Let us introduce n ( 2) nonlinear mappings fi (i = 1,2,,n) defined on complete linear metric spaces (Xi-1,ρ) (i = 1,2,,n), respectively, and let fi: Xi-1 Xi be completely continuous on bounded convex closed subsets Xi-1,(i = 1,2,,n 0), such that fi() . Moreover, let us introduce n fuzzy-set-valued nonlinear mappings Fi: Xi-1 Xi {a family of all non-empty closed compact fuzzy subsets of Xi}. Here, we have a fixed point theorem on the recurrent system of β-level fuzzy-set-valued mapping equations: xi Fiβ(xi-1,fi(xi-1)), (i = 1,2,,n 0), where the fuzzy set Fi is characterized by a membership function µFi(xi): Xi [0,1], and the β-level set Fiβ of the fuzzy set Fi is defined as Fiβ {ξi Xi | µFi(ξi) β}, for any constant β (0,1]. This theorem can be applied immediately to discussion for characteristics of ring nonlinear network systems disturbed by undesirable uncertain fluctuations and to fine estimation of available behaviors of those disturbed systems. In this paper, its mathematical situation and proof are discussed, in detail.

A mathematical theory is proposed, based on the concept of functional analysis, suitable for operation of network systems extraordinarily complicated and diversified on large scales, through connected-block structures. Fundamental conditions for existence and evaluation of system behaviors of such network systems are obtained in a form of fixed point theorem for system of nonlinear mappings.

A grooved circular cavity is designed for the millimeter wave measurements of dielectric substrates. The grooves are introduced to separate the degenerate TE01p and TM11p modes in circular cavities. A rigorous mode-matching method is used to investigate the influence of grooves on both the TE01p and TM11p modes. The dimensions of the grooves are determined from the numerical results. Comparative experiments of circular cavities with and without grooves validate the design method.

A microwave waveform measurement system below 18 GHz was developed and verified with a conventional RF measurement. The current and voltage RF waveforms of AlGaAs HBTs at the fundamental frequency of 1 GHz were directly measured with the system. A new direct method of sweeping and measuring dynamic RF load lines is proposed to measure the operating limits of the device. The maximum operating region was experimentally investigated with this method. The limits with a small input power are found to come from thermal runaway and the avalanche breakdown of the device. With a large input power, the HBT was found to operate beyond the DC limit of thermal runaway. The base ballasting resistance was also found to enhance large signal operating limits beyond those expected from the conventional DC theory.

Two type measurement methods of the unloaded Q-factor of a microwave resonator, the insertion loss method and the return loss method, are reexamined theoretically and compared experimentally. An error formula is derived to estimate the errors between the unloaded Q-factors measured by the two different methods. Measured results of a stripline resonator verified well the derived formula, and proved that the return loss method is more accurate and reliable than the traditional insertion loss method.

An attenuation measurement system, which employs a traceable inductive voltage divider (IVD) at 1 kHz as a reference standard and dual channel intermediate frequency (IF) substitution method, is developed as an attenuation standard in the frequency range of 5 GHz to 12 GHz. The basic properties of the system are experimentally investigated and the expanded standard uncertainty of the system is estimated to be 0.0018 dB for 20 dB and 0.026 dB for 80 dB attenuation.

A pilot needs operational information about wind over sea as well as wave height to provide safety of hydroplane landing on water. Near-surface wind speed and direction can be obtained with an airborne microwave scatterometer, a radar designed for measuring the scatter characteristics of a surface. Mostly narrow-beam antennas are applied for such wind measurement. Unfortunately, a microwave narrow-beam antenna has considerable size that hampers its placement on flying apparatus. In this connection, a possibility to apply a conventional airborne radar altimeter as a scatterometer with a nadir-looking wide-beam antenna in conjunction with simultaneous range Doppler discrimination techniques for recovering the wind vector over sea at low speed of flight is discussed, and measuring algorithms of sea surface wind speed and direction are proposed. The principle considered and algorithms proposed in the paper can be used for creation an airborne radar system for operational measurement of the sea roughness characteristics and for safe landing of a hydroplane on water.

