Some applications of matrices to location of zeros of polynomials†

In previous papers classical theorems on location of zeros of a polynomial with respect to the left half plane Γ₁ or the unit circle Γ₂ have been reformulated more simply in terms of appropriate companion matrices. It is shown how this work can be extended to the problem of zero location with respect to more general regions Γ of the complex plane. The first approach is to apply the bilinear transformation to the given polynomial, so that for example Γ₁ can be mapped into Γ₂ and a matrix representation of this is derived. An alternative method is discussed which relies on transformation of Γ into Γ₂. Some examples illustrate how any theorem involving Hurwitz-typc minors can be expressed in companion matrix terms, with a consequent halving of the orders of the determinants involved.     

The Implementation of Graphic Display of FAS

The principle of the fire alarm system and the implementation techniques of its computer graphic display are presented. With the help of the designing thoughts and technology of OOP, a Fire Alarm System (FAS) has been developed by using visual C++ language. The system has been put into use in many important buildings and has played an important role in monitoring and controlling the fire.     

Measurement of the Kernels of a Non-linear System of Finite Order†

A method of measuring the Volterra kernels of a finite-order non-linear system is presented. The kernels are obtained individually as a multi-dimensional impulse response. The multi-dimensional kernel transforms also can be obtained by the method described. As an extension, a technique of obtaining the Volterra kernels from a multi-dimensional step response is presented. This technique is useful for non-linear systems which can be considered to be of a given finite order for only a limited range of input amplitudes.     

Evaluation of Fourier transform of impulse response of linear time invariant systems†

Evaluation of the Fourior transform of the system impulse response is an important aspect of the design of control systems. A method suggested hero requires only one cycle of sine or cosine wave to be applied as an input to the system. It is proved that the sum of the sampled values of the output response, at the sampling interval equal to the period of the input wave, directly yields the sign and cosine transforms respectively. The procedure is generalized to any number of complete cycles of input wave, as well as to n/2 cycles whore n is any odd positive integer.     

Fault-tree Models of Accident Scenarios of RoPax Vessels

Ro-Ro vessels for cargo and passengers (RoPax) are a relatively new concept that has proven to be popular in the Mediterranean region and is becoming more widespread in Northern Europe. Due to its design characteristics and amount of passengers, although less than a regular passenger liner, accidents with RoPax vessels have far reaching consequences both for economical and for human life. The objective of this paper is to identify hazards related to casualties of RoPax vessels. The terminal casualty events chosen are related to accident and incident statistics for this type of vessel. This paper focuses on the identification of the basic events that can lead to an accident and the performance requirements. The hazard identification is carried out as the first step of a Formal Safety Assessment (FSA) and the modelling of the relation between the relevant events is made using Fault Tree Analysis (FTA). The conclusions of this study are recommendations to the later steps of FSA rather than for decision making (Step 5 of FSA). These recommendations will be focused on the possible design shortcomings identified during the analysis by fault trees throughout cut sets. Also the role that human factors have is analysed through a sensitivity analysis where it is shown that their influence is higher for groundings and collisions where an increase of the initial probability leads to the change of almost 90% of the accident occurrence.     

Stabilization of a class of switched nonlinear systems

The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of （generalized） switched Byrnes-Isidori canonical form, which has all switched models in （generalized） Byrnes- Isidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization problem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to （generalized） switched Byrnes-Isidori canonical systems are presented. Finally, as an application the stability of switched lorenz systems is investigated.     

Optimization of linear systems of constrained configuration†

For the sake of simplicity it is often desirable to restrict the number of feedbacks in a controller. In this case the optimal feedbacks depend on the disturbance to which the system is subjected. Using a quadratic error integral as a measure of the response, three criteria of optimization are considered :

1. The response to a given initial disturbance.

2. The worst response to an initial disturbance of given magnitude.

3. The worst comparison with the unconstrained optimal system.

It is shown that for each of these criteria the gradient with respect to the feedbacks can be calculated by a uniform method. The solution may then be found either directly or by a descent procedure. The method is illustrated by an example.     

On the Equivalence of Some Models of Computation

In[1],a definition of computation was given.In[3],we have clarified the necessity of thedefinition.Here we prove the equivalence between the definition and some models ofcomputation.Hence the sufficiency of the definition is clear abundantly.     

