combinatorial approach to feynman path integration combinatorial relations can be used to convert the non relativistic time sliced feynman path integral into perturbation expansions these methods reveal that when the time interval is sliced into n increments each order of perturbation theory sustains an error o 1 square root n in this way the author provides exact path integral results for the following potentials delta function comb finite well tunnelling barrier and a generalized exponential cusp for the tunnelling barrier it is seen how the celebrated 1 reflection factor arises in the limit of infinite barrier height the one dimensional coulomb problem is solved as a limiting case of the exponential cusp in addition for power potentials the author indicates how this path integral approach yields sometimes divergent nevertheless asymptotic perturbation expansions

lmi based robust control of fractional order uncertain linear systems this paper concerns with the method of observer based control and static output feedback control for fractional order uncertain systems with the fractional commensurate order a 0 a 1 and a email protected email protected 2 via linear matrix inequality lmi approach respectively first the sufficient conditions for robust asymptotical stability of the closed loop control systems are presented next by using matrix s singular value decomposition svd and lmi technics the existence condition and method of designing a robust stabilizing controller for such fractional order control systems are derived unlike previous methods the results are obtained in terms of lmi which can be easily obtained by matlab s lmi toolbox finally two numerical examples demonstrate the validity of this approach

new method for optimal nonlinear filtering of noisy observations by multiple stochastic fractional integral expansions multiple stochastic fractional integral expansions are applied to the problem of non linear filtering of a signal observed in the presence of an additive noise where the noise is modelled by a fractional brownian motion with hurst index greater than 1 2 it is shown that the best mean square estimate of the signal can be represented as a ratio of two multiple integral series where the stochastic integrals are defined in either the ito or stratonovich sense and taken with respect to the observation process which is a persistent fractional brownian motion under a suitable probability measure finally motivated by practical considerations finite expansion approximations to the optimal filter are studied

robust stabilization for rectangular descriptor fractional order interval systems with order 0 α 1 abstract this paper considers the normalization and stabilization of rectangular descriptor fractional order interval systems with fractional order 0

propagator for finite range potentials the schrodinger equation in integral form is applied to the one dimensional scattering problem in the case of a general finite range nonsingular potential a simple expression for the laplace transform of the transmission propagator is obtained in terms of the associated fredholm determinant by means of matrix methods the particular form of the kernel and the peculiar aspects of the transmission problem play an important role the application to an array of delta potentials is shown

derivation of the time dependent propagator for the three dimensional schrodinger equation with one point interaction an explicit formula for the time dependent propagator of the schrodinger equation with one point interaction in three dimensions is given the derivation is based on the inverse laplace transformation applied to the corresponding resolvent

spectral analysis of a flat plasma sheet model the spectral analysis of the electromagnetic field on the background of an infinitely thin flat plasma layer is carried out this model loosely imitates a single base plane from graphite and it is of interest for theoretical studies of fullerenes by making use of the hertz potentials the solutions to maxwell equations with the appropriate matching conditions at the plasma layer are derived and on this basis the spectrum of electromagnetic oscillations is determined the model is naturally split into the te sector and tm sector both the sectors have positive continuous spectra but the tm modes have in addition a bound state namely the surface plasmon this analysis relies on the consideration of the scattering problem in the te and tm sectors the spectral zeta function and integrated heat kernel are constructed for different branches of the spectrum in an explicit form as a preliminary the rigorous procedure of integration over the continuous spectra is formulated by introducing the spectral density in terms of the scattering phase shifts the asymptotic expansion of the integrated heat kernel at small values of the evolution parameter is derived by making use of the technique of integral equations developed earlier by the same authors the local heat kernel green s function or fundamental solution is also constructed as a by product a new method is demonstrated for deriving the fundamental solution to the heat conduction equation or to the schrodinger equation on an infinite line with the like source in particular for the heat conduction equation on an infinite line with the source a nontrivial counterpart is found namely a spectral problem with point interaction which possesses the same integrated heat kernel while the local heat kernels fundamental solutions in these spectral problems are different

