dual state vector of nonlinear coherent state and its application in complex p representation we introduce the dual vector z f n of a single mode nonlinear coherent state ncs by using the contour integral form of function and the explicit form of z f n is obtained in enlarged hilbert space the nonlinear fock states and their contour representation are deduced a new completeness relation composed of z f n and ncs in contour integral form is derived and its application in constructing a complex p representation of density operators is shown

model predictive control of discrete hybrid stochastic automata this paper focuses on optimal and receding horizon control of a class of hybrid dynamical systems called discrete hybrid stochastic automata dhsa whose discrete state transitions depend on both deterministic and stochastic events a finite time optimal control approach optimistically determines the trajectory that provides the best tradeoff between tracking performance and the probability of the trajectory to actually execute under possible chance constraints the approach is also robustified less optimistically to ensure that the system satisfies a set of constraints for all possible realizations of the stochastic events or alternatively for those having enough probability to realize sufficient conditions for asymptotic convergence in probability are given for the receding horizon implementation of the optimal control solution the effectiveness of the suggested stochastic hybrid control techniques is shown on a case study in supply chain management

factorization little or great algorithm the progress of the factorization method since the 1935 work of dirac is briefly reviewed though linked with older mathematical theories the factorization seems an autonomous driving force offering substantial support to the present day darboux and backlund approaches

hyers ulam stability of a first order partial differential equation abstract we prove that the existence of a global prime integral leads in appropriate conditions to the hyers ulam stability of a linear partial differential equation of first order

a characterization of hyers ulam stability of first order linear differential operators abstract let x be a complex banach space and h r c a continuous function let t h c 1 r x c r x be the linear differential operator defined by thu u hu we give a necessary and sufficient condition in order that the operator th has the hyers ulam stability

hyers ulam stability of a system of first order linear differential equations with constant coefficients abstract in this paper using matrix method we prove the hyers ulam stability of a system of first order linear differential equations with constant coefficients

a generalized multi period mean variance portfolio optimization with markov switching parameters in this paper we deal with a generalized multi period mean variance portfolio selection problem with market parameters subject to markov random regime switchings problems of this kind have been recently considered in the literature for control over bankruptcy for cases in which there are no jumps in market parameters see zhu s s li d wang s y 2004 risk control over bankruptcy in dynamic portfolio selection a generalized mean variance formulation ieee transactions on automatic control 49 447 457 we present necessary and sufficient conditions for obtaining an optimal control policy for this markovian generalized multi period mean variance problem based on a set of interconnected riccati difference equations and on a set of other recursive equations some closed formulas are also derived for two special cases extending some previous results in the literature we apply the results to a numerical example with real data for risk control over bankruptcy in a dynamic portfolio selection problem with markov jumps selection problem

on the hyers ulam stability of the linear differential equation abstract we obtain some results on generalized hyers ulam stability of the linear differential equation in a banach space as a consequence we improve some known estimates of the difference between the perturbed and the exact solutions

stochastic receding horizon control of constrained linear systems with state and control multiplicative noise we develop a receding horizon control approach to stochastic linear systems with control and state multiplicative noise that also contain constraints our receding horizon formulation is based upon an on line optimization that utilizes open loop plus linear feedback and is solved as a semi definite programming problem we also provide a characterization of stability performance and constraint satisfaction properties of the receding horizon controlled system under a specific choice of terminal weight and terminal constraint a simple numerical example is used to illustrate the approach

factorization method and new potentials with the oscillator spectrum a one parameter family of potentials in one dimension is constructed with the energy spectrum coinciding with that of the harmonic oscillator this is a new derivation of a class of potentials previously obtained by abraham and moses with the help of the gelfand levitan formalism

hyers ulam stability of non autonomous systems in terms of boundedness of cauchy problems in this paper the concepts of hyers ulam stability are generalized for non autonomous linear differential systems we prove that the k periodic linear differential matrix system z t a t z t t r is hyers ulam stable if and only if the matrix family l e k 0 has no eigenvalues on the unit circle i e we study the hyers ulam stability in terms of dichotomy of the differential matrix system z t a t z t t r furthermore we relate hyers ulam stability of the system z t a t z t t r to the boundedness of solution of the following cauchy problem y t a t y t t t 0 y 0 x x 0 where a t is a square matrix for any t r t is a bounded function and x x 0 c m

the hyers ulam stability constant for chebyshevian bernstein operators abstract on a closed bounded interval a given extended chebyshev space which possesses a bernstein basis generates infinitely many operators of the bernstein type we show that all these operators share the same hyers ulam stability constant this constant is the maximum in absolute value of the bezier coefficients of the generalised chebyshev polynomial associated with the given space we establish an optimality property of these bernstein operators with respect to the hyers ulam stability constant numerical computations of these constants are investigated in two cases rational and muntz bernstein operators with special emphasis on their behaviour with respect to the concerned interval and to dimension elevation

on the completeness of photon added coherent states we demonstrate explicitly the completeness of photon added coherent states pacss introduced by agarwal and tara agarwal g s and tara k 1991 phys rev a 43 492 and defined up to normalization by m z m 0 1 2 where is the boson creation operator and z are conventional glauber klauder coherent states we find the analytical form of the positive weight function in their resolution of unity by solving the associated stieltjes power moment problem we furnish an example of generation of another set of pacss which are complete

