Shapes based trajectory queries for moving objects

Design of Continuous and Discrete Optimal Control Systems with Prescribed Transient Response

The idea of time scales calculus’ theory was initiated and introduced by Hilger (1988) in his PhD thesis order to unify discret and continuous analysis and to expend the discrete and continous theories to cases ``in between''. Since then, mathematical research in this field has exceeded more than 1000 publications and a lot of applications in the fields of science, i.e., operations research, economics, physics, engineering, statistics, finance and biology. Ostrowski proved an inequality to estimate the absolute deviation of a differentiable function from its integral mean. This result was obtained by applying the Montgomery identity. In the present paper we derive a generalization of the Montgomery identity to the various time scale versions such as discrete case, continuous case and the case of quantum calculus, by obtaining this generalization of Montgomery identity we would prove our results about the generalization of the Ostrowski inequalities (without weighted case) to the several time scales such as discrete case, continuous case and the case of quantum calculus and recapture the several published results of different authors of various papers and thus unify corresponding discrete version and continuous version. Similarly we would also derive our results about the generalization of the Ostrowski inequalities (weighted case) to the different time scales such as discrete case and continuous case and recapture the different published results of several authors of various papers and thus unify corresponding discrete version and continuous version. Moreover, we would use our obtained results (without weighted case) to the case of quantum calculus.

A power control framework for selfish users in a wireless DS-CDMA uplink with imperfect successive interference cancellation is offered. After presenting a feasibility constraint and a centralized power control solution, the system is analyzed and simulated as a noncooperative game for both continuous and discrete power control cases. Assuming a fixed a priori cancellation order, a unique Nash equilibrium corresponding to a centralized solution is shown to exist in the continuous case. It is shown that the realizable gains of the SIC receiver in a game-theoretic context, although strongly dependent on spreading gain and residual cancellation error, nevertheless are significant when compared to traditional matched filter detection, as expected. If the action space is discrete and sufficiently coarse, empirical results indicate a high probability of Nash equilibrium existence.

This paper investigates the problem of Hankel norm model reduction for linear systems with time-varying delay in the state. For a given stable system, our attention is focused on the construction of reduced-order model, which guarantees the corresponding error system to be asymptotically stable and has a specified Hankel norm error performance. Two different approaches are proposed to solve this problem. One casts the model reduction into a convex optimization problem by using a linearization procedure, and the other is based on the cone complementarity linearization idea, which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints. Both continuous and discrete time cases are considered. A numerical example is provided to show the effectiveness of the proposed theory.

This survey is intended as an overview of discrete Clifford analysis and its current developments. Since in the discrete case one has to replace the partial derivative with two difference operators, backward and forward partial difference, one needs to modify the main tools for a development of a discrete function theory, such as the replacement of a real Clifford algebra by a complexified Clifford algebra or of the classic Weyl relations by so-called S-Weyl relations. The main results, like Cauchy integral formula, Fischer decomposition, CK-extension, and Taylor series, will be derived. To give a better idea of the differences between the discrete and continuous case, this chapter contains the problem of discrete Hardy spaces as well as some discrete objects which do not have an equivalent object in continuous Clifford analysis, such as the CK-extension of a discrete Delta function.

Modelling non-negative discrete valued for time series analysis was introduced by previous researchers, that is Integer-Valued Autoregressive (INAR) model. The model involves both the parameter index and state space are discrete. Various phenomena within the scope of discrete cases are not only affected by previous discrete observations, but also affected by the discrete observations at surrounding locations in previous time. As a result, this model involves two parameter indices namely time and space, and also state space which are discrete. In continuous cases, a model has been introduced to overcome this problem, namely Generalized Space Time Autoregressive (GSTAR) model (discrete parameter index and continuous state space). Using this model to solve the discrete case produces a continuous forecast value, so it needs a discretization process. In the time series model for discrete cases, thinning operators have been introduced as a substitute for discretization in a continuous time series. The thinning operator paradigm in the discrete time series will be developed in the space-time model proposed in this paper. This paper will also introduce a new model, namely a space-time model for cases related to discrete cases. This means that the index of time and location parameters, as well as the state space used is a discrete state space. The properties that apply to the model are adopted from the INAR model and the GSTAR model for continuous cases. The main focus of this paper is the development of thinning operators from time series to space-time models. This paper also provides a modeling procedure using the GSTAR model for discrete cases. The result of this paper is the formation of a GSTAR model with a discrete state space.

In this paper, Noether theory of Lagrange systems in discrete case are studied. First, we briefly overview the well-known Noether theory of Lagrange system in the continuous case. Then, we introduce some definitions and notations, such as the operators of discrete translation to the right and the left and the operators of discrete differentiation to the right and the left, and give the conditions for the invariance of the difference functional on the uniform lattice and the non-uniform one, respectively. We also deduce the discrete analog of the Noether-type identity. Finally, the discrete analog of Noether's theorem is presented. An example was discussed to illustrate these results.

The maximum and minimum problems of functions which take only discrete values are often omitted from the usual treatises. Now, we are interested not only in the continuous case, and we shall pause for a moment at the discrete case, in order that we should obtain some indications of the situation.