exact and operator rational approximate solutions of the helmholtz weyl composition equation in underwater acoustics the quadratic profile the application of phase space and path integral methods to both mathematical and computational direct and inverse wave propagation modeling at the level of the scalar one way helmholtz equation is briefly reviewed the role of operator symbols is stressed and their properties briefly discussed the construction of the operator symbol requires the exact or approximate solution of the helmholtz weyl composition equation in the weyl pseudodifferential operator calculus the exact symbols for several quadratic profiles are presented and briefly analyzed the symbols exactly corresponding to a family of operator rational approximations are also presented for the quadratic case these results are used to illustrate several points pertinent to wide angle propagation modeling and the refractive index profile reconstruction problem in underwater acoustics

a nonlinear schrodinger equation with two symmetric point interactions in one dimension we consider a time dependent one dimensional nonlinear schrodinger equation with a symmetric double well potential represented by two dirac s among our results we give an explicit formula for the integral kernel of the unitary semigroup associated with the linear part of the hamiltonian then we establish the corresponding strichartz type estimate and we prove local existence and uniqueness of the solution to the original nonlinear problem

explicit solutions of the time dependent schrodinger equation the darboux transformation is used to generate explicit solutions of the time dependent schrodinger equation in one dimension the potentials are a reflectionless potential and certain asymmetric double well potentials if explicit solutions of a second order ordinary differential equation are known then the darboux transformation generates explicit solutions of a related differential equation deift and trubowitz 1979 lamb 1980 when applied to the time indepen dent schrodinger equation this method gives a new equation with a different potential function the purpose of this paper is to apply the procedure to the time dependent schrodinger equation in one dimension a number of new explicit solutions are thereby obtained given by closed formulae which do not require knowledge of the eigenfunc tions

robust stability analysis of fractional order uncertain singular nonlinear system with external disturbance this paper investigates robust stability for fractional order fo singular nonlinear systems the fo system is disturbed by external uncertainty and disturbance a central analysis technique is enabled by proposing a fundamental boundedness lemma for the first time this lemma is used for robust stability analysis of fo systems especially for mittag leffler stability analysis of fo nonlinear systems more importantly how to obtain a more accurate bound is given to reduce conservative an fo proportional derivative pd controller is proposed to normalize the fo singular system furthermore a criterion for stability of the normalized fo nonlinear systems is provided by linear matrix inequalities lmis finally two illustrative simulation examples are presented to illustrate effectiveness of the proposed stability notion

local characterizations of block covers and their applications let g always be a finite group and h g and let f be a held of characteristic p not necessarily a splitting field for g where p is a fixed prime and p 1 igi let b e fg be an fg block with block idempotent e and let b e fh be an fh block with block idempotent e we can regard b as an f g x g module we say that b covers b or e covers

exact propagator for reflectionless potentials the exact space time propagation for a general reflectionless potential is obtained in closed form involving error functions it is indicated how bound states and transmission coefficients may be recovered from asymptotic behaviour of the propagator a sum rule is derived that shows how the leading terms of the short time form of the propagator can be used rigorously in a feynman path integral formalism

the functional integral for a free particle on a half plane a free nonrelativistic particle moving in two dimensions on a half plane can be described by self adjoint hamiltonians characterized by boundary conditions imposed on the systems the most general boundary condition is parameterized in terms of the elements of an infinite dimensional matrix we construct the brownian functional integral for each of these self adjoint hamiltonians nonlocal boundary conditions are implemented by allowing the paths striking the boundary to jump to other locations on the boundary analytic continuation in time results in the green s functions of the schrodinger equation satisfying the boundary condition characterizing the self adjoint hamiltonian

extensions of nilpotent blocks over arbitrary fields in this paper with a suitable condition we describe the algebraic structure of block extensions of nilpotent blocks over arbitrary fields thus generalize the main result of b kulshammer and l puig on block extensions of nilpotent blocks over algebraically closed fields

