a suitable choice of ladder operators we show that these states preserve the usual structure of klauder perelomov s states and thus saturate and minimize the position momentum uncertainty relation pmur under some special restrictions we show that pmur properties can be used to determine the sign of the superpotential

distributing the kalman filter for large scale systems this paper presents a distributed kalman filter to estimate the state of a sparsely connected large scale n dimensional dynamical system monitored by a network of n sensors local kalman filters are implemented on nl dimensional subsystems nl lt n obtained by spatially decomposing the large scale system the distributed kalman filter is optimal under an lth order gauss markov approximation to the centralized filter we quantify the information loss due to this lth order approximation by the divergence which decreases as l increases the order of the approximation l leads to a bound on the dimension of the subsystems hence providing a criterion for subsystem selection the approximated centralized riccati and lyapunov equations are computed iteratively with only local communication and low order computation by a distributed iterate collapse inversion dici algorithm we fuse the observations that are common among the local kalman filters using bipartite fusion graphs and consensus averaging algorithms the proposed algorithm achieves full distribution of the kalman filter nowhere in the network storage communication or computation of n dimensional vectors and matrices is required only nl lt n dimensional vectors and matrices are communicated or used in the local computations at the sensors in other words knowledge of the state is itself distributed

a search for shape invariant solvable potentials the author investigates a simple method of constructing potentials which is related to the work of bhattacharjie and sudarshan 1962 and for which the schrodinger equation can be solved in terms of known special functions it turns out that this method can be related to supersymmetric quantum mechanics and this relationship can help to decide which special functions satisfying linear homogeneous second order differential equations can be solutions of the schrodinger equation with potentials of the form v x w2 x w x the author illustrates this procedure with the example of orthogonal polynomials and obtains explicit expressions of wavefunctions of a wide class of shape invariant potentials

new class of conditionally exactly solvable potentials in quantum mechanics motivated by an idea of dutra 1993 we obtain a new class of one dimensional conditionally exactly solvable potentials for which the entire spectra can be obtained in an algebraic manner provided one of the potential parameters is assigned a fixed negative value it is shown that using shape invariant potentials as input one may generate different classes of such potentials even in more than one dimension we also illustrate that wkb and supersymmetry inspired wkb methods provide very good approximations for these potentials with the latter doing comparatively better

a lie algebraic approach to effective mass schrodinger equations we use lie algebraic techniques to obtain exact solutions of the effective mass schrodinger equation in particular we use the su 1 1 algebra both as a spectrum generating algebra and as a potential algebra to obtain exact solutions of effective mass schrodinger equations corresponding to a number of potentials we also discuss the construction of isospectral hamiltonians for which both the mass and the potential are different

method of measuring transmission paths abstract a theoretical explanation and experimental proof are presented of a method for localizing and evaluating the transmission paths of any signal in a black box among a set of points previously defined in it the signal should behave linearly and the system should be able to receive external excitations separately at each of its points such excitations need not be the signal under study but they should be linearly related to it also presented are the equations that once the transmission paths have been determined allow the evaluation of the excitations which act on the system

exceptional orthogonal polynomials exactly solvable potentials and supersymmetry we construct two new exactly solvable potentials giving rise to bound state solutions to the schrodinger equation which can be written in terms of the recently introduced laguerre or jacobi type x1 exceptional orthogonal polynomials these potentials extending either the radial oscillator or the scarf i potential by the addition of some rational terms turn out to be translationally shape invariant as their standard counterparts and isospectral to them