μ-Bases and singularities of rational planar curves

We provide a technique to detect the singularities of rational planar curves and to compute the correct order of each singularity including the infinitely near singularities without resorting to blow ups. Our approach employs the given parametrization of the curve and uses a μ-basis for the parametrization to construct two planar algebraic curves whose intersection points correspond to the parameters of the singularities including infinitely near singularities with proper multiplicity. This approach extends Abhyankar's method of t-resultants from planar polynomial curves to rational planar curves. We also derive the classical result that for a rational planar curve of degree n the sum of all the singularities with proper multiplicity is (n−1)(n−2)/2. Examples are provided to flesh out our results.     

Development of a skew μ upper bound

Exploitation of the NP hard, mixed μ problem structure provides a polynomial time algorithm that approximates μ with usually reasonable answers. When the problem is extended to the skew μ problem, an extension of the existing method to the skew μ formulation is required. The focus of this paper is to extend the μ upper bound derivation to the skew μ upper bound and show its direct computation by way of an Osborne balancing algorithm and an linear matrix inequality (LMI) algorithm. Copyright © 2005 John Wiley & Sons, Ltd.     

The -basis and implicitization of a rational parametric surface

The concept of a μ-basis was introduced in the case of parametrized curves in 1998 and generalized to the case of rational ruled surfaces in 2001. The μ-basis can be used to recover the parametric equation as well as to derive the implicit equation of a rational curve or surface. Furthermore, it can be used for surface reparametrization and computation of singular points. In this paper, we generalize the notion of a μ-basis to an arbitrary rational parametric surface. We show that: (1) the μ-basis of a rational surface always exists, the geometric significance of which is that any rational surface can be expressed as the intersection of three moving planes without extraneous factors; (2) the μ-basis is in fact a basis of the moving plane module of the rational surface; and (3) the μ-basis is a basis of the corresponding moving surface ideal of the rational surface when the base points are local complete intersections. As a by-product, a new algorithm is presented for computing the implicit equation of a rational surface from the μ-basis. Examples provide evidence that the new algorithm is superior than the traditional algorithm based on direct computation of a Gröbner basis. Problems for further research are also discussed.     

Synthesis Of μ Controllers Using Statistical Iterations

This paper introduces the integration of robust control and quality control, based on which a statistical iteration scheme of μ synthesis is proposed. In this statistical solution, μ controller structures are fully flexible, and controller orders do not increase during iterations. In addition, it can reveal the directions of parameter changes, which may lead to improvements in the performance of the resulting controllers. Statistical interpretations and systematical procedures for this quality‐oriented control design are also addressed.     

AN AFM PROBE CONTROLLER DESIGN BASED ON μ‐SYNTHESIS

The atomic force microscope (AFM) is one of the most important tools for measuring atomic resolution. The AFM system maintains constant force between a tip and the sample in order to track the sample topography. The controller that maintains the constant interaction force plays a significant role in measurement accuracy. This paper presents a μ‐synthesis controller design to deal with model uncertainty and establish a measurement error bound. The system's nonlinearity and the set‐point drift are lumped into a multiplicative uncertainty. The performance bound allows specification of the error magnitude over the frequency range. Simulation results show that the proposed control can tolerate uncertainties. The error spectrum from the experiments shows consistency with the design specifications. Images were taken to compare μ‐synthesis control with a well‐tuned PID control at a 480μm/s scan rate. The results verify the outstanding performance of the μ‐controller.     

Development of G6 exposure tool for 1.2 μm resolution

We have proposed exposure method using Deep UV (DUV) exposure light to realize high resolution and high productivity in FPD lithography. Here, we show development concepts for our new G6 exposure tools with DUV light sources and exposure test results with a test exposure tool.     

MIXED μ PROBLEMS AND BRANCH AND BOUND TECHNIQUES

The computation of the general structural singular value (μ) is NP hard, so quick solutions to medium sized problems must often be approximate. In many of the cases where the current approximate methods are unsatisfactory, improved solutions are highly desirable. It is shown that, despite their worst-case combinatorial nature, branch and bound techniques can give substantially improved solutions with only moderate computational cost. © 1997 by John Wiley & Sons, Ltd.     

K competing queues with geometric service requirements and linear costs: The μc-rule is always optimal

In this note, a discrete-time system of K competing queues with geometric service requirements and arbitrary arrival patterns is studied. When the cost per slot is linear in the queue sizes, it is shown that the μc-rule minimizes the expected discounted cost over the infinite horizon.     

Application of real/mixed μ computational techniques to an H∞ missile autopilot

A multivariable missile autopilot is synthesized using an H_∞ approach. A tradeoff is achieved between performance, actuators solicitation and uncertainties in the actuators and bending modes dynamics. Robust stability and performance of the control law are then studied in the face of large real parametric aerodynamic uncertainties: computational techniques for real and mixed μ analysis (namely De Gaston and Safonov's, Dailey's, Jones’, Young and Doyle's, Fan, Tits and Doyle's and Safonov and Lee's methods) are briefly reviewed before being used to compute either the exact value, or an interval of the structured singular value (SSV). For small amounts of parameters, the upper and lower bounds provided by these methods are compared to the exact value, computed by De Gaston and Safonov's method. For larger amounts of parameters, NP hardness of the problem prohibits the use of algorithms which compute the exact value: these algorithms are indeed necessarily exponential-time. As an alternative in this case, the use of polynomial-time methods for computing upper and lower bounds leads in our examples to accurate approximates of the real and mixed structured singular values.     