In this tutorial, we survey several major methodologies for the optimization of discreteevent systems via simulation. We discuss both the discrete parameter case and the continuous parameter case. For the discrete parameter case, we focus on techniques for optimization from a finite set: multiple-comparison procedures and ranking-and-selection procedures. For the continuous parameter case, we discuss sequential response surface methodology procedures and stochastic approximation gradient-based procedures, Due to space limitations, no attempt is made here to be comprehensive; Fu (1994) expands upon the topics touched on here and provides a more extensive bibliography.

We give an examnple here illustrating a very simple way to obtain a first-order phase transition in a one-dimensional system. We consider discrete cases in this paper (which follow from the use of a step intermolecular potential). Continuous cases (from a smooth intermolecular potential) will be discussed in a second paper.1 One can also introduice length and tension as additional thermodynamic variables (here, tension = 0). Although the basic idea occurred to us in connection with allosteric effects2 in biological macromolecules, it turns out to have been exploited somewhat already in solid-state physics (three-dimensional systems).' The feature of main interest here is not any relation to real one-dimensional systems (the model is quite artificial), but rather the extreme simplicity of the model, which can be treated easily and exactly. Our system consists of a regular one-dimensional lattice (Einstein crystal) of N1 (N1 -- oo) component 1 molecules, which produce a lattice (samne spacing) of N, sites for the adsorption of N2 ? N1 component 2 molecules, at most one per site. The component 2 molecules form a conventional one-dimensional Ising system4 (lattice gas) with nearest-neighbor interactions only. The essential qualitative feature of the model is that the optimal lattice spacing (component 1) does not match the optimal nearest-neighbor spacing (component 2). Hence, adsorption leads to adjustment in the lattice spacing, in amount sufficient to extremalize the appropriate thermodynamic poteintial of the binary system. The artificiality in the model, referred to above and necessary for the phase transition, arises from an imposed restraint of uniform, though variable, lattice spacilig through the whole linear system. As we shall see at the end of the paper, if local (i.e., nonuniform) variations in lattice spacing are allowed-in response to adsorption-no phase transition occurs. The fact that the lattice spacing is restrained to be uniform implies a kind of long-range interaction between component 1 molecules. Statistical Mechanics of the Model.-The nearest-neighbor interaction potential between two adsorbed molecules is denoted by w2(r). For simplicity, we assume that lattice molecules also have, among themselves, nearest-neighbor interactions only with pair potential w1(r). Also, for simplicity, we assume that the partition functions ql(T) and q2(T) (not including e -W1kT and e w2/k17) for individual type 1 and type 2 molecules, respectively, are unaffected by the amount of adsorption or by a change in lattice spacing. The two cases considered in this paper (they can be treated together) are shown

For the analysis of finite-dimensional classical completely integrable Hamiltonian systems the representation by action-angle-variables is an essential tool. This representation can be carried over to the infinite-dimensional situation by use of mastersymmetries, thus leading to a suitable Viasoro algebra in the vector fields. For the quantum case, however, such a structure cannot exist in the corresponding operator algebra, due to a classical theorem of Kaplansky, although the concept of mastersymmetries can be used to give a formal description of the infinitedimensional symmetry group of those “nonlinear” Quantum systems which are accessible by the Quantum Inverse Scattering Transform. In order to make that precise and to transfer classical notions and methods to the quantum case an alternative dynamical concept for quantum systems is proposed. We give two examples, in the discrete case we consider spin chains, like the Heisenberg anisotropic spin chain, and in the continuous case, where additional difficulties arise, we consider the quantization of the KdV.KeywordsQuantum SystemPoisson BracketSpin ChainHamiltonian StructureRecursion OperatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Sklar’s theorem, “the fundamental theorem of copulas”, makes a clear distinction between the continuous case and the discrete case, though. In particular, the copula of a discrete random vector is not fully identifiable, which causes serious inconsistencies. In spite of this, downplaying statements may be found in the related literature, where copula methods are used for modelling dependence between discrete variables. This paper calls to reconsidering the soundness of copula modelling for discrete data. It suggests a more fundamental construction which allows copula ideas to smoothly carry over to the discrete case. Actually it is an attempt at rejuvenating some century-old ideas of Udny Yule, who mentioned a similar construction a long time before copulas got in fashion.

GLOBAL THEORIES OF THE LINEARIZING PROJECTION WITH APPLICATIONS

Laser control in open molecular systems: STIRAP and Optimal Control

A game problem of structural design is formulated as a problem of playing against external circumstances. The compliance plays the role of the pay-off function. Two players — the designer and nature — try to respectively minimize or maximize it, possessing limited resources. Discrete and continual optimization problems are considered. It is proved that the essential game characteristic, the upper game value, is expressed in terms of the minimal eigenvalue of the inverse operator of the system (continual case), or the response matrix (discrete case). For a special case of convex game, this eigenvalue is equal to the value of the game, and the optimal strategies of the designer and nature are uniquely determined.