A transformation of Cauer's third form realized by integrators

Abstract

A new formulation is presented for the Cauer's third form of continued fraction expansion realized by integrators. A transformation of the state‐space model of this new form and the state‐space model of the phase‐variable canonical form is given.     

A transformation of state‐space model to Jordan continued fraction expansion canonical form

Abstract

An algorithm is presented for computing the partial quotients of the Jordan type continued fraction expansion (CFE) of the corresponding transfer function of a linear time‐invariant system from its time‐moments of the impulse response. Explicit formulas for constructing the transformation matrix which transforms a general state‐space model to the Jordan CFE canonical form are derived. The results are given in a recursive form.     

Reduced‐order modelling of linear discrete‐time systems using cauer third continued‐fraction method

Abstract

In this paper a generalization of the Cauer third continued‐fraction expansion (CFE) is introduced for the reduced‐order modelling of linear time‐invariant discrete‐time systems. First, a new algorithm is presented for obtaining the Cauer third continued‐fraction expansion about z=1 and z=8 of the z‐transfer function of a discrete‐time system from its time‐moments and Markov parameters. Next, a realization of the Cauer third continued‐fraction expansion about z=1 and z=8, and the corresponding CFE canonical state‐space model are derived. Finally, an approximate aggregation matrix is constructed for relating the state‐vector of the reduced‐order CFE canonical state‐space model to that of the original system. An example is included to illustrate the use of the method.     

Balanced realization of siso systems using modified Jordan form

Abstract

The balancing method of De Abreu‐Garcia and Fairman [2] uses the Jordan realization. It involves complex arithmetic and is thus inconvenient for computation. This paper presents an improved algorithm that avoids complex arithmetic for De Abreu‐Garcia and Fairman's balancing method. The proposed algorithm is based on the use of the modified Jordan canonical realization of a single‐input single‐output (SISO) system.     

An improved algorithm for finding efficient schedules with respect to total flowtime and maximum tardiness

Abstract

This paper presents a new algorithm for finding efficient schedules with respect to total flowtime and maximum tardiness. A detailed comparison is made between this algorithm and the well‐known Van Wassenhove and Gelders’ algorithm (VGA) on a variety of problem sizes, up to 100 jobs. Computational results show that the proposed algorithm is of considerable value, especially for large problems. In particular, for the 10‐job problem the proposed algorithm requires roughly one‐half the computation time of VGA, and for the 100‐job problem the ratio reduces to one to sixteen.     

Normal form for Mueller Matrices in Polarization Optics

Abstract

The normal (canonical) form for Mueller matrices in polarization optics is derived: it is shown that a non-singular real 4 × 4 matrix M qualifies to be the bona fide Mueller matrix of some physical system if and only if it has the canonical form M = L′ ΛL, where L and L′ are elements of the proper orthochronous Lorentz group L ^↑ ₊, and where Λ = diag (λ₀, λ₁, λ₂, λ₃) with λ₀ ≥ ¦λ_j¦ > 0. It is further shown that λ₁ and λ₂ can be taken to be positive so that the signature of λ₃ is the same as that of det M. Several experimentally measured Mueller matrices are analysed in the light of the normal form. The case of singular Mueller matrices is briefly discussed as a limiting case.     

Addressing for letter‐oriented keys

Abstract

This paper presents a new algorithm for hashing. In this approach each key (x, y) is denoted as a pair of letters, and it is extracted from each letter‐oriented key in the key space according to a certain pre‐determined extraction algorithm. For the keys (x, y), our hashing function hashes as follows:

These functions allow single probe retrieval from minimally sized space of letter‐oriented keys. Various areas can be applied, such as searching reserved words in compilers and filtering frequently used words in natural language processing.     

An algorithm to build convex hulls for 3‐D objects

Abstract

In this paper, a new algorithm based on the Quickhull algorithm is proposed to find convex hulls for 3‐D objects using neighbor trees. The neighbor tree is the data structure by which all visible facets to the selected furthest outer point can be found. The neighboring sequence of ridges on the outer boundary of all visible facets also can be found directly from the neighbor tree. This new algorithm is twice as efficient as Barber's algorithm.     