A Form-Correcting System of Chinese Characters Using a Model of Correcting Procedures of Calligraphists

A support system for form-correction of Chinese Characters is developed based upon a generation model SAM,and its feasibility is evaluated.SAM is excellent as a model for generating Chinese characters,but it is difficult to determine appropriate parameters because the use of calligraphic knowledge is needed.by noticing that calligraphic knowledge of calligraphists is included in their corrective actions, we adopt a strategy to acquire calligraphic knowledge by monitoring,recording and analyzing corrective actions of calligraphists,and try to realize an environment under which calligraphists can easily make corrections to character forms and which can record corrective actions of calligraphists without interfering with them.In this paper,we first construct a model of correcting procedures of calligraphists,which is composed of typical correcting procedures that are acquired by extensively observing their corrective actions and interviewing them,and develop a form-correcting system for brush-written Chinese characters by using the model.Secondly,through actual correcting experiments,we demonstrate that parameters within SAM can be easily corrected at the level of character patterns by our system,and show that it is effective and easy for calligraphists to be used by evaluating effectiveness of the correcting model,sufficiency of its functions and execution speed.     

Contracted product of hypermatrices via STP of matrices

An equivalent definition of hypermatrices is introduced. The matrix expression of hypermatrices is proposed. Using permutation matrices, the conversion between different matrix expressions is revealed. The various kinds of contracted products of hypermatrices are realized by semi-tensor products (STP) of matrices via matrix expressions of hypermatrices.     

Fabrication of a ZnO piezoelectric micro cantilever with a high-aspect-ratio nano tip

This paper reports on a ZnO piezoelectric micro cantilever with a high-aspect-ratio (HAR) nano tip, which is proposed for a ferroelectric material based nano storage system. The system uses the interaction between the nano tip and a storage medium, and the HAR nano tip is needed to suppress undesirable effects caused by the small gap between the cantilever and the storage medium. The fabrication process for the cantilever with the HAR nano tip consists of three parts: the HAR nano tip formation, the cantilever fabrication, and the bonding/releasing process. The HAR nano tip is formed by the Si deep reactive ion etching for a long shaft and the anisotropic wet etching for a nano tip end. The cantilever is made up of 1 m-thick LPCVD poly-Si layer and 0.2 m-thick Si nitride layer, and has 0.5 m-thick ZnO actuation layer. A final releasing process is followed by an anodic bonding process. The fabricated HAR nano tip has 6 m side length, over 18 m height, and less than 15 nm tip radius, which is built on the 85 m-wide, 300 m-long, and 1.2 m-thick cantilever. The experimental results show a linear behavior with respect to input voltage of 1 to 5 V and the first resonance frequency at 17.9 kHz.     

A suction-type, pneumatic microfluidic device for liquid transport and mixing

This study presents a new suction-type, pneumatically driven microfluidic device for liquid delivery and mixing. The three major components, including two symmetrical, normally closed micro-valves and a sample transport/mixing unit, are integrated in this device. Liquid samples can be transported by the suction-type sample transport/mixing unit, which comprised a circular air chamber and a fluidic reservoir. Experimental results show that volume flow rates ranging from 50 to 300 μl/min can be precisely controlled during the sample transportation processes. Moreover, the transport/mixing unit can also be used as a micro-mixer to generate efficient mixing between two reaction chambers by regulating the time-phased deformation of the polydimethylsiloxane (PDMS) membranes. A mixing efficiency as high as 98.4% can be achieved within 5 s utilizing this prototype pneumatic microfluidic device. Consequently, the development of this new suction-type, pneumatic microfluidic device can be a promising tool for further biological applications and for chemical analysis when integrated into a micro-total analysis system (μ-TAS) device.     