The fiber-optic sectorized remote antenna system by using the radio frequency (RF) optical transmission technique was promising for increasing the number of subscribers in the millimeter-wave broadband wireless access (MMW BWA) networks. To realize the cost-effectiveness of the fiber-optic sectorized remote antenna system covering four areas, we reached the conclusion that the best multiplexing schemes were the sub-carrier division multiplexing (SCM) of the intermediate frequency (IF) signals of 2 GHz for the down link, the coarse wavelength division multiplexing (CWDM) with the IF signals optical transmission for the up link and 1.3/1.55 µm-WDM for multiplexing the down link and the up link. In addition, the target specifications of this SCM-CWDM system were described, and the designs of the carrier to noise ratio (CNR) and the third order intermodulation distortion (IM3) were examined.

In this paper, we propose a simple method to find the optimal rational function, with a fixed denominator, which minimizes an integral of polynomially weighted squared error to given analytic function. Firstly, we present a generalization of the Walsh's theorem. By using the knowledge on the zeros of the fixed denominator, this theorem characterizes the optimal rational function with a system of linear equations on the coefficients of its numerator polynomial. Moreover when the analytic function is specially given as a polynomial, we show that the optimal numerator can be derived without using any numerical integration or any root finding technique. Numerical examples demonstrate the practical applicability of the proposed method.

Wall shadow removal problems differ due to configuration of walls in different propagation scenarios. Applying Weiler-Atherton polygon clipping method helps calculate illuminated regions on the building walls, but unfortunately the technique has limitation when there are many walls and the walls configuration is complex. The modified Weiler-Atherton polygon clipping method proposed can solve the problem by regarding all vertices of the subject polygon or clipping polygon, that are also intersection points as simply intersection points. In the case that a certain vertex of the subject polygon is a vertex of the clipping polygon, this vertex of the subject polygon is still considered a vertex. It is found that wall shadow removal using the proposed modified Weiler-Atherton polygon clipping method is more efficient.

This review paper addresses an emerging aspect of the relationship between optics and microwave electronics: the application of short pulses of laser light to the sensing and measurement of continuous-wave microwave fields. In particular, very short duration optical pulses can take on the role of ultrafast sampling gates within the framework of the electro-optic sampling technique in order to realize unprecedented temporal resolution, measurement bandwidth, and probing flexibility. As a result, in numerous instances electro-optic sampling has been demonstrated, primarily within the research laboratory, to be an effective tool in the field of diagnostic testing and the determination of the electrical characteristics of microwave components. Recently, with the emergence of new applications such as microwave electric-field mapping in wireless and radar environments, and as the ultrafast time domain has gained in importance for the area of optical telecommunications, added attention has been directed to electro-optic sampling. Herein, an abbreviated historical perspective of the history of electro-optic field mapping is presented, along with the fundamental concepts that are utilized in the technique. The effectiveness of an optical-fiber-mounted electro-optic probe in a scanning electric-field-mapping system is highlighted in several diagnostic measurements on microwave and millimeter-wave antenna arrays, and a combined electric-field and thermal-imaging capability is also introduced.

The emerging multimedia applications for future mobile communication systems typically require highly diversified Quality of Service (QoS). However, due to the time and location dependent fluctuating nature of radio resources in the radio link, it is very difficult to maintain a constant level of QoS with the current end-to-end QoS control only. Therefore, wireless-aware QoS is the key issue for achieving better end-end QoS. In this paper, a new wireless QoS scheme for a joint CDMA/NC-PRMA cellular system are proposed considering QoS prioritization mechanism, users' diversified requirements and the harmonization with IP-QoS. Two wireless QoS-aware resource allocation algorithms are proposed to support QoS prioritization while achieving high radio resource utilization. By introducing a set of new QoS resource request parameters (minimum, average and maximum requirements), the algorithms can assign radio resource in a more flexible way than the conventional fixed resource allocation. Computer simulations indicate that the proposed QoS algorithms exhibit superior performance with respect to packet dropping probability for realtime application users, and improve transmission rate for non-realtime application users, which evince the effectiveness of the proposed wireless QoS algorithms.

Recent advances of Web information systems such as e-commerce and e-learning have created very large but hidden demands on conceptual multiresolution analysis for more generalized information analysis, cognition and modeling. To meet the demands in a general way, its modeling is formulated based on modern algebraic topology. To be specific, the modeling formulation is worked out in an incrementally modular abstraction hierarchy with emphasis on the two levels of the hierarchy appropriate for conceptual modeling: the adjunction space level and the cellular structured space level. Examples are shown to demonstrate the usefulness of the presented model as well as an implementation of a flower structure case.