A modified floating‐point code for voice coding and its applications

Abstract

A new modified normalized floating‐point code is proposed for the use in voice coding. It has about the same signal‐to‐quantizing noise ratio and dynamic range as the A‐87.6 code. Arithmetic operations encountered in digital signal processing are easier to implement with this code. Furthermore, simple procedures, which are easier to understand, exist for converting between this code and a linear code. According to the similar algorithm of this new code, the A‐87.6 and μ‐255 codes are derived again. The comparisons and other possible modified normalized floating‐point codes are also offered. The structure of a multiplier/accumulator implemented with the VLSI technology or the gate array for this new code is proposed.     

A two‐level nonoverlapping Schwarz algorithm for the Stokes problem without primal pressure unknowns

A two‐level nonoverlapping Schwarz algorithm is developed for the Stokes problem. The main feature of the algorithm is that a mixed problem with both velocity and pressure unknowns is solved with a balancing domain decomposition by constraints (BDDC)‐type preconditioner, which consists of solving local Stokes problems and one global coarse problem related to only primal velocity unknowns. Our preconditioner allows to use a smaller set of primal velocity unknowns than other BDDC preconditioners without much concern on certain flux conditions on the subdomain boundaries and the inf–sup stability of the coarse problem. In the two‐dimensional case, velocity unknowns at subdomain corners are selected as the primal unknowns. In addition to them, averages of each velocity component across common faces are employed as the primal unknowns for the three‐dimensional case. By using its close connection to the Dual–primal finite element tearing and interconnecting (FETI‐DP algorithm) (SIAM J Sci Comput 2010; 32 : 3301–3322; SIAM J Numer Anal 2010; 47 : 4142–4162], it is shown that the resulting matrix of our algorithm has the same eigenvalues as the FETI‐DP algorithm except zero and one. The maximum eigenvalue is determined by H/h, the number of elements across each subdomains, and the minimum eigenvalue is bounded below by a constant, which does not depend on any mesh parameters. Convergence of the method is analyzed and numerical results are included. Copyright © 2011 John Wiley & Sons, Ltd.     

Maximum‐likelihood localization of closely‐spaced sources by MLSUM algorithm

Abstract

In this paper, we present a new scheme called the maximum log‐likelihood sum (MLSUM) algorithm to simultaneously determine the number of closely‐spaced sources and their locations by uniform linear sensor arrays. Based on the principle of the maximum likelihood (ML) estimator and a newly proposed orthogonal‐projection decomposition technique, the multivariate log‐likelihood maximization problem is transformed into a multistage one‐dimensional log‐likelihood‐sum maximization problem. The global‐optimum solution of the approximated ML localization is obtained by simply maximizing the single one‐dimensional log‐likelihood function. This algorithm is applicable to coherent sources as well as incoherent sources. The computer simulations show that the MLSUM algorithm is much superior to the MUSIC when the element SNR is low and/or the number of snapshots is small.     

Fully implicit Lagrange–Newton–Krylov–Schwarz algorithms for boundary control of unsteady incompressible flows

We develop a parallel fully implicit domain decomposition algorithm for solving optimization problems constrained by time‐dependent nonlinear partial differential equations. In particular, we study the boundary control of unsteady incompressible Navier–Stokes equations. After an implicit discretization in time, a fully coupled sparse nonlinear optimization problem needs to be solved at each time step. The class of full space Lagrange–Newton–Krylov–Schwarz algorithms is used to solve the sequence of optimization problems. Among optimization algorithms, the fully implicit full space approach is considered to be the easiest to formulate and the hardest to solve. We show that Lagrange–Newton–Krylov–Schwarz, with a one‐level restricted additive Schwarz preconditioner, is an efficient class of methods for solving these hard problems. To demonstrate the scalability and robustness of the algorithm, we consider several problems with a wide range of Reynolds numbers and time step sizes, and we present numerical results for large‐scale calculations involving several million unknowns obtained on machines with more than 1000 processors. Copyright © 2012 John Wiley & Sons, Ltd.     