Fabrication of the PDMS microchip for serially diluting sample with buffer

We developed a polymer polydimethylsiloxane (PDMS) based microfluidic device that dilutes biological samples with buffer solutions with serially increasing diluted sample concentrations. The device showed the relatively high accuracy in terms of dilution ratios along with the fact that it was faster and easier to operate. With two simple disposable plastic syringes, the plastic microfluidic chip completes ordinary sample dilution sequences faster and more precisely than the conventional manual pipette process in biological or chemical laboratory. The serially diluting mechanism of the microchip is simply that the number of microchannels with the same flow rate determines the total amount of flow into the wells. The soft lithography fabricated the microchannels of tetragonal section length of 50 m of each side of the microfluidic chip. This paper was supported by the Nano Bioelectronics and Systems Research Center of Seoul National University, which is an Engineering Research Center supported by the Korean Science and Engineering Foundation (KOSEF).     

An average complexity measure that yields tight hierarchies

A new definition is given for the average growth of a functionf: ^* N with respect to a probability measure on ^* This allows us to define meaningful average distributional complexity classes for arbitrary time bounds (previously, one could not guarantee arbitrary good precision). It is shown that, basically, only the ranking of the inputs by decreasing probabilities is of importance.To compare the average and worst case complexity of problems, we study average complexity classes defined by a time bound and a bound on the complexity of possible distributions. Here, the complexity is measured by the time to compute the rank functions of the distributions. We obtain tight and optimal separation results between these average classes. Also, the worst case classes can be embedded into this hierarchy. They are shown to be identical to average classes with respect to distributions of exponential complexity.     

Effect of workpiece springback on micromilling forces

The machining forces present in micromilling with tools in the 50–100 m diameter range are dominated by contact pressure and friction between the tool cutting edges and the workpiece. A model of the micromilling process was developed based on the elastic contact between the tool and the workpiece along the side and bottom cutting edges of the tool. Micromilling experiments were conducted on 6061-T6 aluminum to obtain machining forces in the feed and cross-feed directions during slot milling and partial engagement end milling. Comparisons with the experimental data indicate reasonable agreement for full slot milling as well as end milling with radial depths of cut in the range of 2 m to 40 m. It was concluded that this model is adequate for predicting micromilling forces with the precision needed to reduce tool breakage and workpiece clamping forces and for predicting tool deflection that affects wall slope and feature size.This work was supported primarily by the Engineering Research Centers Program of the National Science Foundation under Award Number EEC-9986866. The Engineering Research Center for Wireless Integrated Microsystems is also hereby acknowledged. All machining was performed at the Micromechanical Applications and Processes Laboratory at Michigan Technological University.     

Analytical model of microfluidic transport of non-magnetic particles in ferrofluids under the influence of a permanent magnet

This study describes an analytical model and experimental verifications of transport of non-magnetic spherical microparticles in ferrofluids in a microfluidic system that consists of a microchannel and a permanent magnet. The permanent magnet produces a spatially non-uniform magnetic field that gives rise to a magnetic buoyancy force on particles within ferrofluid-filled microchannel. We obtained trajectories of particles in the microchannel by (1) calculating magnetic buoyancy force through the use of an analytical expression of magnetic field distributions and a nonlinear magnetization model of ferrofluids, (2) deriving governing equations of motion for particles through the use of analytical expressions of dominant magnetic buoyancy and hydrodynamic viscous drag forces, (3) solving equations of motion for particles in laminar flow conditions. We studied effects of particle size and flow rate in the microchannel on the trajectories of particles. The analysis indicated that particles were increasingly deflected in the direction that was perpendicular to the flow when size of particles increased, or when flow rate in the microchannel decreased. We also studied ??wall effect?? on the trajectories of particles in the microchannel when surfaces of particles were in contact with channel wall. Experimentally obtained trajectories of particles were used to confirm the validity of our analytical results. We believe this study forms the theoretical foundation for size-based particle (both synthetic and biological) separation in ferrofluids in a microfluidic device. The simplicity and versatility of our analytical model make it useful for quick optimizations of future separation devices as the model takes into account important design parameters including particle size, property of ferrofluids, magnetic field distribution, dimension of microchannel, and fluid flow rate.     

A variotherm mold for micro metal injection molding

In this paper, a variotherm mold was designed and fabricated for the production of 316L stainless steel microstructures by micro metal injection molding (MIM). The variotherm mold incorporated a rapid heating/cooling system, vacuum unit, hot sprue and cavity pressure transducer. The design of the variotherm mold and the process cycle of MIM using the variotherm mold were described. Experiments were conducted to evaluate the molded microstructures produced using variotherm mold and conventional mold. The experiments showed that microstructures of higher aspect ratio such as 60 m × height 191 m and 40 m × height 174 m microstructures could be injection molded with complete filling and demolded successfully using the variotherm mold. Molded microstructures with dimensions of 60 m × height 191 m were successfully debound and sintered without visual defects.     