a family of complex potentials with real spectrum we consider a two parameter non hermitian quantum mechanical hamiltonian operator that is invariant under the combined effects of parity and time reversal transformations numerical investigation shows that for some values of the potential parameters the hamiltonian operator supports real eigenvalues and localized eigenfunctions in contrast with other parity times time reversal symmetric models which require special integration paths in the complex plane our model is integrable along a line parallel to the real axis

distorted heisenberg algebra and coherent states for isospectral oscillator hamiltonians the dynamical algebra associated with a family of isospectral oscillator hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates it is shown that this representation becomes similar to that of the standard heisenberg algebra and it is dependent on a parameter omega or 0 we call it the distorted heisenberg algebra where omega is the distortion parameter the corresponding coherent states for an arbitrary omega are derived and some particular examples are discussed in detail a prescription to produce the squeezing by adequately selecting the initial state of the system is given

higher order susy linearized nonlinear heisenberg algebras and coherent states using an iterative construction of the first order intertwining technique we find k parametric families of exactly solvable anharmonic oscillators whose spectra consist of a part isospectral to the oscillator plus k additional levels at arbitrary positions below e0 it is seen that the natural ladder operators for these systems give place to polynomial nonlinear algebras and it is shown that these algebras can be linearized the coherent states construction is performed in the nonlinear and linearized cases

model predictive control for systems with stochastic multiplicative uncertainty and probabilistic constraints abstract robust predictive control handles constrained systems that are subject to stochastic uncertainty but propagating the effects of uncertainty over a prediction horizon can be computationally expensive and conservative this paper overcomes these issues through an augmented autonomous prediction formulation and provides a method of handling probabilistic constraints and ensuring closed loop stability through the use of an extension of the concept of invariance namely invariance with probability p

hyers ulam stability of the linear differential operator with nonconstant coefficients abstract we obtain some stability results for the linear differential operator of order one in banach spaces as a consequence we derive a result on hyers ulam stability for the linear differential operator of higher order with nonconstant coefficients

ulam hyers stability of dynamic equations on time scales via picard operators in this paper we study the ulam hyers stability of some linear and nonlinear dynamic equations and integral equations on time scales we use both direct and operatorial methods and we propose a unified approach to ulam hyers stability based on the theory of picard operators see 28 33 our results extend some recent results from 24 25 8 14 13 5 6 to dynamic equations and are more general than the results from 1 the operatorial point of view based on the theory of picard operators allows to discuss the ulam hyers stability of many types of differential and integral equations on time scales and also to obtain simple and structured proofs to the existing results but as we point out at our final remarks there are also a few disadvantages

factorization method and singular hamiltonians the oscillator singular supersymmetric partners are studied in detail and their relationship with the equivalent problem of an oscillator plus an infinite barrier is clearly established interesting potentials with possible applications to different physical models appear as a bonus

hyers ulam stability of linear differential equations of first order iii abstract let x be a complex banach space and let i a b be an open interval in this paper we will prove the generalized hyers ulam stability of the differential equation t y t y t t r x 0 0 for the class of continuously differentiable functions f i x where and r are complex constants and x 0 is an element of x by applying this result we also prove the hyers ulam stability of the euler differential equation of second order

ladder operators for isospectral oscillators we present for the isospectral family of oscillator hamiltonians a systematic procedure for constructing raising and lowering operators satisfying any prescribed distorted heisenberg algebra including the q generalization this is done by means of an operator transformation implemented by a shift operator the latter is obtained by solving an appropriate partial isometry condition in the hilbert space formal representations of the nonlocal operators concerned are given in terms of pseudo differential operators using the new annihilation operators new classes of coherent states are constructed for isospectral oscillator hamiltonians the corresponding fock bargmann representations are also considered with specific reference to the order of the entire function family in each case

coherent states for isospectral oscillator hamiltonians coherent states for a family of isospectral oscillator hamiltonians are derived from a suitable choice of annihilation and creation operators the fock bargmann representation is also considered

constrained stochastic lq control with random coefficients and application to portfolio selection this paper is devoted to the study of a stochastic linear quadratic lq optimal control problem where the control variable is constrained in a cone and all the coefficients of the problem are random processes employing tanaka s formula optimal control and optimal cost are explicitly obtained via solutions to two extended stochastic riccati equations esres the esres introduced for the first time in this paper are highly nonlinear backward stochastic differential equations bsdes whose solvability is proved based on a truncation function technique and kobylanski s results the general results obtained are then applied to a mean variance portfolio selection problem for a financial market with random appreciation and volatility rates and with short selling prohibited feasibility of the problem is characterized and efficient portfolios and efficient frontier are presented in closed forms