robust stability test of a class of linear time invariant interval fractional order system using lyapunov inequality this paper provides a new analytical robust stability checking method of fractional order linear time invariant interval uncertain system this paper continues the authors previous work yangquan chen hyo sung ahn i podlubny robust stability check of fractional order linear time invariant systems with interval uncertainties in proceedings of the ieee conference on mechatronics and automation niagara falls canada july 2005 pp 210 215 where matrix perturbation theory was used for the new robust stability checking lyapunov inequality is utilized for finding the maximum eigenvalue of a hermitian matrix through numerical examples the usefulness and the effectiveness of the newly proposed method are verified

exact constructions of square root helmholtz operator symbols the focusing quadratic profile operator symbols play a pivotal role in both the exact well posed one way reformulation of solving the elliptic helmholtz equation and the construction of the generalized bremmer coupling series the inverse square root and square root helmholtz operator symbols are the initial quantities of interest in both formulations in addition to providing the theoretical framework for the development and implementation of the parabolic equation pe method in wave propagation modeling exact standard left and weyl symbol constructions are presented for both the inverse square root and square root helmholtz operators in the case of the focusing quadratic profile in one transverse spatial dimension extending and ultimately unifying the previously published corresponding results for the defocusing quadratic case j math phys 33 1887 1914 1992 both i spectral modal summation representations and ii contour integral representations exploiting the underlying periodicity of the associated quantum mechanical harmonic oscillator problem are derived and ultimately related through the propagating and nonpropagating contributions to the operator symbol high and low frequency asymptotic operator symbol expansions are given along with the exact symbol representations for the corresponding operator rational approximations which provide the basis for the practical computational realization of the pe method moreover while the focusing quadratic profile is in some respects nonphysical the corresponding helmholtz operator symbols nevertheless establish canonical symbol features for more general profiles containing locally quadratic wells

optimal control of discrete time linear fractional order systems with multiplicative noise abstracta finite horizon linear quadratic lq optimal control problem is studied for a class of discrete time linear fractional systems lfss affected by multiplicative independent random perturbations based on the dynamic programming technique two methods are proposed for solving this problem the first one seems to be new and uses a linear expanded state model of the lfs the lq optimal control problem reduces to a similar one for stochastic linear systems and the solution is obtained by solving riccati equations the second method appeals to the principle of optimality and provides an algorithm for the computation of the optimal control and cost by using directly the fractional system as expected in both cases the optimal control is a linear function in the state and can be computed by a computer program a numerical example and comparative simulations of the optimal trajectory prove the effectiveness of the two methods some other simulations are obtained for different values of the fractiona

extension of diagonal stability and stabilization for continuous time fractional positive linear systems abstract this paper considers an extension of diagonal stability for continuous fractional positive linear systems fpls with the fractional order 0 1 based on diagonal stability of metzler matrix an extension that involves the combination of a diagonal positive definite matrix and a skew symmetric anti diagonal matrix related a hurwitz and metzler matrix is established combining this extension and the linear matrix inequalities lmis criteria of stability for fractional order systems fos a necessary and sufficient condition for extension diagonal stability of fpls is presented a state feedback controller is given which ensures the stabilization and positivity of the closed loop systems numerical examples are provided to demonstrate the effectiveness and applicability of the proposed methods

exact propagator and eigenfunctions for multistable models with arbitrarily prescribed n lowest eigenvalues the author presents a method to construct potentials for schrodinger equations with some prescribed features for which all eigenfunctions and the time dependent propagator can be explicitly calculated the prescribed features can be formulated by choosing arbitrarily the n lowest eigenvalues alternatively one can prescribe some qualitative behaviour for the potential like the number and relative depths of wells and barriers the results can also be applied to the construction of fokker planck models with prescribed properties and explicitly calculable transition probability density the method is based on ideas of supersymmetric quantum mechanics and the theory of solitons that can be traced back to the work of darboux 1894 and crum 1955