In the paper, we propose a new method for chromatic dispersion measurement of WDM components in both transmission and reflection, employing photonic microwave technology. The dispersion can be determined by measuring the frequency spectrum range change of the microwave notch filter. The method features the advantages of low-cost and simplicity. Experimental results demonstrate that our setup is capable of measuring relative group delay with better than 1 ps time resolution and the measurement results show a good agreement with that measured by the conventional phase-shift technique.

The energy conservation law and the optical theorem in the grating theory are discussed: the energy conservation law states that the incident energy is equal to the sum of diffracted energies and the optical theorem means that the diffraction takes place at the loss of the specularly reflection amplitude. A mathematical relation between the optical theorem and the energy conservation law is given. Some numerical examples are given for a TM plane wave diffraction by a sinusoidal surface.

Many feature tracking algorithms have been proposed for motion segmentation, but the resulting trajectories are not necessarily correct. In this paper, we propose a technique for removing outliers based on the knowledge that correct trajectories are constrained to be in a subspace of their domain. We first fit an appropriate subspace to the detected trajectories using RANSAC and then remove outliers by considering the error behavior of actual video tracking. Using real video sequences, we demonstrate that our method can be applied if multiple motions exist in the scene. We also confirm that the separation accuracy is indeed improved by our method.

A simple configuration for millimeter-wave fiber-wireless transmission, with remote local-oscillator (LO) delivery from the central office, both for the uplink and for the downlink, and a simple, cost-effective, base-station solution is proposed. Under the assumption of using commercially available components and a conventional single-mode fiber (with dispersion of 17 ps/nm/km at 1.55 µm), our numerical results show that, with a laser linewidth of 150 MHz, a laser power of 0 dBm and an optical gain of only 6 dB, it is possible to transmit, without repeaters, data rates of 622 Mbit/s across about 18 km at a bit-error-rate of 10-9. By increasing the optical gain to 24 dB, the link length can be increased to approximately 67 km for a laser linewidth of 75 MHz and to 78 km for a laser linewidth 1 MHz.

Some electromechanical devices and systems produced using MEMS fabrication processes are detailed. Two precision measurement metrologies for inspecting electromechanical products are also described. As the trend of electromechanical devices has been towards smaller and smaller sizes possessing robust mechanisms and powerful functions, micro-electric-mechanical system (MEMS) devices are becoming more the choice for meeting such requirements. Three MEMS examples are discussed in detail in this paper: CMOS compatible sensors, RF/microwave components, and packaged and integrated passive devices. The design thinking of a new free-fall sensor, which is an accelerometer and possesses a surprisingly low frequency response and broad bandwidth, is mentioned. In addition, an AVID (dvanced ibrometer/nterferometer evice) system for measuring tiny displacement as well as a Morphinscope system that has the advantage of a confocal microscope combined with a photon tunneling microscope and both developed by NTU's MEMS/NEMS group, are discussed. The excellent sensing ability of the free-fall sensor and the accuracy resolution of the two measurement systems are proved by experimental verification.

One of the difficulties in routing problem is in wirability which is to guarantee a physical connection of a given topological route. Wirability often fails since the width of a wire is relatively large compared with the size of modules. As a possible solution, this paper proposes an incremental wiring algorithm which generates wires net-by-net without overlapping other pre-placed circuit elements. The idea is to divide a wire into a series of rectangles and handles them as modules with additional constraints to keep the shape of the wire. The algorithm was implemented and experimented on a small instance to show its promising performance.

In this paper we present reconfigurable computing as a compelling choice of computing platform for real-time, onboard processing for satellite applications. In particular, we discuss the use of reconfigurable computing in the context of a real-time remote sensing system, providing motivation for such a system and describing attributes of reconfigurable computing that support it as the technology of choice. The High Performance Computing (HPC-I) payload, designed and developed for the Australian scientific satellite FedSat, is introduced as a demonstration of onboard processing in space using reconfigurable logic. We present an overview of the real-time remote sensing system architecture, and describe the design and implementation of three remote sensing algorithms in HPC-I for cloud masking, wildfire detection and volcanic plume detection. Finally, results from simulation and testing are presented which show very promising performance in terms of data throughput and detection capabilities.