an affine control method for optimal dynamic asset allocation with transaction costs in this paper we present a novel and computationally efficient approach to constrained discrete time dynamic asset allocation over multiple periods this technique is able to control portfolio expectation and variance at both final and intermediate stages of the decision horizon and may account for proportional transaction costs and intertemporal dependence of the return process a key feature of the proposed method is the use of a linearly parameterized class of feedback control policies which permits us to obtain explicit analytic expressions for the portfolio statistics over time these expressions are proved to be convex in the decision parameters and hence under these control laws the multistage problem is formulated and solved by means of efficient tools for quadratic or second order cone convex programming

the construction of some important classes of generalized coherent states the nonlinear coherent states method considering some important classes of generalized coherent states known in the literature we demonstrated that all of them can be created via conventional methods i e the lowering operator eigenstate and the displacement operator techniques using the nonlinear coherent states approach as a result we obtained a unified method to construct a large class of coherent states which have already been introduced by different prescriptions

factorization of sturm liouville operators solvable potentials and underlying algebraic structure in this paper a general method of factorization of sturm liouville sl operators is provided a method to solve sl eigenvalue problems is presented new classes of exactly solvable potentials are obtained the supersymmetry and shape invariance approaches are generalized to the sl operators it is shown that the sl shape invariance potentials have an underlying algebraic structure this algebra is in general infinite dimensional the condition of finite algebra is obtained

isospectral susy potentials the authors introduce a new linear transformation in order to construct isospectral potentials within the framework of supersymmetric quantum mechanics under this transformation the adjoint character of the ladder operator is destroyed but with preservation of the energy spectrum leading to some interesting consequences such as the concept of pseudo partnership of the two components connection with the darboux theorem as well as with some other recent methods of construction is analysed

best constant in hyers ulam stability of first order homogeneous linear differential equations with a periodic coefficient abstract this paper is concerned with hyers ulam stability of the first order homogeneous linear differential equation x a t x 0 on r where a r r is a continuous periodic function it is known that if a t 0 then the above equation does not have hyers ulam stability on r however sufficient conditions for hyers ulam stability are presented in spite of a t has infinitely many zeros and changes sign furthermore the best constant in hyers ulam stability is clarified to illustrate the obtained results some examples are included

stochastic model predictive control of lpv systems via scenario optimization a stochastic receding horizon control approach for constrained linear parameter varying discrete time systems is proposed in this paper it is assumed that the time varying parameters have stochastic nature and that the system s matrices are bounded but otherwise arbitrary nonlinear functions of these parameters no specific assumption on the statistics of the parameters is required by using a randomization approach a scenario based finite horizon optimal control problem is formulated where only a finite number m of sampled predicted parameter trajectories scenarios are considered this problem is convex and its solution is a priori guaranteed to be probabilistically robust up to a user defined probability level p the p level is linked to m by an analytic relationship which establishes a tradeoff between computational complexity and robustness of the solution then a receding horizon strategy is presented involving the iterated solution of a scenario based finite horizon control problem at each time step our key result is to show that the state trajectories of the controlled system reach a terminal positively invariant set in finite time either deterministically or with probability no smaller than p the features of the approach are illustrated by a numerical example

on the stability of the linear differential equation of higher order with constant coefficients abstract we obtain a result on stability of the linear differential equation of higher order with constant coefficients in aoki rassias sense as a consequence we obtain the hyers ulam stability of the above mentioned equation a connection with dynamical sytems perturbation is established

on generalized coherent states with maximal symmetry for the harmonic oscillator generalized coherent states for the one dimensional harmonic oscillator with maximal symmetry i e admitting the semidirect sum so 2 1 h 2 as the largest invariance lie algebra pointed out by niederer are constructed the normalization of such states as well as their completeness property are determined and discussed they are also analyzed in the subcontexts of the so 2 1 algebra and of the heisenberg h 2 algebra general considerations on heisenberg relations on minimal dispersions and on quantum mechanical entropies are presented in connection with the uncertainty principle

model predictive control for constrained systems with serially correlated stochastic parameters and portfolio optimization in this paper we consider mpc for constrained discrete time systems with stochastic parameters which are assumed to be a set of serially correlated time series a generalized performance criterion is composed of a weighted sum of a linear combination of the a expected value of quadratic forms of state and control vectors b quadratic forms of the expected value of the state vector and c the linear component of the expected value of the state vector the purpose of the present paper is to design optimal control strategies that are independent of distributional assumptions on the stochastic parameters and subject to hard constraints on the input manipulated variables and to provide a numerically tractable algorithm for practical applications all expressions are presented in terms of the first and second order conditional moments the results are applied to a problem of investment portfolio optimization with serially correlated returns we present the numerical modelling results based on stocks traded on the russian stock exchanges micex

optimal feedback control strategies for state space systems with stochastic parameters two different optimal feedback laws are derived for state space systems parametrized through an independent identically distributed vector sequence both feedback laws are obtained by minimizing the expectation of a multistep quadratic loss function at each time step they differ on the assumptions made about the future inputs the properties and implementability of the feedback laws are discussed for the infinite horizon case

supersymmetry factorisation of the schrodinger equation and a hamiltonian hierarchy the author presents a systematic procedure for constructing a hierarchy of non relativistic hamiltonians with the property that the adjacent members of the hierarchy are supersymmetric partners i e they share the same eigenvalue spectrum except for the missing ground state and the eigenvectors are simply related