relations between blocks of a finite group and its subgroup let g be a group of finite order g and p be a prime number let k be the field which is generated by the gth roots of unity over the p adic number field r be the ring of local integers in k and p be the maximal ideal in r we denote by o the ring r or the residue class field f of r modulo p we view the group algebra og as a right o g x g module in the usual way so that y x y x yy y e og and x y e g an indecomposable direct summand of the o g x g module og is the same as a block ideal of og hence if 1 e e 0 e

explicit derivation of the propagator for a dirac delta potential an explicit derivation of the propagator is given for a particle in a dirac delta potential lambda delta x by making a direct application of a variational technique followed by a systematic use of laplace transforms although the solution of the corresponding schrodinger equation has been known for years the solution of the propagator has been obtained only recently

brief paper stability and resonance conditions of elementary fractional transfer functions elementary fractional transfer functions are studied in this paper some basic properties of elementary transfer functions of the first kind are recalled then two main results are presented regarding elementary fractional transfer functions of the second kind written in a canonical form and characterized by a commensurate order a pseudo damping factor and a natural frequency first stability conditions are established in terms of the pseudo damping factor and the commensurate order as a corollary to matignon s stability theorem they extend the previous result into conditions that are simpler to check then resonance conditions are established numerically in terms of the commensurate order and the pseudo damping factor and give interesting information on the frequency behavior of fractional systems it is shown that elementary transfer functions of the second kind might have up to two resonant frequencies moreover three abaci are given allowing to determine the pseudo damping factor and the commensurate order for respectively a desired normalized gain at each resonance a desired phase at each resonance and a desired normalized first or second resonant frequency

new sufficient conditions for observer based control of fractional order uncertain systems new simple linear matrix inequalities are proposed to ensure the stability of a class of uncertain fractional order linear systems by means of a fractional order deterministic observer it is shown that the conditions of existence of an observer based feedback can be split into a set of linear matrix inequalities that are numerically tractable the presented results show that it is possible to decouple the conditions containing the bilinear variables into separate conditions without imposing equality constraints or considering an iterative search of the controller and the observer gains simulations results are given to approve the efficiency and the straightforwardness of the proposed design

on the quantum mechanical scattering from a potential step the problem of finding the exact spacetime particle s propagator in the presence of a potential step interface between different materials is revisited in contrast to the conventional feynman path integral approach integration over all energy values of the particle s spectral density matrix discontinuity of the energy dependent green s function across the real energy axis is suggested for obtaining the exact spacetime propagator the energy dependent green s functions are found in the framework of the multiple scattering theory mst the problem of finding the step localized energy dependent potentials responsible for the particle s reflection from and transmission through a potential step which are needed for mst application is solved the obtained exact result for the particle s propagator is expressed in terms of integrals of elementary functions and has a significantly simpler form than that reported earlier the obtained expressions allow easy evaluation of all limiting cases including the case of the infinitely large potential step as well as simple numerical visualization the square of the absolute value of the propagator which represents the relative transition probability density between two spacetime points is plotted and discussed in detail for the cases of particle reflection and transmission

propagator for narrow potential barriers the schrodinger equation in integral form is applied to the one dimensional scattering problem in the case of a narrow potential barrier since the kernel can be considered in a first approximation separable an explicit expression for the propagator is found by means of the complementary error function the problem of a particle confined in a half space and interacting with a narrow potential barrier is also considered and solved in an approximate way

brief analysis of fractional delay systems of retarded and neutral type this paper analyses several properties linked to the robust control of fractional differential systems with delays the bibo stability of both retarded and neutral fractional delay systems is related to the location of their poles in the particular case of retarded systems we give some properties of the poles of the system and the singular values of its hankel operator