A novel closed‐loop reconfiguration for radial distribution systems with dispersed generation

Abstract

Currently, Tai‐power Company is attempting to change its power distribution systems from radial distribution configurations to closed‐loop configurations in order to enhance the quality of the supply of electricity. Besides, the dispersed generation (DG) should be considered in making the reconfiguration suitable for present circumstances. To form a closed‐loop configuration, a new tie‐line is added in this paper to interconnect two different feeders of the original radial power distribution systems. The multi‐objective is, not only to reduce power transmission loss, but also reduce the cost representative of power distribution reconfiguration. Assuming that the cost representative is a linear function of the system's short‐circuit capacity, line current and bus voltage. The problem solution procedure in this paper is mainly divided into two steps. The first step is to form objective function by determining the weighting factor of each objective term based on the cost‐benefit analysis scheme. Then, the optimum solution is pursued for the objective function by means of refined genetic algorithm (RGA). An example is studied by using the proposed methodology. The results show that the cost‐benefit analysis scheme is verified capable of finding the weighting factors, that the RGA can render stable solutions and that the transmission loss reduction ratio is satisfactory.     

Disturbance decoupling of nonlinear systems by high gain feedback

Abstract

For a smooth, affine nonlinear system of uniform relative degree one, it is shown that the asymptotic disturbance decoupling of full order system by high gain feedback can be achieved if the slow reduced subsystem can be exactly disturbance decoupled. The analysis is made in a properly selected coordinate system and the system in such a coordinate system is in a canonical form suitable for singular perturbation techniques.     

Queuing network analysis for a mixed voice and data communication network with end‐to‐end window flow control policy

Abstract

A Mixed Voice and Data Communication Network (MVDNET) with end‐to‐end (ETE) window flow control policy is modeled by a closed multichain queuing network. Using an approximate solution of the Mean Value Analysis (MVA) algorithm, the computational complexity of analysing a large‐scale MVDNET and various commodities is dramatically reduced by several orders of magnitude over that required by traditional product‐form solution. We consider the problems concerned with the choice of window size, the effect of voice interruption, the number of voice‐grade (VG) channels per internode link and the selection of appropriate packet length. It is shown that the analytic results are very close to the simulation ones using GPSS language, and that the extensive MVA algorithm is a practical and valuable tool for solving the MVDNET analytical model with ETE window flow control policy.     

Further considerations of a 1‐subcycle parallel thinning algorithm

Abstract

In this paper, we present two improved versions of a pseudo 1‐subcycle parallel thinning algorithm which we proposed earlier [1] and describe a two‐stage structure to realize the 1‐subcycle parallel algorithm.

The purpose of the first improved algorithm is to produce the P8ET (perfect 8‐curve excluding T‐junction)‐type thin line which is well‐defined in general. This algorithm involves local branches containing T‐junctions or quasi T‐junctions. The second improved algorithm obtains an isotropic skeleton of an L‐shape pattern, such that the visual quality of a skeleton is more satisfactory. In this algorithm, another set of thinning conditions especially designed is also involved.

We also describe a two‐stage structure which consists of a thinning table and a control unit. The thinning table is used to provide the attributes of an input 3×3 local pattern. The control unit is used to check the removal of the center “1” pixel of this local pattern. The inputs of the control unit also comprise the outputs of other neighboring thinning tables. This structure can exactly implement the original 1‐subcycle parallel algorithm. The above‐mentioned algorithms have been implemented on this realized structure in this paper.

Several experiments confirm that the improved algorithms can produce the desired effective thin line, and also show that the realized structure is feasible and practicable.     

Quantum-optical Phase and Canonical Conjugation

Abstract

We use a new limiting procedure, developed to study quantum-optical phase, to examine canonically conjugate operators in general. We find that Dirac's assumption that photon number and phase should be canonically conjugate variables, similar to momentum and position, is essentially correct. The difficulties with Dirac's approach are shown to arise through use of a form of the canonical commutator which, although the only possible form in the usual infinite Hilbert space approach, is not sufficiently general to be used as a model for a number-phase commutator. The approach in this paper unifies the theory of conjugate operators, which include photon number and phase, angular momentum and angle, and momentum and position as particular cases. The usual position-momentum commutator is regained from a more generally applicable expression by means of a domain restriction which cannot be used for the phase-number commutator.     

A self‐tuning control approach of mechanical manipulators

Abstract

The dynamic model of a manipulator system is a time‐varying highly nonlinear coupling equation set. When the moving speed increases or the payload, compared to its own weight, is no longer small, the performance of the conventional control schemes is not satisfactory for precision industrial application. Here a new adaptive control approach is developed for the manipulators to solve these problems. This algorithm directly uses a nonlinear dynamic model in the controller design to account for the nonlinear effects of the system. The least‐square time‐varying parameter identification scheme has been used to identify the change in configuration and payload. The simulation results show that this new approach has a very good trajectory tracking performance.