Minimization of norms and logarithmic norms by diagonal similarities

It is a commonly occurring problem to find good norms · or logarithmic norms (·) for a given matrix in the sense that they should be close to respectively the spectral radius (A) and the spectral abscissa (A). Examples may be the certification thatA is convergent, i.e. (A)A<1 or stable, i.e. (A)(A)<0. Often the ordinary norms do not suffice and one would like to try simple modifications of them such as using an ordinary norm for a diagonally transformed matrix. This paper treats this problem for some of the ordinary norms.

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Minimisierung von Normen und Logarithmischen Normen durch Diagonale Transformationen

Zusammenfassung Ein oft vorkommendes praktisches Problem ist die Konstruktion von guten Normen · und logarithmischen Normen (·) für eine gegebene MatrixA. Mit gut wird dann verstanden, daß A den Spektralradius (A)=max |₁| und (A) die Spektralabszisse (A)=max Re _i gut approximieren. Beispiele findet man für konvergente Matrizen wo (A)A<1 gewünscht ist, und für stabile Matrizen wo (A)(A)<0 zu zeigen ist. Wir untersuchen hier, wie weit man mit Diagonaltransformationen und dengewöhnlichsten Normen kommen kann.

     

Deep X-ray lithography using mask with integrated electrothermal actuator

We present a deep X-ray mask with integrated bent-beam electrothermal actuator for the fabrication of 3D microstructures with curved surface. The mask absorber is electroplated on the shuttle mass, which is supported by a pair of 20-m-thick single crystal silicon bent-beam electrothermal actuators and oscillated in a rectilinear direction due to the thermal expansion of the bent-beams. The width of each bent-beam is 10 m or 20 m and the length and bending angle are 1 mm and 0.1 rad, respectively, and the shuttle mass size is 1 mm × 1 mm. For 10-m-wide bent-beams, the shuttle mass displacement is around 15 m at 180 mW (3.6 V) dc input power. For 20-m-wide bent-beams, the shuttle mass displacement is around 19 m at 336 mW (4.2 V) dc input power. Sinusoidal cross-sectional PMMA microstructures with a pitch of 40 m and a height of 20 m are fabricated by 0.5 Hz, 20-m-amplitude sinusoidal shuttle mass oscillation.This research, under the contract project code MS-02-338-01, has been supported by the Intelligent Microsystem Center, which carries out one of the 21st centurys Frontier R & D Projects sponsored by the Korea Ministry of Science & Technology. Experiments at PLS were supported in part by MOST and POSCO.     

Thermal bubble powered microactuators

Thermal bubble powered micro mechanical actuators have been successfully demonstrated in working liquids. Micro mechanical plates which function as the mechanical actuators are 70×60×2 m³ in size. They have been fabricated by surface-micromachining technology and suspended 2 m above the substrate by the supports of cantilever beams. Micro thermal bubbles which are generated by heavily phosphorus doped polysilicon line resistive heaters have been used to lift the mechanical plates in a controllable manner. The typical current required to generate a single, spherical thermal bubble as the actuation source on top of the micro line resistors (60×2×0.3 m³ in size) is 8.4 mA (80 m Watt) in FC 43 liquid (an inert, dielectrical fluid available from the 3M company). The thermal bubbles have been demonstrated to actuate the mechanical plate perpendicularly to the substrate with a maximum elevation distance of 140 m and a maximum actuation force of 2 N. This new actuation mechanism is expected to find applications for micro fluidic devices.The authors would like to thank Prof. V.P. Carey, Mechanical Engineering department, U.C. Berkeley and Dr. A.P. Lee for valuable discussions. The devices were fabricated in the UC Berkeley Microfabrication Laboratory and the FC liquid was provided by 3M company. This work has been supported by Berkeley Sensor and Actuator Center, an NSF/Industry/University Co-operative Research Center.