a numerical algorithm for stability testing of fractional delay systems this paper presents an effective numerical algorithm for testing the bibo stability of fractional delay systems described by fractional order delay differential equations it is based on using cauchy s integral theorem and solving an initial value problem the algorithm has a reliable result which is illustrated by several examples and hence is practically useful in the analysis and design of feedback control for both integer and fractional order systems having time delays

propagator for finite range potentials the case of reflection following a previous study on the transmission propagator for a finite range potential the problem of reflection is considered it is found that the laplace transform of the reflection propagator can be expressed in terms of the usual fredholm determinant and of a new similar determinant containing the peculiar characteristics of reflection as an example an array of delta potentials is considered moreover a possible application to the calculation of quantum traversal time is shown

boundary conditions in path integrals from point interactions for the path integral of the one dimensional dirac particle a proposal is given of how to implement point interactions and boundary conditions in the path integral the starting point is a path integral formulation of a dirac particle in one dimension the implementation of a point interaction yields by means of a perturbation expansion the corresponding green function for a relativistic particle in the non relativistic limit several cases can be distinguished depending on which of the four possibilities of the point interaction has been chosen by a proper combination of the various possibilities of implementing the point interaction the whole range of the four parameter family of boundary conditions for point interactions can be exploited in the relativistic case as well as in the non relativistic limit in addition making the strength of the point interaction infinitely repulsive yields boundary conditions at finite points on the real line in particular dirichlet and neumann boundary conditions emerge the method is illustrated with some examples

scattering for nls with a delta potential abstract we prove h 1 scattering for the mass supercritical defocusing nonlinear schrodinger equation perturbed by a repulsive delta potential

the green correspondence and normal subgroups in a recent paper harris and knorr 6 have discovered a connection between the brauer correspondence and the covering relation between blocks of a finite group and blocks of its normal subgroups green s module point of view of blocks 4 suggests that this result has a moduletheoretic proof and that there is a more general result on indecomposable modules we shall show that this is the case by giving a short moduletheoretic proof of the harris kniirr theorem and then use the ideas of the proof to formulate and establish a result relating the green correspondence is with normal subgroups let us establish some notation let g be a finite group and h a normal subgroup let k be a field of prime characteristic p and b a block of h so b is an indecomposable algebra summand of kh we shall regard b as a k h x hi module in the usual way let d be a defect group of b k n d and b equal the block of k with bf b that is the brauer correspondent of b finally set l n d so k is a normal subgroup of l

scalar generalized screen algorithms in transversely isotropic media with a vertical symmetry axis the scalar generalized screen method in isotropic media is extended here to transversely isotropic media with a vertical symmetry axis vti although wave propagation in a transversely isotropic medium is essentially elastic we use an equivalent acoustic system of equations for the qp waves which we prove to be accurate for both the dispersion relation and the polarization angle in the case of mild anisotropy the enhanced accuracy of the generalized screen method as compared to the split step fourier methods allows the extension to vti media the generalized screen expansion of the one way propagator follows closely the method used in the isotropic case the medium is defined in terms of a background and a perturbation the generalized screen expansion of the vertical slowness is based upon an expansion of the medium parameters simultaneously into magnitude and smoothness of variation we cast the theory into numerical algorithms and assess the accuracy of the generalized screen method in a partic

a note on ℒ p norms of fractional systems this paper discusses p norm 1 p finiteness property of the impulse response of a stable fractional system cascaded with a pure fractional integrator the established results are used to choose a performance index for evaluating the output feedback control system performances

lmi conditions for global stability of fractional order neural networks fractional order neural networks play a vital role in modeling the information processing of neuronal interactions it is still an open and necessary topic for fractional order neural networks to investigate their global stability this paper proposes some simplified linear matrix inequality lmi stability conditions for fractional order linear and nonlinear systems then the global stability analysis of fractional order neural networks employs the results from the obtained lmi conditions in the lmi form the obtained results include the existence and uniqueness of equilibrium point and its global stability which simplify and extend some previous work on the stability analysis of the fractional order neural networks moreover a generalized projective synchronization method between such neural systems is given along with its corresponding lmi condition finally two numerical examples are provided to illustrate the effectiveness of the established lmi conditions