Robust nonlinear ship course‐keeping control by H∞ I/O linearization and μ‐synthesis

In this paper, the H_∞ input/output (I/O) linearization formulation is applied to design an inner‐loop nonlinear controller for a nonlinear ship course‐keeping control problem. Due to the ship motion dynamics are non‐minimum phase, it is impossible to use the ordinary feedback I/O linearization to resolve. Hence, the technique of H_∞ I/O linearization is proposed to obtain a nonlinear H_∞ controller such that the compensated nonlinear system approximates the linear reference model in I/O behaviour. Then a μ‐synthesis method is employed to design an outer‐loop robust controller to address tracking, regulation, and robustness issues. The time responses of the tracking signals for the closed‐loop system reveal that the overall robust nonlinear controller is able to provide robust stability and robust performance for the plant uncertainties and state measurement errors. Copyright © 2002 John Wiley & Sons, Ltd.     

The new route for realization of 1‐μm‐pixel‐pitch high‐resolution displays

A new pixel structure for the realization of a 1‐μm‐pixel‐pitch display was developed. This structure, named vertically stacked thin‐film transistor (VST), was based on the conventional back‐channel etched thin‐film transistor (TFT), but all the layers except the horizontal gate line were vertically stacked on the embedded data line, enabling the implementation of high‐resolution display panels. The VST device with a channel length of 1 μm showed a high field effect mobility of more than 50 cm²/Vs and low subthreshold slope of 78 mV per decade. It also shows a high uniform electrical characteristic over the entire 6‐in. wafer. The development of a new pixel architecture is expected to enable the implementation of 1‐μm‐pixel‐pitch high‐resolution displays such as spatial light modulators for digital holograms.     

A non‐smooth lower bound on ν

A non‐smooth optimization technique to directly compute a lower bound on the skew structured singular value ν is developed. As corroborated by several real‐world challenging applications, the proposed technique can provide tighter lower bounds when compared with currently available techniques. Moreover, in many cases, the determined lower bound equals the true value of ν. Thanks to the efficiency of the non‐smooth technique, the algorithm can be applied to problems involving even a significant number of uncertain parameters. Another appealing feature of the proposed non‐smooth approach is that the dimension of repeated scalar uncertainties in the overall structured uncertainty matrix has little impact on the computational time. The technique can be used to compute a lower bound on the structured singular value μ as well. Copyright © 2012 John Wiley & Sons, Ltd.     

UppDMC: A Distributed Model Checker for Fragments of the μ-Calculus

We present UppDMC, a distributed model-checking tool. It is tailored for checking finite-state systems and μ-calculus specifications with at most one alternation of minimal and maximal fixed-point operators. This fragment is also known as . Recently, efficient game-based algorithms for this logic have been outlined.We describe the implementation of these algorithms within UppDMC and study their performance on practical examples. Running UppDMC on a simple workstation cluster, we were able to check liveness properties of the largest examples given in the VLTS Benchmark Suite, for which no answers were previously known.     

The effect of γ-sterilization on the pH-ChemFET behaviour

One of the key requirements biomedical and pharmaceutical sensors have to satisfy is their ability to withstand sterilization cycle. In this paper, the influence of γ-sterilization on the electrical and electrochemical characterizations of pH-sensitive chemical field effect transistors (pH-ChemFET) is examined before and after γ-irradiation. It is shown that γ-irradiation is suitable for pH-ChemFETs sterilization in the field of in-vitro analysis and more precisely for single-use bioreactors.     

Real-μ bounds based on fixed shapes in the Nyquist plane: Parabolas, hyperbolas, cissoids, nephroids, and octomorphs

In this paper we introduce new bounds for the real structured singular value. The approach is based on absolute stability criteria with plant-dependent multipliers that exclude the Nyquist plot from fixed plane curve shapes containing the critical point − + _jO. Unlike half-plane and circle-based bounds the critical feature of the fixed curve bounds is their ability to differentiate between the real and imaginary components of the uncertainty. Since the plant-dependent multipliers have the same functional form at all frequencies, the resulting graphical interpretation of the absolute stability criteria are frequency independent in contrast to the frequency-dependent off-axis circles that arise in standard real-μ bounds.     

Factors affecting the dynamics of a π‐cell (Invited Paper)

Abstract— The basic factors related to the dynamics of a π‐cell device are reviewed. Specifically, the director dynamics are studied for the case of a periodic drive voltage that is sometimes referred to as “impulse drive.” It is found for this type of drive waveform the desired bend state is more stable against the twisting effect of transverse electric fields found in AMLCD devices. This effect causes the reduction in light transmission due to “impulse drive” to be smaller in π‐cell devices than is expected to be found in other AMLCD modes.     

The Navier–Stokes-αβ equations as a platform for a spectral multigrid method to solve the Navier–Stokes equations

This paper describes a spectral multigrid method for spatially periodic homogeneous and isotropic turbulent flows. The method uses the Navier–Stokes-αβ equations to accelerate convergence toward solutions of the Navier–Stokes equations. The Navier–Stokes-αβ equations are solved on coarse grids at various levels and the Navier–Stokes equations are solved on the “nest grid”. The method uses Crank–Nicolson time-stepping for the viscous terms, explicit time-stepping for the remaining terms, and Richardson iteration to solve linear systems encountered at each time step and on each grid level. To explore the computational efficiency of the method, comparisons are made with results obtained from an analogous spectral multigrid method for the Navier–Stokes equations. These comparisons are based on computing work units and residuals for multigrid cycles. Most importantly, we examine how choosing different values of the length scales α and β entering the Navier–Stokes-αβ equations influence the efficiency and accuracy of these multigrid schemes.