propagator and multiple scattering approach to the time of arrival problem the propagator approach combined with the multiple scattering theory is applied to the particle time of arrival toa problem this approach allows us to naturally include in the consideration the components of the particle initial wavefunction defined at t t0 corresponding to the positive forward moving term and negative backward moving term momenta for a freely moving particle it is shown that the allcock definition of the ideal total toa probability disregards the backward moving and interference terms entirely in the presence of a measuring apparatus modeled by an imaginary step potential with the amplitude v0 the general expression for the toa rate is obtained the forward moving component of which coincides with that obtained by allcock it is shown that when the initial particle wavefunction is well separated from the point of arrival and has a well defined average momentum the contribution of the backward moving and interference terms are small and can be neglected for a small v0 except the well known convolution result by allcock kijowski the exponential form of the toa rate follows at the double limit condition v0 0 t t0 2v0 2v0 t t0 is finite while the backward moving and interference terms vanish we show that the allcock result for the toa rate is valid in the entire range of v0 including the zeno case v0 and the normalized toa rate can be introduced for all values of v0 as a probability distribution the latter is illustrated for the gaussian wave packet

lmi stability conditions for fractional order systems after an overview of the results dedicated to stability analysis of systems described by differential equations involving fractional derivatives also denoted fractional order systems this paper deals with linear matrix inequality lmi stability conditions for fractional order systems under commensurate order hypothesis it is shown that a direct extension of the second lyapunov s method is a tedious task if the fractional order n is such that 0 n 1 the stability domain is not a convex region of the complex plane however through a direct stability domain characterization three lmi stability analysis conditions are proposed the first one is based on the stability domain deformation and the second one on a characterization of the instability domain which is convex the third one is based on generalized lmi framework these conditions are applied to the gain margin computation of a crone suspension

accuracy of the semiclassical approximation for the time dependent propagator for chaotic systems the semiclassical approximation to the time dependent propagator consists of a large number of terms some of which may involve classical trajectories near focal points caustics despite this the approximation has been found to remain accurate for relatively long times in this article that accuracy and potential reasons for its breakdown are studied the principal tool is the jacobi morse equation the eigenvalue equation associated with the second variational derivative of the classical action our explanation for the accuracy lies partly in the following considerations 1 verification of the efficacy of phase space smearing 2 given an explicit form of the near caustic propagator it is seen that the arguments concerning loops in phase space may be less relevant than the determination of the amount of separation in path space 3 and finally the caustics in the chaotic examples studied may not be placed for maximum mischief

an approximate method for numerically solving fractional order optimal control problems of general form in this article we discuss fractional order optimal control problems focps and their solutions by means of rational approximation the methodology developed here allows us to solve a very large class of focps linear nonlinear time invariant time variant siso mimo state input constrained free terminal conditions etc by converting them into a general rational form of optimal control problem ocp the fractional differentiation operator used in the focp is approximated using oustaloup s approximation into a state space realization form the original problem is then reformulated to fit the definition used in general purpose optimal control problem ocp solvers such as riots 95 a solver created as a matlab toolbox illustrative examples from the literature are reproduced to demonstrate the effectiveness of the proposed methodology and a free final time ocp is also solved

distribution theory for schrodinger s integral equation much of the literature on point interactions in quantum mechanics has focused on the differential form of schrodinger s equation this paper in contrast investigates the integral form of schrodinger s equation while both forms are known to be equivalent for smooth potentials this is not true for distributional potentials here we assume that the potential is given by a distribution defined on the space of discontinuous test functions first by using schrodinger s integral equation we confirm a seminal result by kurasov which was originally obtained in the context of schrodinger s differential equation this hints at a possible deeper connection between both forms of the equation we also sketch a generalisation of kurasov s j math anal appl 201 1 297 323 1996 result to hypersurfaces second we derive a new closed form solution to schrodinger s integral equation with a delta prime potential this potential has attracted considerable attention including some controversy interestingly the derived propagator satisfies boundary conditions that were previously derived using schrodinger s differential equation third we derive boundary conditions for super singular potentials given by higher order derivatives of the delta potential these boundary conditions cannot be incorporated into the normal framework of self adjoint extensions we show that the boundary conditions depend on the energy of the solution and that probability is conserved this paper thereby confirms several seminal results and derives some new ones in sum it shows that schrodinger s integral equation is a viable tool for studying singular interactions in quantum mechanics

stability of viscoelastic control systems classical root locus plot analysis is adapted to some one dimensional controlled distributed viscoelastic structures the constitutive law that is used for the viscoelastic material may be modeled with fractional order derivatives provided the control law s involve similar derivatives two sample one dimensional structures and control systems are used to introduce the approach a partial differential equation representation of each structure is used as well as ritz approximation the effect of error due to approximation on stability conclusions is discussed in the context of this comparison

proper incorporation of the self adjoint extension method to the green function formalism one dimensional function potential case the one dimensional function potential is discussed in the framework of the green function formalism without invoking perturbation expansion it is shown that the energy dependent green function for this case is crucially dependent on the boundary conditions which are provided by the self adjoint extension method the most general green function which contains four real self adjoint extension parameters is constructed the relation between the bare coupling constant and the self adjoint extension parameter is also derived

on the relationship between complex potentials and strings of projection operators it is of interest in a variety of contexts and in particular in the arrival time problem to consider the quantum state obtained through unitary evolution of an initial state regularly interspersed with periodic projections onto the positive x axis pulsed measurements echanobe del campo and muga have given a compelling but heuristic argument that the state thus obtained is approximately equivalent to the state obtained by evolving in the presence of a certain complex potential of step function form in this paper with the help of the path decomposition expansion of the associated propagators we give a detailed derivation of this approximate equivalence the propagator for the complex potential is known so the bulk of the derivation consists of an approximate evaluation of the propagator for the free particle interspersed with periodic position projections this approximate equivalence may be used to show that to produce significant reflection the projections must act at time spacing less than e where e is the energy scale of the initial state

pointwise estimates on the green s function for a scalar linear convection diffusion equation abstract pointwise estimates are found on green s functions for the scalar linear convection diffusion equations that arise when a scalar conservation law with non constant diffusion is linearized about a viscous shock profile of arbitrary strength the estimates take the form of gaussian kernels centered around paths determined by the typically different asymptotic states of the convection function the analysis extends the spectral transform method to the non constant coefficient case

fractional order systems and pi sup spl lambda d sup spl mu controllers dynamic systems of an arbitrary real order fractional order systems are considered the concept of a fractional order pi sup spl lambda d sup spl mu controller involving fractional order integrator and fractional order differentiator is proposed the laplace transform formula for a new function of the mittag leffler type made it possible to obtain explicit analytical expressions for the unit step and unit impulse response of a linear fractional order system with fractional order controller for both open and closed loops an example demonstrating the use of the obtained formulas and the advantages of the proposed pi sup spl lambda d sup spl mu controllers is given

time dependent propagator with point interaction we compute the time dependent schrodinger propagator with a point interaction in dimension n or 3 including the new cases of n 2 and the most general interaction supported by a point for n 1 we also give the small time asymptotics for n or 3 the case n 2 has the peculiarity of involving logarithmic terms in the expansion

the propagator for the step potential and delta function potential using the path decomposition expansion we present a derivation of the propagator for a particle in the presence of the step and delta function potentials these propagators are known but we present a direct path integral derivation based on the path decomposition expansion and the brownian motion definition of the path integral the derivation exploits properties of the catalan numbers which enumerate certain classes of lattice paths

diffusion in the presence of a pole from the continuous gaussian to a discrete lattice model abstract the continuous gaussian model with delta function potentials which has been used to describe the effects that interacting centers poles bring to the diffusion of a random walker provides an exact solution only in dimension d 1 its application in dimension d 2 is in need of introduction of cutoffs coming from the finite sizes of poles we therefore formulate an analogous discrete model in the d dimensional lattice space where no cutoffs or their regularization are necessary the discrete model is amenable to numerical treatment and the green s function its first moments and properties derived from them can be determined numerically to all dimensionalities in the one dimensional 1 d case in the presence of a single center the outcomes of the gaussian model are compared with the corresponding results of the discrete lattice model the possibility of extension of the lattice model to higher dimension permits the study of the two dimensional 2 d case too the intensities of interactions considered before to obtain positive values are extended to negative values in order to describe attractions also

the two dimensional harmonic oscillator interacting with a wedge the exact propagator of the author s dynamic system is presented and confirmed by expanding it in terms of the energy eigenfunctions and eigenvalues which agree with those obtained from the corresponding schrodinger equation for the case of a rational wedge the propagator can be expressed as a sum over classical paths but with the modified van vleck formula the author also evaluates the density matrix and the partition functions

heat kernel expansion for semitransparent boundaries we study the heat kernel for an operator of laplace type with a function potential concentrated on a closed surface we derive the general form of the small t asymptotics and explicitly calculate several first heat kernel coefficients

a new constructing approach for a weighted topology of wireless sensor networks based on local world theory for the internet of things iot in this paper we propose a new constructing approach for a weighted topology of wireless sensor networks wsns based on local world theory for the internet of things iot based on local world theory an uneven clustering weighted evolving model of wsns is designed the definitions of edge weight and vertex strength take sensor energy transmission distance and flow into consideration the vertex strengths drive the growth of topology meanwhile the edge weights change correspondingly experimental data demonstrate that the wsn topology we obtain has the property of weighted networks of the iot the edge weight vertex degree and strength follow a power law distribution related iot research work shows that weighted wsns not only share the robustness and fault tolerance of weight free networks but also reduce the probability that successive node breakdowns occur furthermore they enhance the synchronization of wsns

explicit time dependent schrodinger propagators the authors compute explicitly the time dependent schrodinger and heat propagator for the potentials lambda 2m m 1 cosh2 lambda x a delta function potential several cases of periodic delta function potentials and a delta function potential in a square well they also discuss the semiclassical approximation for the delta function potential

path integrals for potential problems with δ function perturbation the author presents several examples of potential problems with a function perturbation by means of path integrals the idea is to sum a perturbation series expansion resulting in an energy dependent green function g e the energy levels en of the perturbed problem are determined by the equation one dimensional case ig v a a en gamma where g v is the green function of the unperturbed problem gamma is the strength of the potential and a its location in r in d dimensional radial problems with a spherically shaped delta function located at r a this equation changes into ig v l a a en ad 1 where l denotes the angular momentum number

indefinite quadratic with linear costs optimal control of markov jump with multiplicative noise systems in this paper we consider the stochastic optimal control problem of discrete time markov jump with multiplicative noise linear systems the performance criterion is assumed to be formed by a linear combination of a quadratic part and a linear part in the state and control variables the weighting matrices of the state and control for the quadratic part are allowed to be indefinite we present a necessary and sufficient condition under which the problem is well posed and a state feedback solution can be derived from a set of coupled generalized riccati difference equations interconnected with a set of coupled linear recursive equations for the case in which the quadratic term matrices are non negative this necessary and sufficient condition can be written in a more explicit way the results are applied to a problem of portfolio optimization

on a class of integral equations having application in quantum dynamics a class of fredholm integral equations of the second kind is studied with kernel separable outside the basic interval a b using theorems of matrix algebra the solution for x outside a b is found in terms of the fredholm determinants in a simple and compact form as a particular case the quantum propagator for one dimensional problems is obtained